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An X-Ray Spectral Fitting Package User's Guide for version 12.8.1

1. Data group 1 1 1 phabs nH 10 22 100 000 0 0 2 2 highecut cutoffE keV 10 0000 0 0 3 2 highecut foldE keV 15 0000 0 0 4 3 powerlaw PhoIndex 1 00000 t 0 0 5 3 powerlaw norm 1 00000 0 0 Data group 2 6 1 phabs nH 10 22 1 00000 0 0 7 2 highecut cutoffE keV 10 0000 2 8 2 highecut foldE keV 15 0000 3 9 3 powerlaw PhoIndex 1 00000 4 48 10 3 powerlaw norm 1 00000 5 Notice how the summary of the model displayed immediately above is different now that we have two groups as opposed to one as in all the previous examples We can see that of the 10 model parameters 6 are free i e 4 of the second group parameters are tied to their equivalents in the first group Fitting this model results in a huge y not shown here because our assumption that only a change in absorption can account for the spectral variation before and after eclipse is clearly wrong Perhaps scattering also plays a role in reducing the flux before eclipse This could be modeled simply at first by allowing the normalization of the power law to be smaller before eclipse than after eclipse To decouple tied parameters we change the parameter value in the second group to a value any value different from that in the first group changing the value in the first group has the effect of changing both without decoupling As usual the newpar command is used XSPEC12 gt newpar 10 1 Fit statistic Chi Squared 2 062941e
2. Covariance Matrix 1 2 2 868e 04 9 336e 09 9 336e 09 2 267e 11 Model phabs lt 1 gt bbody lt 2 gt Source No 1 Active On Model Model Component Parameter Unit Value par comp 1 1 phabs nH 10 22 1 87147E 08 1 00000 2 2 bbody kT keV 0 890205 1 69343E 02 3 2 bbody norm 2 78596E 04 4 76176E 06 Fit statistic Chi Squared 123 77 using 45 PHA bins Test statistic Chi Squared 123 77 using 45 PHA bins Reduced chi squared 2 9470 for 42 degrees of freedom Null hypothesis probability 5 417115e 10 Note that after each set of 10 iterations you are asked whether you want to continue Replying no at these prompts is a good idea if the fit is not converging quickly Conversely to avoid having to keep answering the question i e to increase the number of iterations before the prompting question appears begin the fit with say fit 100 This command will put the fit through 100 iterations before pausing To automatically answer yes to all such questions use the command query yes Note that the fit has written out a warning about the first parameter and its estimated error is written as 1 This indicates that the fit is unable to constrain the parameter and it should be considered indeterminate This usually indicates that the model is not appropriate One thing to check in this case is that the model component has any contribution within the energy range being calculated Plotting the data and residuals
3. A 306 Appendix G Adding a Custom Chain Proposal Algorithm When running a Monte Carlo Markov Chain with the chain command XSPEC provides several built in proposal options from which to draw trial parameter values for the next step in the chain A built in proposal is selected prior to the chain run with the command chain proposal lt distribution gt lt source gt where lt distribution gt is the statistical distribution used to randomize the parameter values e g gaussian cauchy and lt source gt refers to the source of the applied covariance information see the chain command for details It is also possible for the user to create an arbitrary new proposal scheme and add it to the options available under the chain proposal command This is done in a way similar to the adding of local models described in Appendix C though in this case the code can only be written in C Essentially three steps are involved each described in greater detail below e Create a small text file named randomize dat e Write a class which inherits from XSPEC s abstract base class RandomizerBase e Run XSPEC s initpackage and Imod commands to build and load the shared library containing the new proposal class es G 1 The randomize dat Initialization File This file must be placed in the same directory as the user s proposal code files and plays a role similar to the local models dat initialization files though it has a much simple
4. constant and a flat Universe The function is not valid for non zero cosmological constant if the Universe is not flat DGFILT Get a particular XFLT keyword value from a data file DGNFLT Get the number of XFLT keywords in a data file xs_getVersion or Retrieve XSPEC s version string xgvers F 3 Initializing the Models Library The external program should always call the FNINIT routine prior to any other call into the models library This initializes the locations of the various data files needed by the models and also sets the abundance and cross section tables Unless the user has overridden the model ion data directory location with the XSPEC_MDATA_DIR environment variable the initial settings are Model ion data HEADAS spectral modelData location Abundance and cross HEADAS spectral manager section dat files location Solar abundance table angr Photoelectric cross bemc section table F 4 Building with the Models Library The XSFunctions library depends on three lower level XSPEC libraries XS XSUtil and XSModel and also the CCfits and cfitsio libraries distributed with HEASOFT A Makefile for a small Fortran program linking with the models library therefore may look like this on Linux myprog myprog o g77 g myprog o o myprog L path to headas installed location lib 1XSFunctions 1XSModel IXSUtil IXS ICCfits_ 2 1 lcfitsio 3 11 myprog o myprog f g77 g c myprog f
5. Variable fit parameters are created for spectrum 3 response User will be prompted for starting fit parameter values of slope and offset XSPEC12 gt fit Best fit gain values will now be determined for and applied to spectrum 3 response XSPEC12 gt gain nofit 3 Spectrum 3 response will retain its current gain values but values will not be adjusted during future fits NOTE Current gain information may be easily viewed with the show response command Gain fit parameters may also be viewed with the show par or show rpar commands e Historical notes The gain command has been slightly revised for XSPEC12 Previously when a user entered a gain command it was generally interpreted to apply to an entire model This new implementation clearly defines an applied gain as belonging to a particular response It also offers less ambiguity for dealing with XSPEC12 s multiple models scheme So for example if 2 spectra are loaded each in its own data group and the user enters a gain fit command under the old system they would be prompted for 2 sets of parameters since the model is applied to 2 data groups With the new system the user specifies which particular response belonging to either spectrum or 2 they wish to apply the gain fit to and are then prompted for just the 1 set of gain parameters for that response This is more clearly demonstrated with the examples below The new command options gain nofit all and gain of
6. 5 6 5 editmod edit a model component Add delete or replace one component in the current model Syntax editmod lt delimiter gt lt componentl gt lt delimiter gt lt component2 gt lt delimiter gt lt componentN gt lt delimiter gt where lt delimiter gt is Some combination of and and lt componentJ gt is one of the models known to XSPEC The arguments for this command should specify a new model with thesame syntax as the previous model except for one component whichmay be either added deleted or changed to a different component type XSPEC then compares the entered model with the current model determines which component is to be modified prompting the user if necessary to resolve ambiguities and then modifies the model prompting the user for any new parameter values which may be needed Examples XSPEC12 gt mo wabs po XSPEC12 gt ed wabs potga This command will add the component gauss to model in the specified place and prompt the user for its initial parameters XSPEC12 gt mo wabs potzg XSPEC12 gt ed pot zg This command will delete the component wabs from the model leaving the other components and their current parameter values unchanged XSPEC12 gt mo wabs potpo XSPEC12 gt ed wabs po Here an ambiguity exists as to which component to delete In this case XSPEC will print out the current model showing the component number for each component and then
7. Correlation information is also given in the table of variances and principal axes which also appears at the end of a fit Each row in this table is an eigenvalue and associated eigenvector of the Fisher matrix If the parameters are independent then each eigenvector will have a contribution from only one parameter For instance if there are three independent parameters then the eigenvectors will be 1 0 0 0 1 0 and 0 0 1 If the parameters are not independent then each eigenvector will show contributions from more than one parameter Delta Statistic The next most reliable method for deriving parameter confidence regions is to find surfaces of constant delta statistic from the best fit value i e where Statistic StatistiC oyp A This is the method used by the error command which searches for the parameter value where the statistic differs from that at the best fit by a value A specified in the command For each value of the parameter being tested all other free parameters are allowed to vary The results of the error command can be checked using steppar which can also be used to find simultaneous confidence regions of multiple parameters The specific values of A which generate particular confidence regions are calculated by assuming that Statistic Statistic pes m is distributed as with the number of degrees of freedom equal to the number of parameters being tested e g when using the error command there is one degree of
8. The optional modelName qualifier allows the user to address a named model The user is prompted for parameter values for the component If there are m components in the current model then acceptable values for the component number added are to m 116 XSPEC detects the type of the model additive multiplicative etc checks the correctness of the syntax of the output model and adds the component if the resulting models obeys the syntax rules documented in the model command Thus XSPEC12 gt mo wa po Followed by XSPEC12 gt addcomp 2 bb Yields the model achieved by XSPEC12 gt mo wa bb po See also delcomp delete component by number Other Examples will serve to clarify addcomp s behavior Suppose that the current model specification is gatpo which using the show command would yield the description model gaussian 1 powerlaw 2 The comments give the model expression following the entry of addcomp and delcomp commands XSPEC12 gt addcomp 2 wab gaussian 1 wabs 2 powerlaw 3 XSPEC12 gt addcomp 4 pha gaussian 1 wabs 2 powerlaw 3 phabs 4 XSPEC12 gt delcomp 1 wabs 1 powerlaw 2 phabs 3 XSPEC12 gt addcomp 2 zg wabs 1 zgauss 2 powerlaw 3 phabs 4 XSPEC12 gt delcomp 3 wabs 1 zgauss 2 phabs 3 XSPEC12 gt mo wa po XSPEC12 gt addcomp 1 ga gauss 1 wabs 2 powerlaw 3 XSPEC12 gt delcomp 1 XSPEC12 gt
9. Writes last confidence region calculated for parameter n of model with optional name lt mod gt and a string listing any errors that occurred during the calculation The string comprises nine letters the letter is T or F depending on whether or not an error occurred The 9 possible errors are new minimum found non monotonicity detected minimization may have run into problem hit hard lower limit hit hard upper limit parameter was frozen search failed in ve direction search failed in ve direction O AN DWN BW NY reduced chi squared too high So for example an error string of FFFFFFFFT indicates the calculation failed because the reduced chi squared was too high expos n lt s b gt filename n flux n errsims ftest gain lt sourceNum gt lt specNum gt slope offset goodness sims idline ed ignore lt n gt lumin n errsims margin probability lt modName gt lt parNum gt model 82 Same as areascal option but for EXPOSURE value Filename corresponding to spectrum n Last model flux or luminosity calculated for spectrum n Writes a string of 6 values val errLow errHigh in ergs cm val errLow errHigh in photons Error values are 0 if flux was not run with err option If the errsims keyword is supplied this will instead return the completed sorted array of values generated during the most recent flux error calculation The r
10. plasma temperature keV Abundances for He C N O Ne Mg Al Si S Ar Ca Fe Ni wrt Solar defined by the abund command redshift z Gaussian sigma for velocity broadening km s 10 4x D 1 z to the source cm ne and ny are the electron and H densities cm nnydV where D4 is the angular diameter distance For the bvvapec variant the parameters are as follows parl par2 par3 1 Par32 Par33 plasma temperature keV Abundances for H He Li Be B C N O F Ne Na Mg Al Si P S Cl Ar K Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn wrt Solar defined by the abund command redshift z Gaussian sigma for velocity broadening km s 175 1 07 norm 4x D 1 z to the source cm ne and ny are the electron and H densities cm nnydV where Dy is the angular diameter distance 6 2 4 bbody zbbody blackbody A blackbody spectrum Kx8 0525E AB x 8 05 dE 4 kT exp a 1 where parl kT temperature keV ae 2 Where L is the source luminosity in units of 10 ergs norm K D Dao is the distance to the source in units of 10 kpc The zbbody variant allows an additional fixed redshift parameter 8 0525K E 1 z dE where parl kT temperature keV Z Fixed redshift Ls 7 gt where L is the source luminosity in units of 10 norm K D 1 2 ergs Dio is the distance to the source in units of 10 kpc 176 6 2 5 bbodyrad blackbody spec
11. the parameter is a switch parameter which is not used directly as part of the calculation but switches the model component function s mode of operation i e calculate or interpolate Switch parameters only have 2 fields the parameter name and an integer value Ifa P is added at the end of the line for a parameter then the parameter is defined to be periodic During a fit a periodic parameter will not be pegged if it tries to exceed its hard limits Instead it will be assigned a value within its limits f max delta f min delta f min delta f max delta The soft min and max settings are irrelevant for period parameters and will be ignored The model subroutine function The following table lists the function arguments required for the different language options The second column is the way the function name should be included in the model dat entry Call Type Specification Arguments and Type Meaning real 4 ear 0 ne Energy array integer ne Size of flux array Parameter values Dimension must be specified inside the real 4 param yw rn Single precision modelin function fortran integer ifl The spectrum number being calculated real 4 photar ne Output flux array real 4 photer ne Output flux error array optional Double F_modelfunc real 8 ear 0 ne As above integer ne A 293 real 8 param integer ifl real 8 photar ne real 8 photer
12. An X Ray Spectral Fitting Package User s Guide for version 12 8 1 Keith Arnaud Ben Dorman and Craig Gordon HEASARC Astrophysics Science Division NASA GSFC Greenbelt MD 20771 Aug 2013 Updates to the manual viiiasinashiusiscahintitwabteslacchsetibesdiushidehiapbinthiatinethiuabeghiende x XSPEC ove astacat saan ssc sasnoat snap sdatsaansaatsaap aaa aaaea raiat 1 Dl ING I WAZ EN secon ee oes E 1 1 2 Howto find out more information ccccccceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeees 3 TS HISTOry iaaa aa aaea aan advent e aeaa aaki iadi 3 1 4 Acknowledgements cccccccecsessseseeeeeeeeeeeeeeseeeeeeeeeeeeeeeeeseneeseeenees 4 E RREICKENCES A A A T 4 Spectral Fitting and XSPEC ccccecceeseeseeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeenees 5 2 1 Introduction iscccisssetscccicenaisceuisessscatisensscntsanescatisnnasaatsadesantisanesaassatesuatsunssantead 5 2 2 The Basics of Spectral Fitting eeeceeeeeeeeeeeeseeeeeeeeeeeeeseeeeenenees 5 2 3 The XSPEC implementation cccssseeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeenees 6 2 4 Amore abstract and generalized approach ccccceseeeeeeeeeee 9 2 5 XSPEC Data Analysis ovis secsisicccdscnsestinesssdesvessonisensseiesseeneeaseniess 10 2250 1 SOGIP Date ics E A A A 10 2 5 2 INTEGRAL SPI Data isci cc cci cate etter niiinetiie te eles 11 2 6 RETEFENCES saini ea a S aa a E aa SEEN E ian 12 XSPEC Overview and Helpful Hints eeceeeeeeee
13. If E 0 there is no cutoff in the power law The metal and iron abundances are variable with respect to those defined by the command abund The core of this model is a Greens function integration with one numerical integral performed for each model energy The numerical integration is done using an adaptive method which continues until a given estimated fractional precision is reached The precision can be changed by setting PEXRIV_PRECISION eg xset PEXRIV_ PRECISION 0 05 The default precision is 0 01 ie 1 parl I first power law photon index Ng E par2 Es cutoff energy keV if E 0 there is no cutoff par3 relret reflection scaling factor 0 no reflected component lt relret lt 1 for isotropic source above disk par4 redshift z pars abundance of elements heavier than He relative to the solar abundances par6 iron abundance relative to that defined by abund 227 par7 cosine of inclination angle pars disk temperature in K par9 F disk ionization parameter E 4r r where Fion is the 5eV 20keV irradiating flux n is the density of the reflector see Done et al 1992 ApJ 395 275 norm photon flux at 1 keV photons keV cm s of the cutoff broken power law only no reflection in the observed frame 6 2 65 plcabs powerlaw observed through dense cold matter This model describes X ray transmission of an isotropic source of photons located at the center of a uniform spherical distribution of m
14. legacy gsfc nasa gov fits_info fits_formats docs general ogip_92_009 C 2 Loading a new model function New model functions either downloaded from the XSPEC additional models webpage at http heasarc gsfc nasa gov docs xanadu xspec newmodels html A 291 or acquired privately are added using the two commands initpackage which prepares and compiles a library module containing them and the Imod command which actually loads them into the program These commands are described in the XSPEC commands section of the manual to which the user is referred Any number of different user model packages may be added to XSPEC from the user prompt and the user has control over the directory from which models are loaded Note that the Imod command requires write access to the particular directory specified This is because Imod uses the Tcl make package and package require mechanisms for automatic library loads and these require Tcl write an index file pkgIndex tcl to the directory Consequently we recommend using the Tcl load command instead of Imod if the library is being used by a number of users on a local network Note that such a library can be loaded automatically by placin the command in the global_customize tcl script see the section Customizing XSPEC C 3 Writing anew model function A model function is a subroutine that calculates the model spectrum given an input array of energy bins and an array of parameter values The i
15. meka vmeka emission hot diffuse gas Mewe Gronenschild 209 mekal vmekal emission hot diffuse gas Mewe Kaastra Liedahl 210 mkcflow vmcflow cooling flow mekal cccccceseeeseeeeeeeeeeeeeeeneees 212 nei vnei collisional plasma non equilibrium constant temperature 213 npshock vnpshock shocked plasma plane parallel separate ion electron temperatures sissies ccccdasscineieenanescesenensineseenaidenesareeaterdnwienens 215 nsa Neutron Star atmosphere ceeeceeeeseeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeenes 216 nsagrav NS H atmosphere model for different g ccccccesssees 217 nsatmos NS Hydrogen Atmosphere model with electron conduction and Self irradiatiOn cceccsseeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeneeee 218 nsmax Neutron Star Magnetic Atmosphere cccssseccceessseneeeees 219 nteea non thermal pair plasma qu ssseeeeeeeeee ee eeeeeeeeeeeceeeeeeeeeennees 220 Nthcomp Thermally comptonized continuum cceeeeeeeeeeeeeeeees 221 vii 6 2 60 Optxagnf optxagn Colour temperature corrected disc and energetically coupled Comptonisation model for AGN 0 222 6 2 61 pegpwrlw power law pegged normalization 0s eseeee 224 6 2 62 pexmon neutral Compton reflection with self consistent Fe and Ni NMA OS gt wi sasisvvs T e A 224 6 2 63 pexrav reflected powerlaw neutral medium eseeee 225 6 2 64 pexriv reflected powerlaw ioniz
16. tu LT gt csize 0 8 LT gt plot az We make the PostScript file and also save the plot information using the wenv command that in this case writes files figj qdp and figj pco containing the plot data and commands respectively PLT gt hardcopy figj ps ps PLT gt wenv figj PLT gt quit The result of all this manipulation is shown proudly in Figure J Markov Chain Monte Carlo Example To illustrate MCMC methods we will use the same data as the first walkthrough XSPEC12 gt data s54405 XSPEC12 gt model phabs pow XSPEC12 gt renorm XSPEC12 gt chain type gw XSPEC12 gt chain walkers 8 XSPEC12 gt chain length 10000 We use the Goodman Weare algorithm with 8 walkers and a total length of 10 000 For the G W algorithm the actual number of steps are 10 000 8 but we combine the results from all 8 Figure K The statistic from an MCMC run showing the initial burn in phase Results MCMC 58 Parameter Pholndex 0 0 2 0 4 0 6 0 8 1 1 2 Parameter nH Vira dtEp walkers into a single output file We start the chain at the default model parameters except that we use the renorm command to make sure that the model and the data have the same normalization If we had multiple additive parameters with their own norms then a good starting place would be to use the fit 1 command to initially set the normalizations to something sensible XSPEC12 gt chain run testl fits The first thing to check is what happ
17. 1 sec Using fit statistic chi Using test statistic chi Using Response RMF File ginga_lac rsp for Source 1 Spectral Data File hisum pha Spectrum 2 Net count rate cts s for Spectrum 2 1 371e 03 3 123e 00 Assigned to Data Group 2 and Plot Group 2 Noticed Channels 1 48 Telescope GINGA Instrument LAC Channel Type PHA Exposure Time 1 sec Using fit statistic chi Using test statistic chi Using Response RMF File ginga_lac rsp for Source 1 Here the first group makes up the file Losum pha which contains the spectrum of all the low pre eclipse emission The second group makes up the second file hisum pha which contains 47 all the high post eclipse emission Note that file number is absolute in the sense that it is independent of group number Thus if there were three files in each of the two groups 101 pha 1o2 pha 1o3 pha hil pha hi2 pha and hi3 pha say rather than one the six files would be specified as da 1 1 lol 1 2 lo2 1 3 103 2 4 hil 2 5 hi2 2 6 hi3 The ignore command works on file number and does not take group number into account So to ignore channels 1 3 and 37 48 of both files XSPEC12 gt ignore 1 2 1 3 37 48 The model we ll use at first to fit the two files is an absorbed power law with a high energy cut off XSPEC12 gt mo phabs highecut po After defining the model we will be prompted for two sets of parameter values one for the first group of data
18. 153 angr from Anders E amp Grevesse N 1989 Geochimica et Cosmochimica Acta 53 197 aspl from Asplund M Grevesse N Sauval A J amp Scott P 2009 ARAA 47 481 feld from Feldman U 1992 Physica Scripta 46 202 except for elements not listed which are given grsa abundances aneb from Anders E amp Ebihara 1982 Geochimica et Cosmochimica Acta 46 2363 grsa from Grevesse N amp Sauval A J 1998 Space Science Reviews 85 161 wilm from Wilms Allen amp McCray 2000 ApJ 542 914 except for elements not listed which are given zero abundance lodd from Lodders K 2003 ApJ 591 1220 file filename where filename is an ASCII file containing 30 lines with one number on each line All abundances are number relative to H The tables are Element angr aspl feld aneb grsa wilm lodd H 00e 00 00e 00 00e 00 00e 00 00e 00 00e 00 00e 00 He 77e 02 51e 02 77e 02 O1le 02 51e 02 77e 02 92e 02 Li 45e 11 12e 11 26e 11 19e 09 26e 11 00 90e 09 Be 4le 11 40e 11 5le 11 87e 11 dle 11 00 57e 11 B 98e 10 Ole 10 55e 10 82e 10 95e 10 00 03e 10 C 63e 04 69e 04 98e 04 45e 04 31e 04 40e 04 45e 04 N 12e 04 76e 05 00e 04 12e 05 32e 05 59e 05 76e 05 O 51e 04 90e 04 51e 04 39e 04 76e 04 90e 04 90e 04 F 63e 08 63e 08 63e 08 10e 08 63e 08 00 88e 08 Ne 23e 04 51e 05 29e 04 38e 04 20e 04 71e 05 41e 05 Na 1
19. At the end of a fit XSPEC will write out the best fit parameter values along with estimated confidence intervals These confidence intervals are one sigma and are calculated from the second derivatives of the fit statistic with respect to the model parameters at the best fit These confidence intervals are not reliable and should be used for indicative purposes only XSPEC has a separate command error or uncertain to derive confidence intervals for one interesting parameter which it does by fixing the parameter of interest at a particular value and fitting for all the other parameters New values of the parameter of interest are chosen until the appropriate delta statistic value is obtained XSPEC uses a bracketing algorithm followed by an iterative cubic interpolation to find the parameter value at each end of the confidence interval To compute confidence regions for several parameters at a time XSPEC can run a grid on these parameters XSPEC also will display a contour plot of the confidence regions of any two parameters 2 4 Amore abstract and generalized approach The sections above provide a simple characterization of the problem XSPEC actually operates at a more abstract level and considers the following Given a set of spectra C I each supplied as a function of detector channels a set of theoretical models M E each expressed in terms of a vector of energies together with a set of functions R 1 E j that map channels to en
20. COSMO 70 0 73 Default graphics package PLT is currently the only option GRAPH plt Default plotting device e g for PGPLOT PLOTDEVICE null Y axis plotting units when in setplot wave mode angstrom hz WAVE PLOT UNITS angstrom He User scripting directory 25 USER_SCRIPT DIRECTORY HOME xspec Default setting for parameters fit delta values Valid options are fixed proportional lt fraction of parameter value gt If set to fixed the default values come from the settings in the model dat model definition file FIT DELTAS proportional 01 A copy of this file is placed in the SHOME xspec directory on XSPEC12 s first start up or when it is not found After this users can modify settings such as default cosmology or the energy range for dummy response for their own requirements This is also the place where users can select if they want to view PDF help files from the XSPEC distribution or HTML either locally or from the HEASARC site Setting USE ONLINE HELP to true uses the remote HTML files while false will use either PDF or HTML local files depending on the value of LOCAL HELP FORMAT The PDF COMMAND and HTML COMMAND entries determine which applications are run for the two viewing cases The HTML COMMAND value should typically just be the name of a web browser or open for Mac OS X users The default settings for the PDF COMMAND entry
21. If lt par2 gt is omitted lt par1 gt is simply plotted against row number Use the thin lt n gt option to display only 1 out of every lt n gt chain points Example plot one in five chain points using parameters 1 and 4 for X Y plot chain thin 5 1 4 The thin value will be retained for future chain plots until it is reset Enter thin 1 to remove thinning chisq Plot contributions to chisq The contribution is plotted ve or ve depending on whether the residual is ve or ve contour Plot the results of the last steppar run If this was over one parameter then a plot of statistic versus parameter value is produced while a steppar over two parameters results in a fit statistic contour plot plot contour lt min fit stat gt lt levels gt lt levels gt 144 where lt min fit stat gt is the minimum fit statistic relative to which the delta fit statistic is calculated lt levels gt is the number of contour levels to use and lt levels gt lt levell gt lt levelN gt are the contour levels in the deltafit statistic contour will plot the fit statistic grid calculated by the last steppar command which should have gridded on two parameters A small plus sign will be drawn on the plot at the parameter values corresponding to the minimum found by the most recent fit The fit statistic confidence contours are often drawn based on a relatively small grid i e 5x5 To understand fully what
22. Null hypothesis probability 7 320332e 110 Current data and model not fit yet We are not quite ready to fit the data and obtain a better y because not all of the 125 PHA bins should be included in the fitting some are below the lower discriminator of the instrument and therefore do not contain valid data some have imperfect background subtraction at the margins of the pass band and some may not contain enough counts for x to be strictly meaningful To find out which channels to discard ignore in XSPEC terminology consult mission specific documentation that will include information about discriminator settings background subtraction problems and other issues For the mature missions in the HEASARC archives this information already has been encoded in the headers of the spectral files as a list of bad channels Simply issue the command XSPEC12 gt ignore bad ignore 40 channels ignored from source number 1 Fit statistic Chi Squared 799 74 using 85 PHA bins Test statistic Chi Squared 799 74 using 85 PHA bins Reduced chi squared 9 7529 for 82 degrees of freedom Null hypothesis probability 3 545928e 118 Current data and model not fit yet XSPEC12 gt plot ldata chi data and folded model 31 normalized counts s keV aign data model x A x 5 Energy keV Figure B The result of the command plot Idata chi after the command ignore bad on the EXOSAT ME spectrum 1E1048 1 5937 Gi
23. The first file will be type I the second type II containing 2 spectra The same is true for any background files produced If the user asks for more fake spectra to be created than the number of spectra currently loaded for example by typing the following when the same 3 spectra above described are loaded 96 XSPEC12 gt fakeit 5 then fake spectra 1 3 will be placed in the two files as before For the additional fake spectra 4 and 5 fakeit uses the following rule If any of the originally loaded spectra were in a type II file then all of the additional fake spectra will be placed in 1 type II file Otherwise they will each be placed in a separate type I file In this example since a type II file was originally loaded typeIIdata pha when fakeit was called spectra 4 and 5 will be placed together in a type II output file in addition to the type I and type II files for the first 3 fake spectra If there are no currently loaded spectra all output files will be type I unless either of the following situations exist 1 Any of the background files entered on the command line are type II as indicated by row specifiers in brackets 2 The first response file used clearly belongs to a format associated with type II data such as SPI Integral with its multiple RMF format see section on SPI Integral usage Overall though the method of determining output format for additional spectra may seem quite complicated it can be easily summed up
24. The extend option provides the same behavior as the old extend command Models will use associated response energy arrays with an additional low and or high array extension lt energy gt is the value to which the array is extended using lt nBins gt additional log or linear bins With the lt input ascii file gt option the user can instead supply a customized energy array from a text file The format requirements are simply that the bin values must appear 1 to a line and in ascending sorted order Blank lines are allowed and so are comments which must be preceded by a A simple example myEnergyBinning txt l 1 0 10 now some linear bins 15 20 25 which would actually produce the same energy array as energies 1 10 2 log 25 3 lin Once an energy array is specified it will apply to all models and will be used in place of any response energy array from actual or dummy responses for calculating and binning the model flux It will also apply to any models that are created after it is specified To turn off this behavior and return all models back to using their response energies simply type energies reset Similarly an array extension created by the extend option will continue to be applied to all models until it is either overwritten by another extension replaced by a new energies array or removed with the reset option This allows both low and high extensions to exist together When a
25. The latter is to be preferred The goodness of fit statistic can be set using the command statistic test There are a number of options available They can be interpreted using the goodness command which utilizes Monte Carlo methods 3 9 2 Binning and Grouping data Often one does not want to use the full resolution of a spectrum either because the channels over sample the spectral resolution or because the S N is low XSPEC and the associated programs provide a number of ways of handling this Firstly the XSPEC command setplot rebin can be used to add channels together in the plot It is important to realize that this effects only the plot and not the data being fitted Two FTOOLS are available to bin and group data for fitting purposes RBNPHA bins up the data in a non reversible manner and should only be used to ensure that the number of bins in the spectrum is the same as that in the response GRPPHA is the tool of choice for grouping the data to get adequate S N or number of counts in each channel GRPPHA does not actually add together channels but instead sets a flag which is read by XSPEC and causes XSPEC to sum the appropriate channels If a data file is read with some grouping then XSPEC will apply the same operation to any background or response files used 3 10 Plotting Commands XSPEC plotting is currently performed using the PLT interface There are two basic commands plot and iplot The plot command makes a plot and returns t
26. The programs are described more fully in George et al 1992 the directories below refer to the HEAsoft distribution e Spectral Data callib sre gen rdpha2 f wtpha3 f e Responses callib sre gen rdebd4 f rdrmf5 f wtebd4 f wtrmf5 f The rmf programs read and write the RMF extension while the ebd programs write an extension called EBOUNDS that contains nominal energies for the detector channels 11 e Auxiliary Responses callib sre gen rdarf1 f and wtarf1 f 2 5 2 INTEGRAL SPI Data XSPEC also includes an add in module to read and simulate INTEGRAL SPI data which can be loaded by the user on demand The INTEGRAL SPI datasets are similar to OGIP Type II but contain an additional FITS extension that stores information on the multiple files used to construct the responses The INTEGRAL Spectrometer SPI is a coded mask telescope with a 19 element Germanium detector array The Spectral resolution is 500 and the angular resolution is 3 Unlike focusing instruments however the detected photons are not directionally tagged and a statistical analysis procedure using for example cross correlation techniques must be employed to reconstruct an image The description of the XSPEC analysis approach which follows assumes that an image reconstruction has already been performed see the SPIROS utility within the INTEGRAL offline software analysis package OSA OR the positions on the sky of all sources to be analyzed a
27. anonymous ftp from ftp legacy gsfc nasa gov caldb docs memos Example additive table model files are mekal mod and raysmith mod in SHEADAS spectral modelData and testpo mod in SHEADAS spectral session Any number of tabulated model components additive multiplicative or exponential may be used simultaneously 173 6 2 3 bapec bvapec bvvapec velocity broadened APEC thermal plasma model A velocity and thermally broadened emission spectrum from collisionally ionized diffuse gas calculated using the ATOMDB code v2 0 2 More information can be found at http atomdb org which should be consulted by anyone running this model This default version number can be changed by modifiying the ATOMDB_VERSION string in your Xspec init file By default this model reads atomic physics continuum and line data from apec_v version coco fits and apec_v version _line fits in the HEADAS spectral modelData directory Different files can be specified by using the command xset APECROOT There are three options APECROOT can be set to a version number eg 1 10 1 2 0 1 3 1 2 0 1 In this case the value of APECROOT will be used to replace 2 0 2 in the name of the standard files and the resulting files will be assumed to be in the modelData directory Alternatively a filename root eg apec_vl 2 0 can be given This root will be used as a prefix for the coco fits and _line fits files Finally if neither of these work then the model will assum
28. f a XSPEC12 gt mdef junk3 0 2 B e mul 1 m XSPEC12 gt mdef bb E 2 T 4 exp E T 1 wW xx Warning bb is a p Please use a diffe XSPEC12 gt mdef sg exp E 2 2 A E sqrt j XSPEC12 gt mdef junk2 XSPEC12 gt mdef Nam Typ Expression dplaw add E p1 f E p2 junk add a E b LOG E SIN E junk3 mul a tb E sg con EXP E 2 2 A 5 6 15 model define a theoretical model E SORT 6 283 A SORT Ea Define the form of the theoretical model to be fit to the data 133 model lt source num gt lt name gt lt delimiter gt lt component1l gt lt delimiter gt lt component2 gt lt delimiter gt lt componentN gt lt delimiter gt model model lt name gt unnamed none model clear model lt name gt unnamed activelinactive rmodel lt source num gt lt spec num gt lt response function gt none where lt delimiter gt is some combination of and lt componentJ gt is one of the model components known to XSPEC The optional name must be preceded by a source number followed by a colon To specifically refer to the default model use the string unnamed Descriptions of these models may be accessed by typing help models at the prompt The source argument and name if present assign that model to be used with one of the sources found to be in the spectrum during the data pipelining These 2 parameters allow one to simultaneously analyze multiple models each assigned to t
29. loaded file if the gt character preceeds the filename The chain is written to the file as it runs so its performance can be monitored by examining the file For high chatter settings additional information is printed to the screen A long run may be interrupted with Ctrl C in which case the chain file will still exist but will not be automatically loaded If appending to a file the current filetype setting must match the format of the file or XSPEC will prevent it Writes out statistical information on a particular parameter of the chain specified by the parameter index number with optional model name The information displayed is The mean of the parameter over each chain file The parameter mean over all chain files and the variance between chain means The variance within the chains The Rubin Gelman convergence criterion The fraction of repeats defined as the number of lines in the chain file for which all parameter values are identical to the previous line divided by the number of lines in the file 105 temperature lt value gt type mh gw unload lt range gt walkers lt value gt Sets the temperature parameter used in the Metropolis Hastings algorithm for the proposal acceptance or rejection The default value is 1 0 and zero or negative values are forbidden By using the run append option it is possible for different sections of the chain file to use different temperatures The
30. par3 redshift z norm 107 ae nMudV where D4 is the angular diameter A distance to the source cm and ne ny cm are the electron and hydrogen densities respectively For vraymond the parameters are parl plasma temperature keV par2 parl13 Abundances for He C N O Ne Mg Si S Ar Ca Fe Ni wrt Solar defined by the abund command parl4 redshift z norm 107 moor nmidV where D is the angular diameter A distance to the source cm and ne ny cm are the electron and hydrogen densities respectively 6 2 70 redge emission recombination edge Recombination edge emission 0 E lt E A E 232 E E Kuyt exo EE EE Tp where parl E Threshold energy par2 T Plasma temperature keV norm K Photons cms in the line 6 2 71 refsch reflected power law from ionized accretion disk Exponentially cut off power law spectrum reflected from an ionized relativistic accretion disk In this model spectrum of pexriv is convolved with a relativistic disk line profile diskline See Magdziarz amp Zdziarski 1995 MNRAS 273 837 for details of Compton reflection See Fabian et al 1989 MNRAS 238 729 for details of the disk line profile parl par2 par3 par4 pars par6 par7 par8 par9 parl0 T power law photon index N E Ee cutoff energy keV if E 0 there is no cutoff relret reflection scaling factor 0 no direct component lt relret lt 1 for isotropic source above dis
31. proper superset of the XSPEC11 syntax The command XSPEC12 gt model wa po Creates a default model which takes an internal hidden symbol as a name Its parameters are sequenced from 1 as in XSPEC11 Another enhancement is in the newpar command XSPEC12 s expression analyzer developed for parsing model expressions is also used for parameter links Thus newpar link expressions can be polynomials in multiple parameters such as XSPEC12 gt newpar parl par2 par2 or XSPEC12 gt newpar parl 0 5 par3 1 5 par4 In sum most of the syntax enhancements added to XSPEC12 support the presence of multiple models The need to identify parameters of different models uniquely requires that their name and number be specified which requires enhancements in the syntax not only in the model related commands model addcomp delcomp and editmod but also the parameter related commands newpar freeze thaw untie steppar and error However if the model is not named all of these commands can be used identically as in XSPEC11 5 6 1 addcomp add component to a model Add a component to the model Syntax addcomp modelName n lt comp gt where n is the component number before which the new component is to be inserted and lt comp gt is the name of the new component Components are numbered in sequence in order of appearance in the expression entered The new component is regarded as an operator on the component added if it is not additive
32. released in patch v12 4 0v Support for GLAST GBM extensions to the standard file formats including multiple response matrix extensions in the same file released in patch 12 4 0am There are additional diagnostics available at high chatter levels from MCMC chain runs User s custom proposal classes have access to information about acceptances and rejections Initial support for multicore processors using the OpenMP parallel processing compiler option Multiplication of the model and response is performed in parallel across the multiple spectra in a datagroup All bug fixes to v12 4 0 released as patches a ar are included in v12 5 0 In addition the following problems have been corrected A 322 e When aruntime error is encountered during the calculation of a parameter s error bounds using the error command the value is now filled in with 0 0 rather than retaining its previous value e Steppar will now correctly step in reverse direction if the range values were entered in high to low order e Model expression parsing has been improved for nested expressions e Log file output has been fixed so comments are placed correctly e The chi square calculation includes the corfile contribution even if there is no background file associated with the spectrum e There are minor plotting fixes to the confidence line in 1 D steppar margin plots the rescaling of the Y 0 green line in lower panel plots and the Y axis label in plot
33. specified then all free parameters are fit 5 6 3 delcomp delete a model component Delete one or more components from the current model Syntax delcomp modelName lt comp num range gt where lt comp num range gt is range of positions in the model specification of the components to be deleted Examples Suppose that the current model specification is wa potgatga Then 118 XSPEC12 gt delcomp 3 4 Changes the model to wa po XSPEC12 gt delcomp 1 Changes the model to po 5 6 4 dummyrsp create and assign dummy response Create a dummy response covering a given energy range Syntax dummyrsp lt low Energy gt lt high Energy gt lt of ranges gt lt log or linear gt lt channel offset gt lt channel width gt lt source Num spec_ Num gt This command creates a dummy response matrix based on the given command line arguments which will either temporarily supersede the current response matrix or create a response matrix if one is not currently present There are two main uses for this command to do a quick and dirty analysis of uncalibrated data mode 1 and to examine the behaviour of the current model outside the range of the data s energy response mode 2 Note that mode 2 usage has now been rendered redundant by the more flexible energies command All parameters are optional The initial default values for the arguments are 0 01 keV 100 keV 200 logarithmi
34. temperatures and the line numbers to which they apply are stored in the header of the FITS format chain files or in the metadata section at the top of the ASCII text format files Determines the algorithm used to generate the chain Choices are mh Metropolis Hastings or gw Goodman Weare the default If using Goodman Weare must also set the walkers parameter Removes the chains specified by lt range gt from the list in xspec Note that this does NOT delete the chain files Sets the walkers parameter for the Goodman Weare chain algorithm see type This must be an even integer and both the chain length and burn length should be divisible by it XSPEC will adjust the lengths to make them so if necessary 106 All loaded chains must contain the same fit parameters xspec will prevent the loading of a chain with a different number of parameters from the currently loaded chains Examples XSPEC12 gt chain length 100 Sets length of chains produced by the run command to 100 XSPEC12 gt chain run chain filel out Runs a chain based on current valid fit parameters output to 5 5 3 107 chain_filel out XSPEC12 gt chain run gt chain_ filel out Appends another run of length 100 to the end of chain _filel out XSPEC12 gt chain load chain _old out Loads a pre existing chain file the result of an earlier run command Warning is issued if not the same length as chain_filel out XSPEC12 g
35. them by detector The Y then indicates that yes I wish to ignore the spectral data channels corresponding to the known detector electronic noise contamination this is the default Instead of det as the grouping option I could have selected time to group by time quantized into dither pointing intervals A lead to the data being initialzed into a single group The command XSPEC12 gt SPIdata MyData Dir rev0044 crab pha 475 65 Reads the 475 spectra into a single data group and ignores the undesirable channels If you forget all this the command XSPEC12 gt SPIdata h will remind you The scripts SPlIuntie and SPIfreeze have similar command line syntax SPlIuntie and SPIfreeze XSPEC12 gt SPIuntie bkg 475 19 1 The SPlIuntie command script will accomplish the same result as the sequence of untie commands in the INTEGRAL SPI example presented in this document In that case we had loaded 475 spectra associated with a single 5x5 dither pattern centered on the Crab nebula The spectra were grouped by detector which is a common approach to SPI analysis given the known detector to detector variations in the background rates Suppose after an initial fitting pass for which we assumed a single background spectrum we know wish to untie the individual data group i e detector background models This can be accomplished by issuing 25 untie commands as previously noted or in a single command line using the SPIunt
36. which makes use of XSPEC s now obsolete udmget function for dynamic memory allocation None of the functions in XSPEC s built in models library use udmget anymore and the necessary xsudmeget cxx file no longer resides there If a user still requires this code for their own local models they should add udmget without the quotes at the end of the comamnd line initipackage will then copy the files xsudmget cxx and xspec h into the user s local model directory initpackage performs the following tasks reads the model description file writes code that will load the new component calculation functions writes a makefile that will drive the compilation and installation of the new code invokes the compiler and builds the library 129 A separate command Imod actually loads the library This two step process makes it easier to determine where the user is during the process if compilation failures arise Further if the model is complete and working correctly only the Imod command need be invoked Initpackage can also be run as a stand alone program outside of XSPEC When used like this however after initpackage has finished the user must manually run hmake to build their library XSPEC performs this part automatically using a script file 5 6 12 imod localmodel load a package of local models The Imod command localmodel is an alias for this command loads a user model package Further details are given in Appendix C Note T
37. 1 10 The first 10 channels of all 4 spectra are noticed XSPEC12 gt notice 80 an attempt will be made to notice channels gt 80 in all 4 spectra as that was the last spectrum range specified but the result is that only channels 80 100 will be noticed for spectra 1 and 2 with no change for spectra 3 and 4 as they have no channels greater than 50 XSPEC12 gt notice 1 1 5 No channels are noticed as these channels were noticed in the beginning 101 5 4 10 response change the detector response for a spectrum Modify one or more of the matrices used to describe the response s of the associated spectrum to incident X rays Syntax response lt filespec gt response lt source num gt lt spectrum num gt none where lt filespec gt lt source num gt lt spectrum num gt lt file name gt and lt file name gt is the name of the response file to be used for the response of the associated spectrum If lt file name gt ends ina n specifier then the nth response will be read from the file lt spectrum num gt is the spectrum number for the first file name in the specification and follows similar rules as described in the data command description An important difference however is that the response command may only be used to modify the response of a previously loaded spectrum an error message is printed if the lt spectrum num gt is greater than the current number of spectra as
38. 124 The results of a flux command may be retrieved by the tclout flux lt n gt command where n is the particular spectrum of interest If the flux was calculated for the case of no loaded spectra the results can be retrieved by tclout flux with the lt n gt argument omitted The err noerr switch sets whether errors will be estimated on the flux The error algorithm is to draw parameter values from the distribution and calculate a flux lt number gt of sets of parameter values will be drawn The resulting fluxes are ordered and the central lt level gt percent selected to give the error range You can get the full array of simulated flux values by calling tclout flux with the errsims option see telout command When Monte Carlo Markov Chains are loaded see chain command they will provide the distribution of parameter values for the error estimate Otherwise the parameter values distribution is assumed to be a multivariate Gaussian centered on the best fit parameters with sigmas from the covariance matrix This is only an approximation in the case that fit statistic space is not quadratic There is also a model component cflux which can be used to estimate fluxes and errors for part of the model For instance defining the model as wabs pow cflux ga provides a fit parameter which gives the flux in the gaussian line Examples The current data have significant responses to data within 1 5 to 18 keV XSPEC12
39. 59 4 7 1 A Walk Through Example cccecessssseeeeneeeeeseseeensnsneeneeeeeeeensesees 59 4 7 2 INTEGRAL Specific Command Line Scripts ccsssseeeeeeseeteeeees 64 XSPEC COMMANAS wissecisssscseccssecssssessessvcssantecssecssadsusasseusssusseasssussaasusasceuees 67 5 1 Summary Of COMMANAS eeeecccceeeeeeeeeeeeeeeeeeeeeeeeeeeneeeeeeeeeeeeeeeeseenees 67 5 2 Description of SyntaX sccsasasesassaacasarsnacasapsaaiunarsaapeaarsaniwaansaassGereaateaasins 72 5 3 Control CommandS sssssssseeennnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn nnne 72 5 3 1 autosave set frequency of saving COMMANGG s eeeeeeeeeeeeeneeee 72 5 3 2 chatter set verboseness level ccccssseeeesseeeeeeseeeensesneeeeeeeeeeenseesees 73 5 3 3 exit quit exit program oasucsciveceansascuteadeccsjasvetenwacaewendiiinstvieiatdeeceneedatandaine 73 5 3 4 help display manual or help for a specific command theoretical model COMPONGIN viccssscaas cevautsiiacrdiaracenindessidesdinseedientivatibetadnvednednneadsae 73 5 3 5 log log the SESSION OUTPUL cccereessssseeeeeneneeeeseeeensnsneeeeeeeeeeeensesees 74 5 3 6 parallel enable parallel processing for particular tasks in XSPEC 75 5 3 7 query set a default answer for prompts iN SCIipts ccceeeeeeeeeees 76 5 3 8 save save the current SESSION COMMAMNAS ccsssseeeeeeeeeeeeeeeeeeeeeeeeee 76 5 3 9 script write commands to a script fil ceeeteeeeeeeeeeee
40. Fakeit will place all additional spectra and backgrounds ie those not based on already loaded data in type I output files unless it detects any evidence of type II file usage amongst the command line input in which case it will produce type II output Note on grouped spectra If an input spectrum has grouping information ie a GROUPING column telling XSPEC how to bin up the data then fakeit will simulate the number of counts in each of the grouped bins However the spectrum that is written out must have the ungrouped number of channels and a copy of the GROUPING column from the original spectrum The solution that XSPEC adopts is to place all the counts from a grouped bin in the first channel which goes to make up that bin This is of no consequence for future uses of the simulated spectrum provided that the GROUPING column is not changed So in this case grppha or similar tools cannot be run on the simulated spectrum Note For SPI Integral Format Since the SPI Integral format builds its responses from a combination of multiple RMFs and ARFs it must use a different scheme than the OGIP type I and II formats for storing RMF and ARF file location information This information is stored in a FITS extension named RESPFILE DB added to the PHA file Therefore when fakeit prompts the user for the location of the response file simply enter the name of a FITS file which contains a RESPFILE_DB extension pointing to the RMFs and ARFs to
41. Irt likelihood ratio test between two MOdeIS ccseseeeeeeeeeeeeeeeeeees 161 5 9 2 multifake perform multiple fakeit iterations and save to file 161 5 9 3 rescalecov rescale the covariance Matrix ccccccsseeseeeeeeeeeeeeeeeeees 162 5 9 4 simftest estimate the F test probability for adding a component 162 5 9 5 writefits write information about the current fit and errors to a FITS A E dares E E E see sstaacteiatiesseeart 162 XSPEC V12 MOIS i nitecctcsccccctetrncatecaccecctetctactenstcataesttceceesautiesstensteettes 164 6 1 Alphabetical Summary of Models cccccsssessseeeeeeeeeeeeeeeeeeeeneees 164 6 2 Additive Model Components Sources ssseeeeeeeeeeeees 170 6 2 1 apec vapec vvapec APEC emission Spectrum cccccccsseeees 170 6 2 2 atable tabulated additive MOdel ssseseeeeeeeeeeeeeeeeeeeeeeeeeeeennenes 172 6 2 3 bapec bvapec bvvapec velocity broadened APEC thermal plasma AVVO isaac ce E E fh cuca sve stivev savers toe siededasenedechentuveladn AT 173 6 2 4 bbody Zbbody blackbody ccceeceeeseseeeeeeeeeeeeeeeeeneeneeeeeeeeeeeeenens 175 6 2 5 bbodyrad blackbody spectrum area normalized 2 2 0 0 176 6 2 6 bexrav reflected e folded broken power law neutral medium 176 6 2 7 bexriv reflected e folded broken power law ionized medium 177 6 2 8 bknpower broken power law c ccecssseesseeeeeeeeeeeeeneeneeeeneeeeeeneee
42. J Epstein R I 1989 ApJ 336 896 Press W H Teukolsky S A Vetterling W T Flannery B P 1992 Numerical Recipes 2nd edition p687ff CUP Wheaton W A et al 1995 ApJ 438 322 14 3 XSPEC Overview and Helpful Hints 3 1 Syntax XSPEC is a command driven interactive program You will see a prompt XSPEC12 gt whenever input is required Command recall and inline editing are available using the arrow keys XSPEC uses Tcl as its user interface providing looping conditionals file T O and so on For further details of the Tcl syntax consult the Description of Syntax section the User Interface appendix and links therein 3 2 Howto return to the XSPEC gt prompt The string acts as an emergency escape back to the XSPEC prompt This string in answer to any question should bounce XSPEC out of whatever it is doing and back to the command prompt 3 3 Getting Help Quick help If you are uncertain about command syntax typing a command followed by a will print a one line summary The help command XSPEC12 gt help without arguments will bring up the full XSPEC manual in a PDF document reader e g Adobe Acrobat Reader or will open a browser to the XSPEC manual home page either locally or on the HEASARC site See Customizing XSPEC later in this section to see how to select between these options and how to assign a PDF reader and web browser to XSPEC Typing XSPEC12 gt help l
43. M E par 6 N E par7 R E Thus the actual physical situation described above corresponds to par6 1 0 par7 1 0 You may decide to float par6 and or par7 In that case you must decide what the best fitting values of these parameters mean physically for your case It may imply time lags between the direct and reflected components different source and or disk geometries to those assumed or something else 6 3 15 Iyman Voigt absorption profiles for H I or He Il Lyman series This model calculate the Voigt absorption profiles for the H I and He II Lyman series parl n HI or He II column density 10 atoms cm par2 b b value km s par3 z Redshift par4 ZA Atomic number of species being calculated 6 3 16 mtable multiplicative tabular model A multiplicative table model The filename to be used should be given immediately after mtable in the model command For example XSPEC12 gt model mtable mymod mod uses mymod mod as the input for the model For specifications of the table model file see the OGIP memo 92 009 on the FITS file format for table model files available on the WWW or by anonymous ftp from ftp legacy gsfc nasa gov caldb docs memos A sample multiplicative table model file is testpcfabs mod in SHEADAS spectral session 246 6 3 17 notch absorption line notch A notch line absorption This is model is equivalent to a very saturated absorption line f forE W 2 lt E lt E W 2 M E 1 elsew
44. Note that if all the rate parameters in use are thawed then the norm parameter is degenerate and must be frozen Freezing one of the rate parameters will not work because if that vertex is driven to zero in the fit then the norm will be zero and the other rate parameters infinite parl energy00 keV par2 energy01 keV par3 energy02 keV par4 energy03 keV pars energy04 keV par6 energy05 keV par7 energy06 keV par8 energy07 keV par9 energy08 keV par10 energy09 keV parl1 log _rate00 par12 log _rate01 par13 log_rate02 parl4 log rate03 par15 log_rate04 parl6 log rate05 parl7 log rate06 parl8 log rate07 parl9 log rate08 parl0 log rate09 193 norm 6 2 23 cutoffpl power law high energy exponential cutoff A power law with high energy exponential rolloff A E KE exp 4 parl a power law photon index par2 p e folding energy of exponential rolloff in keV norm K Photons keV cm7s at 1 keV If POW_EMIN and POW_EMAX have been defined by the xset command then the norm becomes the flux in units of 10 ergs cm s over the energy range POW_EMIN POW_EMAX keV unless POW_EMIN POW_EMAX in which case the norm becomes the flux density in micro Jansky at POW_EMIN keV In these cases it is important that POW_EMIN and POW_EMAX lie within the energy range on which the model is being evaluated 6 2 24 disk accretion disk black body The spectrum from an accretion disk where the opacities are
45. PLT is built on top of the PGPLOT package which comes with a standard set of device drivers Any machine running X windows should support xs and xw while xterm windows should support xt PGPLOT supports monochrome and color postscript and both landscape and portrait orientation with the drivers ps eps vps and veps The easiest way to make a hardcopy of an XSPEC plot is to use XSPEC12 gt iplot command and then at the PLT prompt to enter PLT gt hard ps This will make a file called pgplot ps which can be printed Alternatively the sequence XSPEC12 gt cpd lt filename gt ps XSPEC12 gt plot commands XSPEC12 gt cpd none will place the plots in a PostScript file lt filename gt 3 11 Setting Commands The fit and goodness of fit test statistics are set using the statistic command Other fit minimization algorithms are available and can be selected using the method command The various fit methods require first and in some cases second derivatives of the statistic with respect to the parameters By default XSPEC calculates these analytically using an approximation for the second derivatives This may be changed by setting the USE NUMERICAL DIFFERENTIATION flag in the user s startup Xspec init file The weighting algorithm used to calculate x can be altered by the weight command Other setting commands modify cosmological parameters used to calculate luminosity cosmo solar abundance
46. Roderick Johnstone parl Index power law dependence of emissivity scales as R par2 inner radius units of GM c par3 outer radius units of GM c par4 inclination degrees par5 radius at which emissivity power law index changes par6 Emissivity power law index for radii gt par6 263 6 4 7 kerrconv accretion disk line shape with BH spin as free parameter Convolves the current spectrum with the line shape from the kerrdisk model A detailed description can be found in Brenneman amp Reynolds 2006ApJ 652 1028B This model is quite slow so is best used after models such as laor or diskline have been employed to get an estimate of the best fit parameters parl emissivity index for the inner disk par2 emissivity index for the outer disk par3 break radius separating the inner and outer portions of the disk gravitational radii par4 dimensionless black hole spin parS disk inclination angle to the line of sight degrees par6 inner radius of the disk in units of the radius of marginal stability par7 outer radius of the disk in units of the radius of marginal stability 6 4 8 Ismooth lorentzian smoothing Lorentzian smoothing with a variable width which varies as the par2 power of the energy The width at 6 keV is set with par1 X E 27 E LX F 2 E 2 dC E A X dX X E o E 6 where parl o lorentzian sigma at 6 keV par2 a power of energy for sigma variation 6 4 9 par
47. USE NUMERICAL DIFFERENTIATION variable in the user s Xspec init file is changed from the default false to true The speed up that one can expect is highly dependent upon the model in use For simpler models with quick calculation times you will probably see little to no speed gain with parallel leven But with multi core CPUs gains should be quite noticeable when the model calculation consumes a large fraction of the overall fitting time For example with fits using the time intensive sedov model on a 4 core machine we ve typically seen about a 40 reduction in fit time compared with the single processing case The error option is for running parallel computations within XSPEC s error command This enables the error calculations for multiple parameters to be performed simultaneously The speed up here should simply be proportional to the number of cores available However for cases where complications are reported such as a new minimum found or a non monotonicity in the statistic space it is recommended that you perform the error calculations in standard single process mode When the steppar option is set XSPEC will divide the N dimensional steppar grid into lt max num gt sections of equal size and spawn a separate process for calculating each section If both parallel leven and error or steppar are in use XSPEC will temporarily disable the lower level leven parallelization when running the higher level parallel error
48. XSPEC For example if after initialization users wishing to load a different version of the standard tcl unknown procedure should name that procedure tclunknown rather than unknown A 8 Aliases Command name aliases can be constructed using the tcl interp command interp alias lt command alias gt lt xspec_command gt where lt xspec_command gt is the name of the command you wish to make an alias for and lt command_alias gt is the name of the alias you wish to set for the command The are required syntax To delete the alias lt command_alias gt simply nullify it with interp alias lt command_alias gt A 9 Initialization Script When running interactively the user has the option of providing an initialization script which will be executed after XSPEC completes its startup procedure ie just before it begins prompting for commands The file should be named xspec rc and located in the directory HOME xspec If one runs XSPEC in batch mode by specifying a script on the command line this initialization script is not executed When multiple users are accessing a single system wide XSPEC build the installer can also provide additional initialization that will apply to all users See the section XSPEC Overview and Helpful Hints Customizing XSPEC for more details A 10 XSPEC Command Result A 276 After being executed many tcl commands return a result string which is echoed to the terminal when the
49. a 2 response XSPEC12 gt response 2 1 resp2 rsp then define a background model to apply to source 2 XSPEC12 gt model 2 my background model name wa po This model will now apply to spectrum and any other spectrum that has a response loaded for source 2 To apply a different background model to spectrum 2 load a response for source 3 rather than 2 XSPEC12 gt response 3 2 another response rsp XSPEC12 gt model 3 another background model ga An arf can also be assigned to a particular source number and spectrum XSPEC12 gt arf 2 1 arf _file pha Source numbers do not need to be entered in consecutive order for a given spectrum and gaps in numbering are allowed Please see the individual model and response entries in the XSPEC Commands section for more information and examples 3 9 Fitting Commands The basic fit command is called fit This command performs a minimization using the currently selected algorithm default Levenberg Marquardt fit takes arguments that are passed to the fitting method by default these are the number of iterations to execute before asking the user whether to continue and the numerical convergence criterion A systematic model uncertainty can be included using the systematic command The error or uncertain command calculates error bounds for one interesting parameter for the specified parameters and confidence levels To produce multi dimensional errors the step
50. addcomp 1 pha phabs 1 wabs 2 powerlaw 3 XSPEC12 gt mo wabs po XSPEC12 gt addcomp 3 bb wabs 1 powerlaw 2 bbody 3 XSPEC12 gt delcomp 1 XSPEC12 gt addcomp 3 pha 117 wabs 1 powerlaw 2 pha 3 XSPEC12 gt addcomp 3 po ERROR po additive is interpreted as being added to the multiplicative model pha 3 which is a context error For multiply nested models XSPEC12 gt mo wa po pha bb ga XSPEC12 gt addcomp 6 po wabs 1 powerlaw 2 phabs 3 bbody 4 ga 5 powerlaw 6 XSPEC12 gt addcomp 5 peg wabs 1 powerlaw 2 phabs 3 bbody 4 pegpwlw 5 ga 6 powerlaw 7 XSPEC12 gt addcomp 7 wa wabs 1 powerlaw 2 phabs 3 bbody 4 pegpwlw 5 ga 6 wabs 7 powerlaw 8 5 6 2 addline add spectral lines to a model Tcl script to add one or more lines to the current model in an optimum fashion Syntax addline lt nlines gt lt modeltype gt fit nofit lt nlines gt additional lines are added one at a time Line energies are set to that of the largest residual between the data and the model For each line a fit is performed with the line width and normalization as the only free parameters The default option is one gaussian line The other lt modeltype gt that can be used is lorentz If no third argument is given then the sigma and normalization of each line are fit If nofit is specified then the fit is not performed but if fit is
51. after the XSPEC plot command has finished producing the same graph At this point you can enter PLT commands to inspect interesting parts of the graph add labels or make a hardcopy file for later printing D 1 Getting started with PLT In the following description of PLT commands the full command is descried Capital letters denote the shortest abbreviation of the command that will be recognized Here is a brief guide to some of the PLT commands that can be entered when iplot is invoked HEIlp will provide you with descriptions of the PLT commands Plot redraws the display using all of the commands that change the graph entered since the last plot Rescale lt X Y gt j PGPLOT is the name of a Graphics Subroutine Library written by T J Pearson at the California Institute of Technology A 298 followed by two numbers will set the minimum and maximum of the plotted x range to the numbers specified Without further arguments Rescale X or Y will reset the minimum and maximum values to their default values Rescale also updates the screen immediately Other commands allow you to make several changes to the the graph without having to wait for the screen to be updated after every change LAbel lt Top X Y gt lt string gt add labels to various locations on the graph For example typing LA Top EXOSAT was great Will cause the message EXOSAT was great to appear at the top of the graph the next time the display is re
52. age of the remnant pars redshift z norm 10 f W _ n n ia D 1 2 H where Dy is the angular diameter distance to the source cm and ne ny cm are the electron and hydrogen densities respectively 6 2 73 sirf self irradiated funnel The multi blackbody Self IrRadiated Funnel model is designed to model optically thick outflow dominated accretion The basic idea is simple you just assume a lot of matter angular momentum and energy emerges in a limited volume Momentum conservation leads to non sphericity of the flow that has subsequently conical funnel like shape The model calculates temperature distribution at the funnel walls taking into account irradiation by iterative process and the outer photosphere We also assume that inside the cone there is a deep pseudo photosphere Relativistic boosts are taken into 235 account for high velocities For a comprehensive description of the physical model see Abolmasov P Karpov S and Kotani T PASJ 61 2 213 parl tin inner temperature at the inner inside the funnel photosphere par2 rin inner inside the funnel photosphere radius in spherisation radius units the latter is defined as 3 K Mdot Q c par3 rout outer photosphere radius in spherisation radius units par4 theta half opening angle of the cone pars incl inclination angle of the funnel Affects mainly self occultation and relativistic boost effects
53. and Gronenschild as amended by Kaastra The model includes line emissions from several elements Abundances are the number of nuclei per Hydrogen nucleus relative to the Solar abundances set by the abund command The vmeka variant allows the user to set the abundances for the model Parameters for the meka model are parl plasma temperature in keV par2 H density cm par3 Metal abundances He fixed at cosmic The elements included are C N O Ne Na Mg Al Si S Ar Ca Fe Ni 210 par4 redshift z norm 107 aoa nnydV where Dy is the angular diameter A distance to the source cm and ne ny cm are the electron and hydrogen densities respectively Parameters for the vmeka model are parl plasma temperature in keV par2 H density cm par3 parl4 Abundances for He C N O Ne Mg Si S Ar Ca Fe Ni wrt Solar given by the Anders amp Grevesse mixture parl5 redshift z norm 107 j a nn 4 zi D 1 2 H where Dy is the angular diameter distance to the source cm and ne ny em are the electron and hydrogen densities respectively The references for the MEKA model are as follows Mewe R Gronenschild E H B M and van den Oord G H J 1985 A amp AS 62 197 Mewe R Lemen J R and van den Oord G H J 1986 A amp AS 65 511 Kaastra J S 1992 An X Ray Spectral Code for Optically Thin Plasmas Internal SRON Leiden Report updated version 2 0 Similar credit may also
54. and absorption Other scenarios are possible the important thing is to recognize the flexibility of XSPEC in this regard As an example we will look at a case of fitting the same model to two different data files but where not all the parameters are identical Again this is an older dataset that provides a simpler illustration than more modern data The massive X ray binary Centaurus X 3 was observed with the LAC on Ginga in 1989 Its flux level before eclipse was much lower than the level after eclipse Here we ll use XSPEC to see whether spectra from these two phases can be fitted with the same model which differs only in the amount of absorption This kind of fitting relies on introducing an extra dimension the group to the indexing of the data files The files in each group share the same model but not necessarily the same parameter values which may be shared as common to all the groups or varied separately from group to group Although each group may contain more than one file there is only one file in each of the two groups in this example Groups are specified with the data command with the group number preceding the file number like this XSPEC12 gt data 1 1 losum 2 2 hisum 2 spectra in use Spectral Data File losum pha Spectrum 1 Net count rate cts s for Spectrum 1 1 401e 02 3 549e 01 Assigned to Data Group 1 and Plot Group 1 Noticed Channels 1 48 Telescope GINGA Instrument LAC Channel Type PHA Exposure Time
55. are isotropic and homogeneous 5 sphere with the source of photons distributed according to the eigenfunction of the diffusion equation f tau sim pi tau tau pi tau tau where tau varies between 0 and tau par8 H R for cylinder geometry only par9 cosIncl cosine of inclination angle if lt 0 then only black body par10 cov_fac covering factor of cold clouds if geom 4 5 then cov_fac is dummy parl1 R amount of reflection Omega 2 pi if R lt 0 then only reflection component par12 FeAb iron abundance in units of solar par13 MeAb abundance of heavy elements in units of solar par14 xi disk ionization parameter L nR 2 par15 temp disk temperature for reflection in K par16 beta reflection emissivity law r beta if beta 10 then non rotating disk if beta 10 then 1 sqrt 6 rg rg 3 parl7 Rin Rg inner radius of the disk Schwarzschild units par18 Rout Rg outer radius of the disk par19 redshift 6 2 19 compST Comptonization Sunyaev amp Titarchuk A Comptonization spectrum after Sunyaev and Titarchuk 1980 A amp A 86 121 This model is the Comptonization of cool photons on hot electrons parl temperature in keV par2 optical depth norm rome where N is the total number of photons from the source d is the 1 189 z z 3 y T 2z 4 z index y is the injected photon energy in units of the temperature and I is the incomplete gamma function distance to the source and f is the
56. are what work best for launching Adobe Acrobat Reader 7 0 x on Linux Unix systems For those launching earlier versions the openInNew Window flag should be replaced with useFrontEndProgram For Mac users again we recommend the entire entry simply be replaced with open The second file that is searched for is the xspec rc file This contains users own customizations for example Tcl or XSPEC command abbreviations packages to be loaded on startup or Tcl scripts containing procedures that are to be executed as commands Please consult Appendix A and references links therein for details of Tcl commands and scripting 3 13 1 Customizing system wide When an XSPEC build is intended for many users across a system it is also possible for the installer or whoever has write access to the distribution and installation areas to globally customize XSPEC This is done through the file global_customize tcl located in the Xspec sre scripts directory This was done in the xspec tcl file prior to v12 2 1 Any of the customizations mentioned above for the individual s own xspec rc file can also be placed in the global_customize tcl file After making the additions run hmake install out of the Xspec src scripts directory in order to copy the modified global_customize tcl file to the installation area This additional code will be executed for all users upon startup BEFORE any of their own customizations in their xspec rc
57. axis of the Se ihe Aah ah instrument the X statistic is D TODDI 1 E oM E xs B 15X 2 J L IP am a P d I d p where Pd run over instrument pointings and detectors I runs over individual detector channels j enumerates the sources detected in the field at different position 0 9 E indexes the energies in the source model Xs parameters of the source model which is combined with the response Xp parameters of the background model expressed as a function of detector channel Examination of this equation reveals one more complication the term B represents the background which unlike for chopping scanning or imaging experiments must be solved for simultaneously with the desired source content The proportion of background to source counts for a bright source such as the Crab is 1 Furthermore the background varies as a function of detector and time dither points making simple subtraction implausible Thus a model of the background is applied to a special response matrix and included in the de convolution algorithm 2 6 References Arnaud K A George I M Tennant A F 1992 Legacy 2 65 Avni Y 1976 ApJ 210 642 13 Bevington P R 2002 3 Edition Data Reduction and Error Analysis for the Physical Sciences McGraw Hill Blissett R J Cruise A M 1979 MNRAS 186 45 George I M Arnaud K A Pence W Ruamsuwan L 1992 Legacy 2 51 Kahn S M Blissett R J 1980 ApJ 238 417 Loredo T
58. be applied When prompted for an ARF name enter nothing The prompts will only appear for the first spectrum in the data set and the ARFs will be assigned row by row to 1 with the spectra For example if no data is currently loaded to create 3 fake SPI spectra from the RMFs and ARFs named in the RESPFILE_DB extension of the file realSpiData pha XSPEC12 gt fakeit 3 various prompts will follow For fake spectrum 1 response file is needed realSpiData pha and ancillary file lt Ret gt more fakeit prompts 97 This will create 3 fake spectra each making use of the same RMFs ARFs spectrum 1 using the first row of the ARFs spectrum 2 using the second etc CAUTION SPI Integral As currently implemented the RESPFILE DB method of storing ARF locations does not retain specific row information The assumption is that the rows in the ARF correspond 1 to 1 with the rows in the spectral data extension Therefore much confusion can arise when the row numbers of the loaded spectra do not match that of the fake spectra For example XSPEC12 gt data my_spi_ data pha 3 4 my_spi_data pha contains a RESPFILE DB table pointing to arfl fits avf2 fit arf3 fits it to some model s XSPEC12 gt fakeit This will produce 2 fake spectra generated from the model response operation where the model has parameters based on a fit to the original spectra in rows 3 and 4 of my spi_da
59. be thrown away prior to storing the chain clear Does a reset and removes all chains from the list filetype fits ascii Chooses the format of the output chain file fits the default writes the chain to a binary table in a FITS file ascii writes the chain to a simple text file Either format is readable when using the load command info Prints out information on the current chains length lt length gt Sets the length for new chains load lt filename gt Loads a chain which has been run earlier stored in file given by lt filename gt proposal lt distr gt lt source gt Selects the proposal distribution and source of covariance information to be used when running new chains The default is proposal gaussian fit Currently implemented lt distr gt options are gaussian and cauchy lt source gt options are 104 chain Covariance is taken from the currently loaded chains diagonal lt values gt The values of a diagonal covariance matrix are entered directly on the command line separated by commas and or spaces C 11 C_22 C_nn lt filename gt Covariance is read in from a user specified text file The file must contain the values of an NxN matrix where N is the current number of freely varying parameters The values of each matrix row should be entered on one line with whitespace separation Since this matrix is always symmetrical values above the diagonal may be omitted For example a 2x2 ma
60. c par4 outer radius units of GM c par5 inclination degrees norm photons cm s in the line 6 2 46 laor2 accretion disk with broken power law emissivity profile black hole emission line An emission line from an accreti on disk with a broken power law emissivity profile around a black hole Uses Ari Laor s calculation including GR effects ApJ 376 90 Modified from laor model by Andy Fabian parl Line energy in keV par2 Index power law dependence of emissivity scales as R77 par3 inner radius units of GM c par4 outer radius units of GM c par5 inclination degrees par6 radius at which emissivity power law index changes par7 Emissivity power law index for radii gt par6 norm photons cm s in the line 6 2 47 logpar log parabolic blazar model logpar is a power law with an index which varies with energy as a log parabola A E E pivork OSa parl a Slope at the pivot energy par2 p Curvature term 209 par3 pivotE Fixed pivot energy best near low end of energy range norm K See for instance Massaro et al 2004 6 2 48 lorentz lorentz line profile A Lorentzian line profile o 2n A E K ce E E Y o 2 where parl E line energy in keV par2 o FWHM line width in keV norm K photons cm s in the line 6 2 49 meka vmeka emission hot diffuse gas Mewe Gronenschild An emission spectrum from hot diffuse gas based on the model calculations of Mewe
61. command is entered on the command line When writing complex tcl scripts this result can be stored and or used as a test in loops etc When XSPEC commands are executed they write information to the terminal by writing directly to the appropriate output channel However when running interactively the tcl result string is also written to the terminal after the command is executed The tclout command see command description creates tcl variables from xspec s calculations A 11 Script Files XSPEC tcl script files can be executed in three different ways as follows xspec lt script gt executing script on initialization XSPEC12 gt lt script gt executing script from within the program XSPEC12 gt source tclscript use tcl s source command from within the program Each of these usages does something slightly different In the first form XSPEC will execute a file called lt script gt One may execute a series of script files at startup with the following command syntax unix gt xspec filel file2 file3 Note that the space following the is required The second form is lt name gt where lt name gt is the name of the script file to be executed Here the default extension of xcm is assumed Scripts containing valid tcl or XSPEC commands will be executed using this form and unless the script ends in quit or exit will return to the interactive prompt after completion The final form using tcl s source command is intended
62. data 232 MyDataDir rev0044 Crab pha fits 2 XSPEC12 gt data 33 MyDataDir rev0044 Crab pha fits 3 XSPEC12 gt data 19 19 MyDataDir rev0044 Crab pha fits 19 XSPEC12 gt data 1 20 MyDataDir rev0044 Crab pha fits 20 XSPEC12 gt data 2 21 MyDataDir rev0044 Crab pha fits 21 XSPEC12 gt data 3 22 MyDataDir rev0044 Crab pha fits 22 XSPEC12 gt data 19 38 MyDataDir rev0044 Crab pha fits 38 XSPEC12 gt data 1 39 MyDataDir rev0044 Crab pha fits 39 XSPEC12 gt data 2 40 MyDataDir rev0044 Crab pha fits 40 XSPEC12 gt data 3 41 MyDataDir rev0044 Crab pha fits 41 XSPEC12 gt data 18 474 MyDataDir rev0044 Crab pha fits 474 XSPEC12 gt data 19 475 MyDataDir rev0044 Crab pha fits 475 One might then for example make a first cut attempt by fitting a constant background Then as a next step one might allow the normalization terms of the background model to vary over the groups i e over the detector plane This is accomplished with the untie command using the following sequence XSPEC12 gt untie bkg 52 XSPEC12 gt untie bkg 78 XSPEC12 gt untie bkg 104 XSPEC12 gt untie bkg 130 XSPEC12 gt untie bkg 156 XSPEC12 gt untie bkg 182 XSPEC12 gt untie bkg 208 XSPEC12 gt untie bkg 234 XSPEC12 gt untie bkg 260 XSPEC12 gt untie bkg 286 XSPEC12 gt untie bkg 312 XSPEC12 gt untie bkg 338 XSPEC12 gt untie bkg 364 XSPEC12 gt untie bkg 390 XSPEC12 gt untie bkg 416 64 XSPEC12 gt untie bkg
63. data is compared to a source model multiplied by the source response plus a background model multiplied by the background response and the background data is compared to the background model multiplied by the background response The background models fitted to the source and background data are constrained to be the same XSPEC12 gt show param Parameters defined Model phabs lt 1 gt powerlaw lt 2 gt Source No 1 Active On Model Model Component Parameter Unit Value par comp Data group 1 1 1 phabs nH 10322 1 00000 0 0 2 2 powerlaw PhoIndex 1 00000 f 02 0 3 2 powerlaw norm 1 00000 0 0 Data group 2 4 1 phabs nH 104222 1 00000 1 5 2 powerlaw PhoIndex 1 00000 2 6 2 powerlaw norm 1 00000 3 Model myback powerlaw lt 1 gt Source No 2 Active On Model Model Component Parameter Unit Value par comp Data group 1 51 1 1 powerlaw PhoIndex 1 00000 0 0 2 1 powerlaw norm 1 00000 0 0 Data group 2 3 1 powerlaw PhoIndex 1 00000 myback 1 4 1 powerlaw norm 1 00000 myback 2 It is often the case that the response information is split into an RMF and ARF where the RMF describes the instrument response and the ARF the telescope effective area The particle background can then be included by using the RMF but not the ARF XSPEC12 gt data 1 1 source pha 2 2 back pha XSPEC12 gt response 1 source rmf 2 source rmf XSPEC12 gt arf 1 source arf XSPEC12 gt response 2 1 source rmf 2 2 source r
64. delchi e Tclout peakrsid no longer fails for a spectrum whose model was not assigned to source 1 The XSFunctions library now also depends on XSModel requiring the addition of a IXSModel flag to the Makefile of external programs linking with the XSPEC model functions library See Appendix F The modellonData model data files directory has been renamed to modelData Portions of some model functions have been translated from Fortran to C to reduce use of the udmget memory allocation function Future versions will remove all references to udmget
65. determination of the lt delta gt derivatives used during the fitting process When delta is set to zero the parameter is not adjustable during the fit This value may be overriden for all parameters by the xset delta command 138 option which will apply a proportional rather than a fixed delta The four arguments of the range specification determine the range of acceptable values for the parameter The soft limits should include the range of expected parameter behavior Between the hard and soft limits the parameter is made stiffer to adjustment by the minimization routine invoked by the fit command The parameter is never allowed to have a value at or outside the hard limits A slash will set all the six parameter specification values value delta range specification to the previous value default for a new model current value if the parameter has previously been set or fit The sequence leaves all parameters unchanged in the case of a new model to be set to the default newpar 0 Prints the current parameter settings Parameter Links Coupling of parameters allows parameters in a model to always have the same value or to be related by an expression The expression is a polynomial function of the other parameters XSPEC will reject attempts to link parameters to themselves Also XSPEC12 allows parameters to be designated in their initialization file to be fixed i e never variable during a fit or to act as swit
66. does introduce some changes in the spectrum from earlier versions For the case of a neutral reflector i e the ionization parameter is zero more accurate opacities are calculated For the case of an ionized reflector the old version assumed that for the purposes of calculating opacities the input spectrum was a power law with index based on the 2 10 keV spectrum The new version uses the actual input spectrum which is usually not a power law giving different opacities for a given ionization parameter and disk temperature The Greens function integration required for the Compton reflection calculation is performed to an accuracy of 0 01 i e 1 This can be changed using e g xset EQPAIR PRECISION 0 05 The parameters for all three models are parl 1 l ratio of the hard to soft compactnesses par2 lbp the soft photon compactness kT pp if gt 0 then temperature of the inner edge of the accretion par3 disk for the diskbb model if lt 0 then abs kTy is the Tmax parameter for the diskpn model lnt In fraction of power supplied to energetic particles which pars goes into accelerating non thermal particles pars Tp the Thomson scattering depth par6 radius the size of the scattering region cm par7 gmin Minimum Lorentz factor of the pairs par8 max Maximum Lorentz factor of the pairs ar9 Ginj if lt 0 then non thermal spectrum is assumed mono P energetic at gmax if gt 0 then a power law from gmin tO Emax pairinj if 0 t
67. dominated by free free absorption i e the so called blackbody disk model Not correct for a disk around a neutron star parl accretion rate in Eddington Luminosities par2 central mass in solar mass units par3 inner disk radius in gravitational 3 Schwarzschild radii norm 2cosi d where i is the inclination of the disk and d is the distance in units of 10 kpc 6 2 25 diskbb accretion disk multi black body components The spectrum from an accretion disk consisting of multiple blackbody components For example see Mitsuda et al PASJ 36 741 1984 Makishima et al ApJ 308 635 1986 parl temperature at inner disk radius keV 194 R km cos where Rin is an apparent inner disk radius D 1 Okpc m PP norm D the distance to the source and the angle of the disk 8 0 is face on On the correction factor between the apparent inner disk radius and the realistic radius see e g Kubota et al 1998 PASJ 50 667 6 2 26 Diskir Irradiated inner and outer disk The inner disk can be irradiated by the Compton tail This can substantially change the inner disk temperature structure from that expected from an unilluminated disk in the limit where the ratio of luminosity in the tail to that in the disk Lc Ld gt gt 1 This is generally the case in the low hard state of accreting black holes and neglecting this effect leads to an underestimate of the inner disk radius Gierlinski Done amp Page 2008a MNRAS
68. energy range This energy range must be within that defined by the current response matrix If a larger energy range is required then the energies command can be given to compute the model over the desired range The lumin command calculates the luminosity for the source redshift given The eqwidth command determines the equivalent width of a model component usually a line The user of either of these last two commands should read the help descriptions carefully The Tcl script addline can be used to automatically add lines to a model These can be identified using identify and modid New model components which can be described by a simple algebraic formula can be set up using mdefine and used in the same way as the standard models except they will run slower being interpreted rather than compiled 19 3 8 1 Models with multiple responses and background models Multiple models and responses can be assigned to a single spectrum This generalizes and replaces the b technique of specifying background models in v11 In the FITS file format a single response file can be associated with a spectrum either through a header keyword or a table column entry XSPEC always assigns this response to a spectrum s source number 1 The model command by default also creates new models for source number The response command in tandem with model can be used to create additional sources For example to add a background model to loaded spectrum 1 first load
69. estimated by CW see e g Wheaton et al 1995 for other possibilities Once a best fit model is obtained one must ask two questions 1 How confident can one be that the observed C I can have been produced by the best fit model f E The answer to this question is known as the goodness of fit of the model The 7 statistic provides a well known goodness of fit criterion for a given number of degrees of freedom v which is calculated as the number of channels minus the number of model parameters and for a given confidence level If Z exceeds a critical value tabulated in many statistics texts one can conclude that f E is not an adequate model for C I As a general rule one wants the reduced 7 7 V to be approximately equal to one X v A reduced 7 that is much greater than one indicates a poor fit while a reduced V that is much less than one indicates that the errors on the data have been over estimated Even if the best fit model f E does pass the goodness of fit test one still cannot say that E is the only acceptable model For example if the data used in the fit are not particularly good one may be able to find many different models for which adequate fits can be found In such a case the choice of the correct model to fit is a matter of scientific judgment 2 Fora given best fit parameter p1 what is the range of values within which one can be confident the true value of the paramet
70. exp n o E 1 z parl nH equivalent hydrogen column in units of 1022 atoms cm 2 par2 z redshift 6 3 33 wndabs zwndabs photo electric absorption warm absorber Photo electric absorption from approximation to a warm absorber using Balucinska Church and McCammon ApJ 400 699 cross sections Relative abundances are set by the abund command 1 E gt Ey M E exp n o E E lt E where o E is the photo electric cross section NOT including Thomson scattering and parl ny equivalent hydrogen column in units of 10 atoms cm par2 Eyw window energy keV 254 The zwndabs variant allows the user to specify a fixed redshift and uses the corresponding formula n o E l EXE ee exp n o z 1 E gt Ew with parameters parl nH equivalent hydrogen column in units of 1022 atoms cm 2 par2 EW window energy keV par3 z redshift 6 3 34 xion reflected spectrum of photo ionized accretion disk ring This model describes the reflected spectra of a photo ionized accretion disk or a ring if one so chooses The approach is similar to the one used for tables with stellar spectra Namely a large number of models are computed for a range of values of the spectral index the incident X ray flux disk gravity the thermal disk flux and iron abundance Each model s output is an un smeared reflected spectrum for 5 different inclination angles ranging from nearly pole on to nearly face on stored in a look up tab
71. files Losum pha the other for the second group hisum pha Here we ll enter the absorption column of the first group as 10 cm and enter the default values for all the other parameters in the first group Now when it comes to the second group of parameters we enter a column of 10 cm and then enter defaults for the other parameters The rule being applied here is as follows to tie parameters in the second group to their equivalents in the first group take the default when entering the second group parameters to allow parameters in the second group to vary independently of their equivalents in the first group enter different values explicitly XSPEC12 gt mo phabs highecut po Input parameter value delta min bot top and max values for Current il 0 001 0 0 1E 05 1E 06 DataGroup 1 phabs nH gt 100 Current 10 0 01 0 0001 0 01 1E 06 1E 06 DataGroup 1 highecut cutoffE gt Current 15 0 01 0 0001 0 01 1E 06 1E 06 DataGroup 1 highecut foldE gt Current 1 0 01 3 2 9 10 DataGroup 1 powerlaw PhoIndex gt Current 1 0 01 0 0 1E 24 1E 24 DataGroup 1 powerlaw norm gt Current 100 0 001 0 0 1E 05 1E 06 DataGroup 2 phabs nH gt 1 Current 10 0 01 0 0001 0 01 1E 06 1E 06 DataGroup 2 highecut cutoffE gt Model phabs lt 1 gt highecut lt 2 gt powerlaw lt 3 gt Source No 1 Active On Model Model Component Parameter Unit Value par comp
72. fixed redshift parameter parl Z equivalent hydrogen column in units of 10 atoms cm redshift tbgrain allows the user to vary the molecular hydrogen column and the grain distribution parameters parl par2 par3 par4 par5 par6 equivalent hydrogen column in units of 10 atoms cm molecular hydrogen column in units of 10 atoms cm grain density in gm cm grain minimum size in um grain maximum size in um power law index of grain sizes tbvarabs additionally allows the user to vary the elemental abundances and the redshift parl equivalent hydrogen column in units of 10 atoms cm 252 par2 parl8 abundance relative to Solar of He C N O Ne Na Mg Al Si S Cl Ar Ca Cr Fe Co Ni parl9 molecular hydrogen column in units of 10 atoms cm par20 grain density in gm cm par21 grain minimum size in um par22 grain maximum size in um par23 power law index of grain sizes par24 grain depletion fractions of He C N O Ne Na Mg Al Si S Cl par41 Ar Ca Cr Fe Co Ni par42 redshift 6 3 30 uvred interstellar extinction Seaton Law A UV reddening using Seaton s law M N R A S 187 75p Valid from 1000 3704A The transmission is set to unity shortward of the Lyman limit This is incorrect physically but does allow the model to be used in combination with an X ray photoelectric absorption model such as phabs parl E B V 6 3 31 varabs zvarabs p
73. for the special case where the script contains the implementation of a new command written in tcl tk See the section on writing custom commands for more details In current tcl versions it compiles the script into bytecode representation for more efficient execution and adds any procedures defined in the script to the set of commands understood by the interpreter It will not work for general scripts containing XSPEC tcl commands for example those produced by XSPEC s save command These should rather be executed using the form Note that only in the second case is there a default filename suffix i e xcm for both the other methods of script execution the filename must be given in full tcl internally switches off the mechanism that expands command abbreviations when scripts are executed If this were not done the user could specify command abbreviations that change the behavior of the tcl command set e g set for the setplot command would redefine tcl s command for setting variables This behavior can be overridden with the statement set tcl_interactive 1 A 277 near the beginning of the script but it is not recommended to do so Instead we strongly recommend spelling out command names in full within XSPEC scripts A 12 Command Echoing By default when XSPEC is executing a script file it echoes each command to the terminal before it is executed This can be controlled using the tcl variable xs_echo_ script whose default
74. freedom when using steppar for two parameters followed by plot contour there are two degrees of freedom This assumption is correct for the S statistic and is asymptotically correct for other statistic choices Monte Carlo A 287 The best but most computationally expensive methods for estimating parameter confidence regions are using two different Monte Carlo techniques The first technique is to start with the best fit model and parameters and simulate datasets with identical properties responses exposure times etc to those observed For each simulation perform a fit and record the best fit parameters The sets of best fit parameters now map out the multi dimensional probability distribution for the parameters assuming that the original best fit parameters are the true ones While this is unlikely to be true the relative distribution should still be accurate so can be used to estimate confidence regions There is no explicit command in XSPEC to use this technique however it is easy to construct scripts to perform the simulations and store the results The second technique is Markov Chain Monte Carlo MCMC and is of much wider applicability In MCMC a chain of sets of parameter values is generated which describe the parameter probability distribution This determines both the best fit the mode and the confidence regions The chain command runs MCMC chains which can be converted to probability distributions using margin which takes th
75. gain shift specified by the lt slope gt and lt intercept gt parameters to the response belonging to spectrum lt specNum gt and optionally specified lt sourceNum gt if the data is analyzed with multiple models The initial default lt specNum gt is 1 later the default is the number of the spectrum last modified Initially all responses are assumed to have nominal gains determined implicitly by the data in the response files This is equivalent to a lt slope gt of 1 and an lt intercept gt of zero All responses can be reset back to this original state by entering gain off Note that in this mode of usage the slope and intercept values do NOT become variable fit parameters They are simply fixed values used to modify the response The gain fit mode is used when the user wishes to have the slope and intercept parameters determined by the results of a fit The lt specNum gt and optional lt sourceNum gt parameters specify to which response the fit gain values are to be applied These may be omitted only if a single spectrum is loaded with a single model source Otherwise at least a spectrum number is required The user will then be prompted for slope and intercept parameter information in the same way as model parameters are normally entered These values are then immediately applied to the response and will be adjusted the next time a fit is run Gain fit parameters belong to the more general category of response parameters in XSPEC
76. in future The PLT plotting package is described briefly in Appendix D and in more detail in the QDP PLT User s Guide Tennant 1989 v12 communicates with the user through the familiar command line interface The input output streams however can in future be easily redirected to communicate with the user through a graphical user interface GUI Finally the design implements a new error handling system can return the program safely to the user prompt when an error occurs and leave the program in a state from which the user can continue working Also for the first time there is now an undo command Integral Spectrometer Coded Mask Instrument Support The INTEGRAL Spectrometer SPT is a coded mask telescope with a 19 element Germanium detector array There are several complications regarding the spectral de convolution of coded aperture data For XSPEC the most obvious problem is the source confusion issue as there may be multiple sources in the FoV leading to different degrees of shadowing on different detectors Thus a separate instrumental response must be applied to a spectral model for each possible source for each detector If there are multiple sources in the FoV then additional spectral models can be applied to an additional set of response matrices enumerated as before over detector and dither pointing This capability to model more than one source at a time in a given minimization procedure did not exist in XSPEC prio
77. is implemented using the tcl unknown procedure part of which is a script file loaded by tcl at run time and may be different or not exist on your system See the section in this help file on the unknown command for more details on how it is implemented in XSPEC Note that the tcl exec command executes the given command directly without first passing it on to the shell Thus no globbing ie expansion of wildcards such pha is performed If you wish to pass you command through a shell for wildcard expansion etc use the syscall command If you want to start a subshell from within XSPEC simple type the command for starting that shell ie type XSPEC12 gt csh A 278 in order to start a C shell Note that typing XSPEC12 gt exec csh will not work properly Giving the XSPEC12 gt syscall command with no arguments will start a subshell using your current shell csh tesh bash sh etc A 15 Writing Custom XSPEC commands XSPEC commands can be written by users as tcl procedures which have similarities with fortran subroutines Within XSPEC tcl procedures can take arguments and execute XSPEC and tcl commands The syntax for specifying arguments to a tcl procedure is as follows proc my proc argl arg2 data 1 1 argl _s0 20 data 2 2 arg2 sl 20 Here argl arg2 are values supplied by the user here part of a filename from the command line and substituted wherever arg1 arg2 appear within the script
78. le 06 l data group 1 phabs nH gt 1 0 01 0 01 3 2 9 10 2 data group 1 powerlaw PhoIndex gt 1 0 01 0 01 0 0 1le 24 let 24 3 data group 1 powerlaw norm gt Input parameter value delta min bot top and max values for 1 0 001 0 01 0 0 100000 le 06 4 data group 2 phabs nH gt 1 0 01 0 01 3 2 9 10 5 data group 2 powerlaw PhoIndex gt 1 0 01 0 01 0 0 le 24 let 24 6 data group 2 powerlaw norm gt 0 0 50 Note that we have fixed the normalization of the source model for the background dataset at zero so it doesn t contribute Now we need to set up the background model for both datasets with its own response matrix XSPEC12 gt response 2 1 back rsp 2 2 back rsp This tells XSPEC that both these datasets have a second model which must be multiplied by the back rsp response matrix We now define the background model to be used In this case take the simple example of a single power law XSPEC12 gt model 2 myback pow Input parameter value delta min bot top and max values for 1 0 01 0 01 3 2 9 10 l myback data group 1 powerlaw PhoIndex gt J 0 01 0 01 0 0 1le 24 let 24 2 myback data group 1 powerlaw norm gt Input parameter value delta min bot top and max values for 1 0 01 0 01 9 2 9 10 3 myback data group 2 powerlaw PhoIndex gt 1 0 01 0 01 0 0 1le 24 let 24 4 myback data group 2 powerlaw norm gt We have now set up XSPEC so that the source
79. lt n gt none indicates that no background subtraction is to be performed for that spectrum If a file is not found or cannot be opened for input then the user is prompted for a replacement background file an lt EOF gt at this point is equivalent to backgrnd lt spectrum number gt none The current ignore status for channels is not affected by the bkgrnd command See the ignore and notice commands Finally any grouping specification will be overridden by the grouping in the source spectral file so that the source and background are binned in the same way The format of the background file must match that of the spectrum file for this purpose OGIP Type I and II are considered to be the same format For details of how to remove spectra see the data command documentation Examples Suppose there are currently three spectra Then XSPEC12 gt backgrnd a b c New files for background subtraction are given for all three spectra XSPEC12 gt backgrnd 2 none No background subtraction will be done for the second spectrum XSPEC12 gt backgrnd d a pha becomes the background for the second spectrum XSPEC12 gt backgrnd 2 e 4 5 Rows 4 and 5 of Type II file e pha become the background for the second and third spectrum respectively 5 4 3 corfile change the correction file for a given spectrum Reset the files used for background correction Syntax corfile lt filespec gt where lt filesp
80. models perform transformations on the available spectra The spectra must be assigned to more than one data group in order have any effect Each data group is a region of the observation and the mixing transformation allows the model flux from one such region to influence another region Thus these models unlike all the others can be two dimensional in effect It follows they that differ from all the other models in that the data must be read before the model can be defined In most cases also the input data must contain additional information in order to use the model This additional information can be in the form of the OGIP standard XFLT keys which allow a set currently up to 10 of scalar real values or in some cases additional files to be read containing spatial information XSPEC12 will return error messages if the data are not loaded not compatible with the model i e do not contain the required additional information loaded inconsistently with the use of the model the division of data into regions is incorrect or data within a given region fail consistency checks It will also return error messages if the data are subsequently changed to a set that violates these consistency checks and additionally remove the model definition 6 6 1 ascac ASCA surface brightness model Mixing model for ASCA data Written for cluster data so uses beta or two power law surface brightness models Includes a calculation of the te
81. ne C C C style c_modelfunc const Real energy Energy array size Nflux 1 int Nflux Size of flux array const Real parameter Parameter values int spectrum Spectrum number of model component being calculated Real flux Output flux array Real fluxError Output flux error array optional const char init Initialization string see below C C style C_modelfunc const RealArray amp energy Energy array const RealArray amp parameter Parameter values int spectrum Spectrum number of model component being calculated RealArray amp flux Output flux array RealArray amp fluxError Output flux error array optional const string amp init Initialization string see below For example a model component in double precision fortran is specified by A 294 modelentry 57 Os 1 e20 F_modelfunc add 0 XSPEC then picks out the right function definition and calls the function modelfunc which expects double precision arguments The C style call can clearly be compiled and implemented by either a C or a C compiler however we recommend using the C call if the model is written in C as it will reduce overhead in copying C arrays in and out the XSPEC internal data structures To prevent unresolved symbol linkage errors we also recommend prefacing C local model function definitions with the extern C direct
82. node display screen xw XSERVE An XWINDOW window that persists for re use Examples XSPEC12 gt setplot device xt sets the device to the xterm XSPEC12 gt setplot device none closes the plot file energy Change the X axis on plots to energies and optionally change the units setplot energy lt units gt where lt units gt 1s an optional string for modifying X axis energy units Valid choices currently are keV MeV Gev and Hz which are case insensitive and can be abbreviated Energy units initially default to kev The selection made here also determines the units in ignore notice energy range specifiers Where applicable Y axis units will be modified to match the X axis selection The exception is for the choice of Hz when emodel eufspec is in Jy and eemodel eeufspec in ergs cm 2 s group Define a range of spectra to be in the same group for plotting purposes only setplot group lt spectrum range gt where lt spectrum range gt is a range of contiguous spectra to be treated as a single spectrum for plotting purposes The spectra still are fit individually If multiple ranges are given each range becomes a single group Initially all spectra read in are treated as single spectra See also ungroup Examples Assume that there are five spectra currently read in all of them ungrouped initially XSPEC12 gt setplot group 1 4 The first four spectra are treated as one group with the fifth spect
83. of the statistic and the dotted line marks that for the observed data There is no reason to reject the model Now that we think we have the correct model we need to determine how well the parameters are determined The screen output at the end of the fit shows the best fitting parameter values as well as approximations to their errors These errors should be regarded as indications of the uncertainties in the parameters and should not be quoted in publications The true errors i e the confidence ranges are obtained using the error command We want to run error on all three parameters which is an intrinsically parallel operation so we can use XSPEC s support for multiple cores and run the error estimations in parallel XSPEC12 gt parallel error 3 XSPEC12 gt error 1 2 3 Parameter Confidence Range 2 706 1 0 107599 1 00722 0 430244 0 469381 2 20 03 T75 2 44916 0 198717 0 2127 3 0 00954178 0 0181617 0 00349017 0 00512978 Here the numbers 1 2 3 refer to the parameter numbers in the Model par column of the output at the end of the fit For the first parameter the column of absorbing hydrogen atoms the 90 confidence range is 3 3x10 lt N lt 9 3x107 cm_ This corresponds to an excursion in 7 of 2 706 The reason these better errors are not given automatically as part of the fit output is that they entail further fitting When the model is simple this does not require much CPU but for complicated mode
84. only gt 0 and both up and down scattering lt 0 6 4 13 Zashift Redshift an additive model This convolution model redshifts an additive model It takes the calculated model and shifts energies by 1 1 z then applies an additional 1 1 z factor to the model values The energies command must be to used to extend the maximum energy over which the model is being calculated to 1 z times the maximum energy in the response 266 The parameter is parl Redshift An example model use is XSPEC gt model phabs zashift pow ga which redshifts the power law and gaussian then multiplies by local absorption 6 4 14 Zmshift Redshift a multiplicative model This convolution model redshifts a multiplicative model It takes the calculated model and shifts energies by 1 1 z The energies command must be to used to extend the maximum energy over which the model is being calculated to 1 z times the maximum energy in the response The parameter is parl Redshift An example model use is XSPEC gt model phabs zmshift phabs pow which multiplies the power law by both a redshifted and local absorption 6 5 Pile Up Model Components 6 5 1 pileup CCD pile up model for Chandra CCD pile up model used for brightish point sources observed by Chandra This is an implementation of the fast pile up algorithm proposed by John Davis see http space mit edu davis papers pileup2001 pdf The frame time and maximum numbe
85. or steppar command calculations Examples XSPEC12 gt model cflow Using a model with 5 variable fit parameters XSPEC12 gt parallel leven 4 XSPEC12 gt fit Calculations for the 5 parameters will be divided amongst 4 processes during the fit XSPEC12 gt parallel leven 1 Restores single process calculation to the A Levenberg Marquardt algorithm XSPEC12 gt parallel error 3 Allow up to 3 simultaneous error parameter calculations to be performed in parallel 76 XSPEC12 gt error 2 3 6 Perform error calculations on parameters 2 3 and 6 in parallel XSPEC12 gt parallel steppar 4 The following 20x30 steppar grid will be split amongst 4 parallel processes XSPEC12 gt steppar 110 11 20 2 5 8 30 Display current settings XSPEC12 gt parallel Maximum number of parallel processes error 3 leven 1 steppar 4 5 3 7 query set a default answer for prompts in scripts Switch on off the continue fitting questions Syntax query lt option gt where lt option gt is yes no or on If on then the continue fitting question in fit steppar and error will be asked when the number of trials is exceeded Also when the number of trials to find the error is exceeded a question will be asked For either of the other two options the questions will not be asked but the answer will be assumed to be yes or no depending on the value set To ensure that fitting conti
86. parameters The setplot delete option has been enhanced to allow removal of all or a range of commands For external programs calling XSPEC new wrapper functions have been added for retrieving XFLT keywords from data files Norm parameters are now set with a default soft upper limit below their hard upper limit In PyXspec the Fit statMethod and statTest attributes can now be set for individual spectra Enhancements previously released as patches to 12 8 0 AtomDB has been upgraded to version 2 0 2 The tclout stat and statmethod options can now retrieve the test statistic as well as the fit statistic The simftest Tcl script command now takes an optional filename argument for output Attributes added to PyXspec classes Xset parallel Fit statTest All bug fixes to v12 8 0 released as patches are included in v12 8 1 In addition the following problems have been corrected The command history file xspec hty in the user s xspec directory is now updated when exiting XSPEC with the quit command Previously it was only updated when exiting with exit The chain command can now read write files in ASCII format when running in the default Goodman Weare mode Previously this feature was only available for Metropolis Hastings chains Fix to an array access error in the nthcomp model PyXspec fix removes error messages generated when accessing response parameters in Python versions 2 6 x 1 2 Howto find out more i
87. produce an internal Sum Component These Sum Components from each such component group are then added to produce the output model note that if there is an overall component for example a convolution or mixing component then all of the model will be contained inside one Component Group The syntax rules that are checked for are as follows 66399 Expression must not begin with a A must be preceded and followed by words or a brace redundant braces are removed A standalone component must be additive A standalone component is defined as a single component model or a single component at the beginning end of the expression followed preceded by a or in the middle of the expression delimited by 2 signs A convolution component must not appear at the end or followed by a closing brace A mixing model component must appear first in the expression and apply to all components thus a model including a mixing component always has one Component Group When using convolution components the order in which they are applied is in general significant For example the two models C M A A and M Ci AtA are not necessarily equivalent here the C s represent convolution models The way XSPEC handles the ordering of components is by first computing the spectrum for the additive components of a given additive group A1 A2 in the above example It then applies all multiplicative or convolution component
88. prompt The character is used in tcl for continuing a command onto the next line Additionally note that in tcl commands and their arguments are delimited by white space They are terminated by a newline or semicolon unless there is an open set of parentheses constituting a loop or test structure In other words in tcl the following starts a loop while condition but A 273 while condition is incorrect since in the latter case the while command terminates at the end of the first line A 4 Command Recall Editing The XSPEC tcl interface also uses gnu readline for command input which allows command line editing and interactive command recall On most systems the left and right arrow keys and the backspace delete key can be used to navigate and edit the command line The up and down arrow keys can be used to step thru the command history list Gnu readline is highly customizable and many more editing recall functions are available Readline documentation can be generated in either postscript or html format from the files in the xanadu readline doc directory distributed with the source The default implementation of tcl also supports a C shell like command recall mechanism The history command gives a numbered list of the most recently entered commands Any command in the list can be re executed by entering n where n is the number of the command in the history list The previous command can be
89. prompt the user for which component he wants deleted XSPEC12 gt mo wabs potga XSPEC12 gt ed wabs potzg The component gauss will be replaced by the component zgauss and the user will be prompted for parameter values for the new component 5 6 6 energies specify new energy binning for model fluxes Supply an energy binning array to be used in model evaluations in place of their associated response energies The calculated model spectra are then interpolated onto the response energy arrays before multiplying by the response matrix This command replaces and enhances the extend command from earlier versions Syntax energies lt range specifier gt lt additional range specifiers gt 121 energies lt input ascii file gt energies extend lt extension specifier gt energies reset where the first lt range specifier gt lt low E gt lt high E gt lt nBins gt log lin lt additional range specifiers gt lt high E gt lt nBins gt log lin lt extension specifier gt low high lt energy gt lt nBins gt log lin All energies are in keV Multiple ranges may be specified to allow for varied binning in different segments of the array but note that no gaps are allowed in the overall array Therefore only the first range specifier accepts a lt low E gt parameter Additional ranges will automatically begin at the lt high E gt value of the previous range
90. re executed by entering The most recent command that begins with a string can be re executed by entering prefix where prefix is the string the command begins with Note that command recall is implemented using the tcl unknown procedure part of which is a script file loaded by tcl at run time See the section on the unknown command for more details on how it is implemented in XSPEC A 5 Logging The log command can be used to open a log file to which all input and and output to tcl will be written Reading these log files can potentially be confusing when logging tcl flow control commands such as while or for This is because tcl treats the body of these commands as an argument of the command Thus when the command is echoed to the log file the entire body of the command is echoed with it In order to make this situation less confusing before commands are echoed to the command file all newline characters are replaced by semicolons and the resulting command line is trucated to 80 characters Then any commands executed with in the body of a flow control command are echoed as they are executed Consider the following sequence of tcl commands within XSPEC XSPEC12 gt log Logging to file xspec log XSPEC12 gt set i 1 set product 1 1 XSPEC12 gt while i lt 5 XSPEC12 gt set product expr Sproduct i XSPEC12 gt incr i XSPEC12 gt XSPEC12 gt set product A 274 120 XSPEC12 gt This would pr
91. represent sources of emission 6 2 1 apec vapec vvapec APEC emission spectrum An emission spectrum from collisionally ionized diffuse gas calculated using the ATOMDB code v2 0 2 More information can be found at http atomdb org which should be consulted by anyone running this model This default version number can be changed by modifiying the ATOMDB VERSION string in your Xspec init file By default this model reads atomic physics continuum and line data from the files apec_v version coco fits and apec_v version _line fits in the HEADAS spectral modelData directory Different files can be specified by using the command xset APECROOT There are three options APECROOT can be set to a version number eg 1 10 1 2 0 1 3 1 2 0 1 In this case the value of APECROOT will be used to replace 2 0 2 in the name of the standard files and the resulting files will be assumed to be in the modelData directory Alternatively a filename root eg apec_vl 2 0 can be given This root will be used as a prefix for the _coco fits and _line fits files Finally if neither of these work then the model will assume that the APECROOT value gives the complete directory path e g XSPEC12 gt xset APECROOT foo bar apec v1 2 0 will use the input files ce foo bar apec_v1 2 0_coco fits foo bar apec_ v1 2 0 line fits Thermal broadening of lines can be included by using xset APECTHERMAL yes This runs significantly slower
92. resolved Responses which abstractly represent a mapping from the theoretical energy space of the model to the detector channel space may be represented in new ways For example the INTEGRAL SPI responses are implemented as a linear superposition of 3 fixed components Instead of explicitly combining responses and models through convolution XSPEC places no prior constraint on how this combination is implemented For example analysis of data collected by future large detectors might take advantage of the form of the instrumental response by decomposing the response into components of different frequency Other differences of approach are in the selection of the statistic of the techniques used for deriving the solution Statistics and fitting methods may be added to XSPEC at execution time rather than at installation time so that the analysis package as a whole may more easily keep apace of new techniques 2 5 XSPEC Data Analysis XSPEC is designed to support multiple input data formats Support for the earlier SF and Einstein FITS formats are removed Support for ASCII data is planned which will allow XSPEC to analyze spectra from other wavelength regions optical radio transparently to the user 2 5 1 OGIP Data The OGIP data format both for single spectrum files Type I and multiple spectrum files Type II is fully supported These files can be created and manipulated with programs described in Appendix E and the provided links
93. source 2 of spectrum 1 XSPEC12 gt rmodel 2 1 gain which is equivalent to XSPEC12 gt gain fit 2 1 The nofit argument switches off the fitting and leaves the gain at the current values of the parameters Unless the argument all is given it is applied to a single response specified by lt specNum gt and optional lt sourceNum gt As with gain fit both arguments may be omitted if only a single spectrum with 1 source is loaded When all is specified fitting is switched off for the gain parameters of all responses gain off will switch off fitting for all gain parameters and will reset all of them to their nominal value Whenever a new response file is defined for a spectrum the response will return to the nofit state with nominal value The ignore and notice commands however will not affect the current gain of the response THE GAIN COMMAND IS NOT CURRENTLY IMPLEMENTED FOR DUMMY RESPONSES Examples XSPEC12 gt gain 1 0 98 The response belonging to spectrum is adjusted with a slope of 0 98 The 1 may be omitted if only 1 spectrum with 1 source is loaded XSPEC12 gt gain 1 03 The offset also is moved now by 0 03 keV XSPEC12 gt gain 2 4 1 1 0 1 The response belonging to source number 2 spectrum 4 is adjusted with slope 1 1 127 and offset 0 1 keV XSPEC12 gt gain off The above 2 responses and any others that have been adjusted are reset to slope 1 0 offset 0 0 XSPEC12 gt gain fit 3
94. statistic Istat a statistic for Poisson data with assumed known background pstat a statistic for Poisson data with Gaussian background pgstat and the Whittle statistic whittle for power density functions If the statistic is given as whittle with a number appended e g whittle5 then the statistic is appropriate for that number of power density functions averaged together The test statistic options are Anderson Darling ad chi squared chi Cramer von Mises cvm Kolmogorov Smirnov ks Pearson chi square pchi and Runs runs These statistics are described in the appendix on Statistics in XSPEC If a spectrum number or spectrum range is given the chosen statistic will only apply to those spectra It is therefore possible for a multi spectrum fit to use more than one fit or test statistic If no spectrum number or range is given the chosen statistic will apply to all loaded spectra and will be the default statistic for any future loaded spectra Note that if the chosen statistic is not compatible with the currently used weight method the weight method will be changed to standard weighting until the conflict is removed Examples Assume 3 spectra are currently loaded all using the chi squared statistic and that chi squared is the default statistic XSPEC12 gt statistic cstat 2 3 Spectrum 1 continues to use chi sq 2 and 3 use cstat XSPEC Models 157 XSPEC12 gt data 4 spec4 pha New spectrum 4 will use chi s
95. tau 223 Electron temperature for the soft Comptonisation component soft excess in keV Optical depth of the soft Comptonisation component If this parameter is negative then only the soft Compton component is used Spectral index of the hard Comptonisation component power law which has temperature fixed to 100 keV Fraction of the power below rcor which is emitted in the hard comptonisation component If this parameter is negative then only the hard Compton component is used Must be frozen Black hole mass in solar masses Comoving proper distance in Mpc Eddington ratio Dimensionless black hole spin Coronal radius in Ry GM c marking the transition from colour temperature corrected blackbody emission to a Comptonised spectrum If this parameter is negative then only the blackbody component is used Log of the outer radius of the disc in units of R if this is ve the code will use the self gravity radius as calculated from Laor amp Netzer 1989 Electron temperature for the soft Comptonisation component soft excess in keV Optical depth of the soft Comptonisation component If this parameter is negative then only the soft Compton component is used 224 par9 Gamma Spectral index of the hard Comptonisation component power law which has temperature fixed to 100 keV parl0 fpl Fraction of the power below rcor which is emitted in the hard comptonisation component If this parameter is negat
96. then the non stepped parameters are reset to the best fit values at each grid point Alternatively if current is given as an argument then the non stepped parameters are started at their values after the last grid point the default If multiple lt step spec gt are given for different parameters then a raster scan of the parameter ranges is performed At the end of the set the parameters and chi squared are restored to the values they had initially If the model is in a best fit state when a steppar run is started and a new best fit is found during the run the user will be prompted at the end of the run to determine if they wish to accept the new best fit values for their parameters This prompting can be disabled by the setting of the query flag Depending on the machine a steppar run may be sped up significantly by assigning it to multiple processes See the parallel command with the steppar option for more details Examples Assume that the current model has four parameters XSPEC12 gt steppar 3 1 5 2 5 Step parameter 3 from 1 5 to 2 5 in steps of 1 XSPEC12 gt steppar log Repeat the above only use multiplicative steps of 1 0524 XSPEC12 gt step nolog 2 2 2 20 Step parameter 2 linearly from 2 to 2 in steps of 0 02 XSPEC12 gt step 2 delta 0 02 5 Step parameter 2 linearly from the best fit value 0 1 to the best fit value 0 1 in a total of 11 steps 5 5 11 thaw allow fixed parameter
97. then the norm becomes the flux in units of 10 ergs cm s over the energy range POW_EMIN POW_EMAX keV unless POW_EMIN POW_EMAxX lt in which case the norm becomes the flux density in micro Jansky at POW_EMIN keV In these cases it is important that POW _EMIN and POW_EMAX lie within the energy range on which the model is being evaluated 6 2 9 bkn2pow broken power law 2 break energies A three segment broken power law ie with two break energies A E KETI E lt Ebreak 1 179 T T p KES ep 2 Ebreak 1 lt E lt Ebreak 2 rir is KE eai Fiai ev Ns Ebreak 2 lt E where parl power law photon index for E lt Ebpreak 1 par2 Epreak 1 first break point for the energy keV par3 T power law photon index for Ebreak lt E lt Ebreak 2 par4 Epreak 2 second break point for the energy keV par5 1 power law photon index for E gt Epreak2 Norm K photons keV em s at 1 keV If POW_EMIN and POW_EMAX have been defined by the xset command then the norm becomes the flux in units of 10 ergs cm s over the energy range POW_EMIN POW_EMAX keV unless POW_EMIN POW_EMAX in which case the norm becomes the flux density in micro Jansky at POW_EMIN keV In these cases it is important that POW _EMIN and POW_EMAX lie within the energy range on which the model is being evaluated 6 2 10 bmc Comptonization by relativistic matter This is an analytic model describing Comptonization of soft photons b
98. these plots are telling you it is useful to know a couple of points concerning how the software chooses the location of the contour lines The contour plot is drawn based only on the information contained in the sample grid For example if the minimum fit statistic occurs when parameter 1 equal 2 25 and you use steppar 1 1 05 0 4 then the grid values closest to the minimum are 2 0 and 3 0 This could mean that there are no grid points where delta fit statistic is less than your lowest level which defaults to 1 0 As a result the lowest contour will not be drawn This effect can be minimized by always selecting a steppar range that causes XSPEC to step very close to the true minima For the above example using steppar 1 1 25 5 25 4 would have been a better selection The location of a contour line between grid points is designated using a linear interpolation Since the fit statistic surface is often quadratic a linear interpolation will result in the lines being drawn inside the true location of the contour The combination of this and the previous effect sometimes will result in the minimum found by the fit command lying outside the region enclosed by the lowest contour level Examples XSPEC12 gt steppar 20 5 1 431 2 4 create a grid for parameters 2 and 3 XSPEC12 gt plot contour Plot out a grid with three contours with delta fit statistic of 2 3 4 61 and 9 21 XSPEC12 gt plot cont 4 1 2 3 4 61 9 21 same as above but wit
99. to the black hole in units of kpc par7 spectral hardening factor T_col T_eff It should be greater than 1 0 and considered to be 1 5 1 9 for accretion disks around a stellar mass black hole See e g Shimura and Takahara 1995 ApJ 445 780 par8 a flag to switch on off the effect of self irradiation never allowed to be free Self irradiation is included when gt 0 Self irradiation is not included when lt 0 par9 a flag to switch on off the effect of limb darkening never allowed to be free The disk emission is assumed to be limb darkened when gt 0 The disk emission is assumed to be isotropic when Iflag is lt 0 K normalization Should be set to 1 if the inclination mass and distance are frozen kerrd optically thick accretion disk around a Kerr black hole Optically thick extreme Kerr disk model based on the same tranfer function used in the laor Kerr disk line model Local emission is simply assumed to be the diluted blackbody See Laor 1991 ApJ 376 L90 for explanation of the transfer function See Ebisawa et al 2003 ApJ examples of using this model parl distance kpc par2 spectral hardening factor Tcol Teff Should be greater than 1 0 and considered to be 1 5 1 9 207 for accretion disks around a stellar mass black hole See e g Shimura and Takahara 1995 ApJ 445 780 par3 mass of the central object solar unit par4 mass accretion rate le18 g s pars disk incl
100. unknown command for more details on how it is implemented in XSPEC N B tcl explicitly switches off command completion for scripts Because of the way scripts are implemented in XSPEC however command abbreviations nevertheless do work in scripts entered with the command but not when entered from the command line or using the source command See below for more details about tcl scripting A 7 Unknown Procedure A 275 tcl provides a facility whereby if it cannot match an entered command to its list of known commands it calls the unknown procedure with the unmatched command along with its arguments as its argument The version of init tc1 distributed with tcl contains a version of the unknown procedure When tcl initializes it looks in several standard places for a script file named init tcl which it executes if found The unknown procedure is where tcl does command completion and automatic shell command execution At start up time XSPEC loads its own unknown procedure which it uses to intercept script processing requests of the form XSPEC12 gt lt script gt and renames the previously defined unknown procedure to tclunknown If XSPEC is not doing any special processing it simply passes any unmatched commands on to tclunknown which then processes them as usual XSPEC has its own special version of the unknown procedure These factors need to be taken into consideration for programmers writing tcl scripts for use within
101. 0 6 2 41 6 2 42 6 2 43 6 2 44 6 2 45 6 2 46 6 2 47 6 2 48 6 2 49 6 2 50 6 2 51 6 2 52 6 2 53 6 2 54 6 2 55 6 2 56 6 2 57 6 2 58 6 2 59 vi cplinear a non physical piecewise linear model for low count background spectra ssssssssssssennnnnnnunnnnnnnnnnnunnnnnnnnnnnnnnnnnn nnnm nnna 191 cutoffpl power law high energy exponential cutoff eseee 193 disk accretion disk black body cccccececeeeeeeeeeeeeeeeeeneeneeeeeeneneeens 193 diskbb accretion disk multi black body components 000 193 Diskir Irradiated inner and outer GISK cccescceeeeeeeeeeeeeeeeeeeeeeeeeeeees 194 diskline accretion disk line emission relativistic 0000 195 diskm accretion disk with gas pressure VISCOSItY eeeee 195 disko accretion disk inner radiation pressure viscosity 195 diskpbb accretion disk power law dependence for T r 000 196 diskpn accretion disk black hole black body cccssssseeeeeeeereeees 196 eplogpar log parabolic blazar model with vFv normalization 197 Eqpair eqtherm compth Paolo Coppi s hybrid thermal non thermal hot plasma emission Models c eeseeeeeeeeeeneeeeeeeeeeeeeeees 197 equil vequil collisional plasma ionization equilibrium 199 expdec exponential CeCay eseseceeeeenssseeeseeeeeeeeensnseneneceeeeeees 200 ezdiskbb multiple blackbody disk
102. 0 95 using 1024 PHA bins Reduced chi squared 0 34407 for 1020 degrees of freedom Null hypothesis probability 1 000000e 00 x Warning Chi square may not be valid due to bins with zero variance in spectrum number s 1 Current data and model not fit yet The first thing we should note is that the default statistics are not correct for these data For Poisson data and no background we should cstat for the fit statistic and pchi for the test statistic XSPEC12 gt statistic cstat Default fit statistic is set to C Statistic This will apply to all current and newly loaded spectra Fit statistic C Statistic 513 63 using 1024 PHA bins and 1020 degrees of freedom Test statistic Chi Squared 350 95 using 1024 PHA bins Reduced chi squared 0 34407 for 1020 degrees of freedom Null hypothesis probability 1 000000e 00 x Warning Chi square may not be valid due to bins with zero variance in spectrum number s 1 Current data and model not fit yet XSPEC12 gt statistic test pchi Default test statistic is set to Pearson Chi Squared This will apply to all current and newly loaded spectra Fit statistic C Statistic 513 63 using 1024 PHA bins and 1020 degrees of freedom Test statistic Pearson Chi Squared 639 35 using 1024 PHA bins 54 Reduced chi squared 0 62682 for 1020 degrees of freedom Null hypothesis probability 1 000000e 00 xx Warning Pearson Chi square may not be valid due to bins wi
103. 03e 01 Assigned to Data Group No 1 Assigned to Plot Group No 19 XSPEC12 gt mo l crab po Input parameter value delta min bot top and max values for 1 PhoIndex 1 0000E 00 1 0000E 02 3 0000E 00 2 0000E 00 9 0000E 00 1 0000E 01 crab powerlaw PhoIndex gt 2 11 0 01 1 5 1 6 2 5 2 6 2 norm 1 0000E 00 1 0000E 02 0 0000E 00 0 0000E 00 1 0000E 24 1 0000E 24 crab powerlaw norm gt 8 0 11 2 18 20 XSPEC12 gt mo 2 bkg spibkg5 Input parameter value delta min bot top and max values for 1 Par 1 0 0000E 00 1 0000E 02 2 0000E 01 1 5000E 01 1 5000E 01 2 0000E 01 bkg spibkg5 Par_1 gt XSPEC12 gt ign 1 19 68 80 XSPEC12 gt ign 1 19 90 100 XSPEC12 gt fit Number of trials and critical delta 10 1 0000000 E 02 61 Model bkg spibkg5 Source No 2 Active On Model Component Name spibkg5 Number 1 N Name Unit Value Sigma 1 Par 1 9 0650E 03 2 8651E 03 2 Par 2 1 6174E 02 3 4778E 03 25 Par 25 1 9537E 02 6 1429E 03 26 norm 9 7286E 01 1 3527E 03 Model crab powerlaw Source No 1 Active On Model Component Name powerlaw Number 1 N Name Unit Value Sigma 1 PhoIndex 2 1163E 00 1 8946E 02 2 norm 1 1390E 01 8 1414E O01 Chi Squared 1 8993005E 03 using 1463 PHA bins Reduced chi squared 1 3235544E 00 for 1435 degrees of freedom Null hypothesis probability 1 5268098E 15 XSPEC12 gt Note that the syntax used for the data statement a
104. 06 using 66 PHA bins Test statistic Chi Squared 2 062941e 06 using 66 PHA bins Reduced chi squared 34965 10 for 59 degrees of freedom Null hypothesis probability 0 000000e 00 Current data and model not fit yet XSPEC12 gt fit Model phabs lt 1 gt highecut lt 2 gt powerlaw lt 3 gt Source No 1 Active On Model Model Component Parameter Unit Value par comp Data group 1 1 1 phabs nH 10 22 2052531 0 181904 2 2 highecut cutoffE keV 14 6846 5 59251E 02 E 2 highecut foldE keV 7 41660 8 99545E 02 4 3 powerlaw PhoIndex 1 18690 6 33054E 03 5 3 powerlaw norm 5 88294E 02 9 30380E 04 Data group 2 6 1 phabs nH LO 22 1 27002 3 77708E 02 7 2 highecut cutoffE keV 14 6846 2 8 2 highecut foldE keV 7 41660 3 9 3 powerlaw PhoIndex 1 18690 4 10 3 powerlaw norm 0 312117 4 49061E 03 Fit statistic Chi Squared 15423 79 using 66 PHA bins After fitting this decoupling reduces y by a factor of six to 15 478 but this is still too high Indeed this simple attempt to account for the spectral variability in terms of blanket cold absorption and scattering does not work More sophisticated models involving additional components and partial absorption should be tried 49 4 4 Multiple Models a Background Modeling Example In the previous section we showed how to fit the same model to multiple datasets We now demonstrate how to fit multiple models each with their own respo
105. 12 gt newpar 6 1 XSPEC12 gt newpar 7 2 XSPEC12 gt newpar 11 1 And so on Examples The total number of model parameters for the example is four Ea XSPEC12 gt newpar 2 0 1 The value of the second parameter is set to 0 1 C12 gt newpar 3 4 The program will prompt for a specification for the 3 parameter comp gives the name of the corresponding model component comp param3 gt 0 001 0 which has its value set to 0 001 and its delta set to zero fixing it in later fits The program now prompts for a specification for the 4th parameter comp param4 gt 21 which is set to 21 As there is no 5 parameter the program displays a summary and returns to command level XSPEC12 gt newpar 001 The value of the delta of the 3rd parameter which is the default index as it was the first parameter modified in the previous newpar invocation is set to 0 001 allowing it to be adjusted during any fits Cy XSPI The total number of parameters for this example is eight XSPEC12 gt newpar 4 1 The value of parameter 4 is set to the value of parameter 1 This has the consequence of model parameter 4 being frozen at the value of parameter 1 during subsequent fitting procedures If model parameter 1 is a free parameter then both parameters 1 and 4 change their values simultaneously in the fit procedure C12 gt newpar 4 3 5 6 7 The value of parameter 4 is se
106. 388 753 The irradiated inner disk and Compton tail can illuminate the rest of the disk and a fraction f_out of the bolometric flux is thermalized to the local blackbody temperature at each radius This reprocessed flux generally dominates the optical and UV bandpass of LMXBs Gierlinski Done amp Page 2008b MNRAS submitted parl kT disk innermost temperature of the UNILLUMINATED disk par2 Gamma asymptotic power law photon index par3 kT e electon temperature high energy rollover par4 Lc Ld ratio of luminosity in the Compton tail to that of the UNILLUMINATED disk pars fin fraction of luminosity in the Compton tail which is thermalized in the inner disk generally fix at 0 1 as appropriate for an albedo of 0 3 and solid angle of 0 3 par6 rirr radius of the Compton illuminated disk in terms of the inner disk radius par7 fout fraction of bolometric flux which is thermalized in the outer disk par8 logrout log10 of the outer disk radius in terms of the inner disk radius K normalization as in diskbb 195 6 2 27 diskline accretion disk line emission relativistic A line emission from a relativistic accretion disk See Fabian et al MNRAS 238 729 Setting par2 to 10 is the special case of the accretion disk emissivity law 1 Vo7R R parl line energy power law dependence of emissivity If this parameter is 10 or 1 V6 R R pee greater then the accretion disk emissivity law is used Otherwise
107. 4 6 3 35 zbabs EUV ISM attenuation ccccccccsssseesseeeeeeeseeeeeeeseeneeeeeeeeeeneens 256 6 3 36 zdust extinction by dust grains ccccssseeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeenens 256 6 3 37 zigm UV Optical attenuation by the intergalactic medium 256 6 3 38 zredden redshifted version Of redden s eeeceeseseeeseeeeeeeeeeeeeneees 257 6 3 39 zsmdust extinction by dust grains in starburst galaxies 257 6 3 40 zvfeabs photoelectric absorption with free Fe edge energy 258 6 3 41 zxipcf partial covering absorption by partially ionized material 258 6 4 Convolution Model Components sseseseeeeeeeeeeeeeeees 258 6 4 1 cflux calculate fIUX 0 c eseeeeeeeeeeeeeeeeeneeeeeeeseeeseeesneeeneeeseeeseenseeess 259 6 4 2 cpflux calculate photon fIUX cece eeseeeeeeeeeeeeeeeeeeeseeneeeeeeeeeenness 260 6 4 3 gsmooth GAUSSIAN SMOOTHING ceeceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeneees 260 6 4 4 ireflect reflection from ionized material 2 sseeeeeeeeeeeeeeees 261 6 4 5 kdblur convolve with the laor model Shape cceeeeeeeeeeeeeeeeees 262 6 4 6 kdblur2 convolve with the laor2 model shape sseceeeeeeeees 262 6 4 7 kerrconv accretion disk line shape with BH spin as free parameter 263 6 4 8 Ismooth lorentzian smoothing cceccccessseeeeeeeee eee eeeeeeeeeeeeeeeeeeeeennenes 263 6 4 9 partcov parti
108. 442 XSPEC12 gt untie bkg 468 XSPEC12 gt untie bkg 487 Note that use of the bkg identifier which associates the parameters index with the background model The specific sequence of numbers use here requires some explanation the particular background model employed has 25 parameters which simply correspond in rank order to the 25 most variable individual bins and a normalization term i e parameter 26 Thus the normalization for the second detector group is parameter 52 for the third parameter 78 and so on Similar command sequences can be used to untie additional background model parameters Supposing that we did this and refitted the data We then might for example wish to go back and freeze the individual normalization terms with the freeze command XSPEC12 gt freeze bkg 26 XSPEC12 gt freeze bkg 52 XSPEC12 gt freeze bkg 487 By now though you probably get the idea that this all requires an unreasonable amount of command line input To circumvent this problem a number of INTEGRAL SPI specific tcl scripts are available which greatly streamline this process 4 7 2 INTEGRAL Specific Command Line Scripts SPIdata The SPIdata procedure which when installed can be treated as an XSPEC command greatly facilitates the data initialization step For example the command XSPEC12 gt SPIdata MyData Dir rev0044 crab pha 475 det Y Opens the Crab observation spectral data file reads the 475 spectra into memory grouping
109. 4e 06 74e 06 14e 06 10e 06 14e 06 45e 06 99e 06 Mg 80e 05 98e 05 80e 05 95e 05 80e 05 51e 05 55e 05 Al 95e 06 82e 06 95e 06 12e 06 95e 06 14e 06 88e 06 Si 55e 05 24e 05 55e 05 68e 05 35e 05 86e 05 47e 05 P 82e 07 57e 07 82e 07 82e 07 82e 07 63e 07 88e 07 154 S 1 62e 05 1 32e 05 1 62e 05 89e 05 14e 05 23e 05 1 55e 05 Cl 1 88e 07 3 16e 07 1 88e 07 93e 07 16e 07 32e 07 1 82e 07 Ar 3 63e 06 2 51e 06 4 47e 06 82e 06 51e 06 57e 06 3 55e 06 K 1 32e 07 1 07e 07 1 32e 07 39e 07 32e 07 00 1 29e 07 Ca 2 29e 06 2 19e 06 2 29e 06 25e 06 29e 06 58e 06 2 19e 06 Sc 1 26e 09 1 41e 09 1 48e 09 24e 09 48e 09 00 1 17e 09 Ti 9 77e 08 8 91e 08 1 05e 07 82e 08 05e 07 46e 08 8 32e 08 V 1 00e 08 8 51e 09 1 00e 08 08e 08 00e 08 00 1 00e 08 er 4 84e 07 4 37e 07 4 84e 07 93e 07 68e 07 24e 07 4 47e 07 Mn 2 45e 07 2 69e 07 2 45e 07 50e 07 45e 07 19e 07 3 16e 07 Fe 4 68e 05 3 16e 05 3 24e 05 31e 05 16e 05 69e 05 2 95e 05 Co 8 60e 08 9 77e 08 8 60e 08 27e 08 32e 08 32e 08 8 13e 08 Ni 1 78e 06 1 66e 06 1 78e 06 8le 06 78e 06 12e 06 1 66e 06 Cu 1 62e 08 1 55e 08 1 62e 08 89e 08 62e 08 00 1 82e 08 Zan 3 98e 08 3 63e 08 3 98e 08 63e 08 98e 08 00 4 27e 08 5 8 2 cosmo set the cosmology Set the cosmology used i e lt H gt lt qy gt and lt A gt Sy
110. 73 3 2 powerlaw norm 1 59131E 02 3 94947E 03 4 3 gaussian LineE kev 6 40000 frozen 5 3 gaussian Sigma kev 0 100000 frozen 6 3 gaussian norm 7 47368E 05 4 74253E 05 The energy and width have to be frozen because in the absence of an obvious line in the data the fit would be completely unable to converge on meaningful values Besides our aim is to see how bright a line at 6 4 keV can be and still not ruin the fit To do this we fit first and then use the error command to derive the maximum allowable iron line normalization We then set the normalization at this maximum value with newpar and finally derive the equivalent width using the eqwidth command That is XSPEC12 gt err 6 Parameter Confidence Range 2 706 xx xWarning Parameter pegged at hard limit 0 6 O 0 000151164 7 476e 05 7 64036e 05 XSPEC12 gt new 6 0 000151164 Fit statistic Chi Squared 46 03 using 45 PHA bins Test statistic Chi Squared 46 03 using 45 PHA bins Reduced chi squared 1123 for 41 degrees of freedom Null hypothesis probability 2 717072e 01 Current data and model not fit yet XSPEC12 gt eqwidth 3 Data group number 1 Additive group equiv width for Component 3 0 784168 kev Things to note The true minimum value of the gaussian normalization is less than zero but the error command stopped searching for a Ay of 2 706 when the minimum value hit zero the hard lower limit of the parameter Hard limits can
111. 83 Number of components in model with optional model name Number of model parameters with optional model name Write to Tcl the last calculated model values for the specified spectrum and optional model name Writes a string of blank separated numbers Note that the output is in units of photons cm 2 s bin Total number of channels in spectrum n including ignored channels Range low high of noticed channels for spectrum n The noticed energies for spectrum n When using chi square for fits this will retrieve the reported null hypothesis probability value delta min low high max for model parameter n Energies and strengths of the peak residuals ve and ve for the spectrum n Optional arguments lo hi specify an energy range in which to search Parameter name and unit for parameter n of model with optional name Information on parameter linking for parameter n This is in the form true false T or F for linked not linked followed by the multiplicative factor and additive constants if linked Write a string of blank separated values for the array lt option gt is one of the valid arguments for the plot or iplot commands lt array gt is one of x xerr y yerr or model xerr and yerr output the 1 sigma error bars generated for plots with errors The model array is for the convolved model in data and Idata plots For contour plots this command just dumps the steppar results The command does not wor
112. 988 and xset neivers 2 0 uses the same ionization fractions as 1 1 but uses APED to calculate the resulting spectrum Note that versions 1 x have no emission from Ar The default is version 1 1 The vnei variant allows the user to set the abundance vector 214 For the nei version the parameters are parl par2 par3 par4 norm plasma temperature keV Metal abundances He fixed at cosmic The elements included are C N O Ne Mg Si S Ar Ca Fe Ni Relative abundances are defined by the abund command Ionization timescale in units of s cm redshift z 107 P FENG nydV where D4 is the angular diameter A distance to the source cm and ne ny cm are the electron and hydrogen densities respectively For the vnei variant the parameters are parl par2 par3 par14 parl5 parl6 norm plasma temperature keV H density in cm Abundances for He C N O Ne Mg Si S Ar Ca Fe Ni wrt Solar defined by the abund command Ionization timescale in units of s cm redshift z 1074 4x D 1 z distance to the source cm and ne ny em are the electron and hydrogen densities respectively fron dV Where D1 is the angular diameter 215 6 2 53 npshock vnpshock shocked plasma plane parallel separate ion electron temperatures Plane parallel shock plasma model with separate ion and electron temperatures This model is slow par1 provides a measure of the average energy
113. AR of the original model of Gierlinski amp Done 2004 parl column density 1077 cm par2 log xi where xi L nr par3 sigma Gaussian sigma for velocity smearing v c par4 redshift 6 3 29 tbabs ztbabs tbgrain tovarabs ISM grain absorption The Tuebingen Boulder ISM absorption model This model calculates the cross section for X ray absorption by the ISM as the sum of the cross sections for X ray absorption due to the gas phase ISM the grain phase ISM and the molecules in the ISM In the grain phase ISM the effect of shielding by the grains is accounted for but is extremely small In the molecular contribution to the ISM cross section only molecular hydrogen is considered In the gas phase ISM the cross section is the sum of the 251 photoionization cross sections of the different elements weighted by abundance and taking into account depletion onto grains In addition to the updates to the photoionization cross sections the gas phase cross section differs from previous values as a result of updates to the ISM abundances These updated abundances are available through the abund wi 1m command Details of updates to the photoionization cross sections as well as to abundances can be found in Wilms Allen and McCray 2000 ApJ 542 914 tbabs allows the user to vary just the molecular hydrogen column parl equivalent hydrogen column in units of 10 atoms cm ztbabs is similar but allows the user to set a
114. Adding models to XSPEC ccccccceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeees 290 Appendix D Overview Of PLT ccccceessseeseeeeeeeeeeeeeeeseeeeeneeeeeeees 6 6 297 Appendix E Associated programs cssecccsseseeneeeseeseeneesseeneeneesseneeeees 301 Appendix F Using The XSPEC Models Library In Other Programs 303 Appendix G Adding a Custom Chain Proposal Algorithm 306 Appendix H Changes between v11 and V12 cccssssseeessssseeeeesseeneees 310 Appendix Older Release Notes cssescesssseeeeessseeeeeeeseeeeeeeesseseeeees 313 Updates to the manual Aug 2013 v12 8 1 release New models cpflux heilin lyman zbabs New pstat option for statistics and new option for whittle statistic setplot delete now has additional all and range options fakeit has new nowrite option parallel has new steppar option Updates to tclout command s chain stat and statmethod options The improve command has been removed It is no longer supported by the new Minuit library that is contained within v12 8 1 New ATOMDB VERSION Xspec init setting mentioned in apec and bapec model docs New DGNFLT and DGFILT routines added to Appendix F Updates and revisions to Irt and simftest Tcl script commands Updated the default values for the cosmo command Correction to gamma equat
115. CISION 0 05 The default precision is 0 01 ie 1 parl r first power law photon index par2 Ebreak break energy keV par3 Is second power law photon index par4 Ec the e folding energy in keV if E 0 there is no cutoff 177 par5 relrefl reflection scaling factor 1 for isotropic source above disk par6 redshift z par7 abundance of elements heavier than He relative to the solar abundances par8 iron abundance relative to the above par9 cosine of inclination angle norm photon flux at 1 keV of the cutoff broken power law only no reflection in the observed frame 6 2 7 bexriv reflected e folded broken power law ionized medium Broken power law spectrum multiplied by exponential high energy cutoff exp E E and reflected from ionized material See Magdziarz amp Zdziarski 1995 MNRAS 273 837 for details Ionization and opacities of the reflecting medium is computed as in the absori model The output spectrum is the sum of an e folded broken power law and the reflection component The reflection component lt 0 Note alone can be obtained for r el n lt 0 Then the actual reflection normalization is r el en that you need to change then the limits of n el en lt 0 excluding zero as then the direct component appears If E 0 there is no cutoff in the power law The metal and iron abundances are variable with respect to those set by the command abund The core of this model is a Greens function i
116. CT IFILE1 fact _obsl fits Multiple observations can be fit simultaneously In this case the observations should be read in each datagroup in the same order e g XSPEC12 gt data 1 1 obslregl 1 2 obs2regl 1 3 obs3regl 2 4 obslreg2 2 5 obs2reg2 part Alpha not used if Switch 0 par2 Beta par3 Core arcmin par4 Switch 0 beta model 1 2 power law 6 6 4 xmmpsf xmm surface brightness model Mixing model for XMM data Mixes the spectra between datagroups based on the PSF overlap between selected regions A surface brightness model is required to calculate the mixing and this can be supplied in several ways If XMMPSF IMAGE has been set to some image file using xset then this image will be used for the surface brightness distribution If XMMPSF IMAGE has not been set then either a beta or two power law model is used In this case the model parameters determine the shape of the surface brightness distribution If XMMPSF RA and XMMPSF DEC are set they are used as the center of the distribution They should be specified either in decimal degrees or as hh mm ss s and dd mmiss s If XMMPSF RA and XMMPSF DEC are not set then the centroid of the wmap will be used as the center of the surface brightness distribution The model works by calculating the mixing factors It will recalculate these factors if any of the XMMPSF or any of the model parameters are changed Calculating 270 271 the mixing factors is very slow so should be
117. It is worth emphasizing that goodness of fit testing only allows us to reject a model with a certain level of confidence it never provides us with a probability that this is the correct model Chi square chi The standard goodness of fit test for Gaussian data is y as defined above At the end of a fit XSPEC writes out the reduced y y v where v is the number of degrees of freedom number of data bins number of free parameters A rough rule of thumb is that the reduced x should be approximately one If the reduced x is much greater than one then the observed data are likely not drawn from the model If the reduced x is much A 288 less than one then the Gaussian sigma associated with the data are likely over estimated XSPEC also writes out the null hypothesis probability which is the probability of the observed data being drawn from the model given the value of x andthe number of degrees of freedom Pearson chi square pchi Pearson s original 1900 chi square test was not for Gaussian data but for the case of dividing counts up between cells This corresponds to the case of Poisson data with no background y N BG ee Kolmogorov Smirnov ks There are a number of test statistics based on the empirical distribution function EDF The EDF is the cumulative spectrum Dar and M 2am Zam The EDF can be plotted using plot icounts The best known of these tests is Kolmogorov Smirnov whose s
118. M central mass solar masses D norm 6 2 32 eplogpar log parabolic blazar model with vFv normalization eplogpar is a power law with an index which varies with energy as a log parabola A E 1 Poet E E JE parl Ep The peak energy in vF par2 Curvature term norm K The flux in vF units at energy Ep keV See for instance Tramacere et al 2007 and Tramacere et al 2009 6 2 33 Eqpair eqtherm compth Paolo Coppi s hybrid thermal non thermal hot plasma emission models These models are based on Paolo Coppi s hybrid thermal non thermal hot plasma emission model for X ray binaries The underlying physics and a detailed description of the code are included in the draft paper http www astro yale edu coppi eqpair eqpap4 ps Do not use these models without reading and understanding this paper Simplified models eqtherm and compth are provided for cases where non thermal processes are not important and photon photon pair production can be ignored These should only be used if lbp lt 10 The temperature of the thermal component of the electron distribution and the total electron optical depth for both ionization electrons and electron positron pairs are written out if the chatter level is set to 15 This information is important for checking self consistency 198 In versions 1 10 and above the Compton reflection is done by a call to the ireflct model code and the relativistic blurring by a call to rdblur This
119. Note that the energy values are two separate arguments and are NOT connected by a dash see parameter ranges in the freeze command description The lumin will be calculated for all loaded spectra If no spectra are loaded or none of the loaded spectra have a response the model is evaluated over the energy range determined by its dummy response In XSPEC12 models are automatically assigned default dummy responses 130 when there is no data so the dummyrsp command need not be given If more than 1 model has been loaded whichever model the user has specified to be the active one for a given source is the one used for the lumin calculation The results of a lumin command may be retrieved by the tclout lumin lt n gt command where n is the particular spectrum of interest If lumin was calculated for the case of no loaded spectra the results can be retrieved by tclout lumin with the lt n gt argument omitted The err noerr switch sets whether errors will be estimated on the luminosity The error algorithm is to draw parameter values from the distribution and calculate a luminosity lt number gt of sets of parameter values will be drawn The resulting luminosities are ordered and the central lt level gt percent selected to give the error range You can get the full array of simulated lumin values by calling tclout lumin with the errsims option see telout command The parameter values distribution is assumed to be
120. One may also give an argument a default value so that the command so created may be invoked even without needing to specify the argument proc my proc argl arg2 file2 Note that the parentheses enclosing both arg2 and file2 in this expression distinguish this from the case where 3 arguments are required for my_ proc Once this file is created it needs to be source d once which compiles the script into an internal bytecode representation this is similar to the way Java operates Alternatively one may place it in the user script directory and create an index in that directory after which case it will be found automatically and compiled the first time it is invoked The user script directory is given by the line USER SCRIPT DIRECTORY in the Xspec init file that is copied into HOME xspec when the user starts xspec12 for the first time the supplied default value for this directory is the HOME xspec directory itself After the script is placed there perform the following command sxspecl2 XSPEC12 gt cd lt USER SCRIPT DIRECTORY gt A 279 XSPEC12 gt auto_mkindex XSPEC12 gt exit This will instruct XSPEC to build an index of scripts to be loaded on xspec startup On the next invocation of XSPEC the script will be sourced on startup and will appear in the list of commands XSPEC understands The my proc procedure is then defined such that one may type XSPEC12 gt my_proc eso103 eso104 and t
121. PEC12 unlike XSPEC11 the channels that are ignored are a property of the spectrum and therefore must be reset when the spectrum is replaced by another If the file contains multiple spectra such as an OGIP Type II PHA file then the desired spectrum can be specified by appending ranges to the end of the filename where n is the row number of the spectrum in the file XSPEC12 allows any combination of multiple ranges in the parentheses delimited by commas The wildcard characters and may also be used A on either side of a hyphen indicates either the first or last row in the file based on whether it is to the left or right of the hyphen Ifa is entered on the left or right side of a hyphen it is substituted by the most recently entered left or right value respectively All rows in the file may be selected simply with a single or between the brackets with no hyphen Examples XSPEC12 gt data pha2data 1 3 5 8 14 26 75 In addition to the various specified rows between 1 and 26 also load rows 75 through the end of the file XSPEC12 gt data pha2data Select all rows in the file 91 For files with multiple spectra the data may either specify a header keyword specifying the response auxiliary response background and correction files or these may be string valued columns specifying a different filename per row Consult the http heasarc gsfc nasa gov docs software ftools package documentati
122. PEC12 gt show fit Fit information XSPEC12 gt show model The model specification XSPEC12 gt show noticed Channel ranges noticed for each file XSPEC12 gt show parameters All current parameter values including gain parameters if any XSPEC12 gt show parameters lt par range gt Show subset of all model parameters given by lt par range gt e g show parameters 1 3 5 8 XSPEC12 gt show pha Current data error and model values for each channel XSPEC12 gt show plot Current plot settings from setplot command includes rebinning info XSPEC12 gt show rates Folded model correction rates for each file XSPEC12 gt show response show responses loaded XSPEC12 gt show rparameters All current gain response parameters XSPEC12 gt show rparameters lt par range gt Show subset of all gain response parameters XSPEC12 gt show xsect show description of cross section table 5 3 11 syscall execute a shell command Execute command in a shell Syntax syscall lt shell command gt gt 79 This command executes its arguments by passing them to the users current shell for execution Thus file name globbing i e wildcard expansion are performed on the command before execution This is in contrast to the exec command which executes commands directly without first passing them on to a shell If no arguments are given then the com
123. RKM is the source radius in km 2 Tbb lt 0 K RKM 2 D10 2 cos theta where theta is the inclination angle Thomson optical depth of the cloud is not always good parameter to fit Instead the Compton parameter y 4 tau Theta where Theta Te keV 511 can be used Parameter y is directly related to the spectral index and therefore is much more stable in fitting procedure The fitting can be done taking 6th parameter negative and optical depth then can be obtained via tau y 4 Te 511 The region of parameter space where the numerical method produces reasonable results is constrained as follows 1 Electron temperature Te gt 10 keV 2 Thomson optical depth tau lt 1 5 for slab geometry and tau lt 3 for other geometries In versions 4 0 and above the Compton reflection is done by a call to the ireflct model code and the relativistic blurring by a call to rdblur This does introduce some changes in the spectrum 187 from earlier versions For the case of a neutral reflector i e the ionization parameter is zero more accurate opacities are calculated For the case of an ionized reflector the old version assumed that for the purposes of calculating opacities the input spectrum was a power law with index based on the 2 10 keV spectrum The new version uses the actual input spectrum which is usually not a power law giving different opacities for a given ionization parameter and disk temperature The Greens function int
124. SPEC read the FTOOLS help for that utility carefully your first time You are now ready to run XSPEC a sample session might look like this some repetitive output has been suppressed ole xspec XSPEC version 12 2 1 Build Date Time Wed Nov 2 17 14 21 2005 XSPEC12 gt package require Integral 1 0 1 0 XSPEC12 gt data myDataDir rev0044 crab pha 1 19 19 spectra in use RMF 1 Using Response RMF File resp compl 100x100 rmf RMF 2 Using Response RMF File resp comp2_100x100 rmf RMF 3 Using Response RMF File resp comp3 100x100 rmf Using Multiple Sources For Source 1 Using Auxiliary Response ARF Files resp rev0044 100ch crab cmpl arf resp rev0044 100ch crab cmp2 arf resp rev0044 100ch crab cmp3 arf 60 fits fits fits For Source 2 Using Auxiliary Response ARF Files resp rev0044 100ch_bkg cmpl arf fits resp rev0044 100ch_ bkg cmp2 arf fits resp rev0044 100ch_bkg cmp3 arf fits Source File myDataDir rev0044 crab pha 1 Net count rate cts s for Spectrum No 1 3 7011e 01 1 2119e 01 Assigned to Data Group No 1 Assigned to Plot Group No 1 Source File myDataDir rev0044 crab pha 2 Net count rate cts s for Spectrum No 2 3 7309e 01 1 2167e 01 Assigned to Data Group No 1 Assigned to Plot Group No 2 Source File myDataDir rev0044 crab pha 19 Net count rate cts s for Spectrum No 19 3 6913e 01 1 21
125. SPEC minimization method using the modified Levenberg Marquardt algorithm based on the CURFIT routine from Bevington lt of eval gt is the number of trial vectors before the user is prompted to say whether they want to continue fitting lt crit delta gt is the convergence criterion which is the absolute not fractional difference in fit statistic between successive iterations less than which the fit is determined to have converged lt crit beta gt refers to the beta N value reported during a fit This is the norm of the vector of derivatives of the statistic with respect to the parameters divided by the number of parameters At the best fit this should be zero and so provides another measure of how well the fit is converging When this is set to a positive value it will provide another fit stopping criterion in addition to that of the lt crit delta gt setting Including the string delay as an argument turns on delayed gratification It is turned off by nodelay Delayed gratification modifies the way the damping parameter is set and has been shown in many cases to speed up convergence The default is nodelay lt of eval gt lt crit delta gt lt crit beta gt delay and nodelay may also be set through the fit command This method requires an estimate of the second derivative of the statistic with respect to the parameters By default XSPEC calculates these using an analytic expression which assumes that partial 2 derivati
126. Synchrotron radiation from cut off electron distribution sresc Synchrotron radiation from escape limited electron distribution SSSice Einstein Observatory SSS ice absorption step Step function convolved with gaussian suzpsf Suzaku PSF mixing model swind1 Absorption by partially ionized material with large velocity shear tbabs ztbabs tbgrain tbvarabs uvred varabs zvarabs wabs zwabs wndabs zwndabs xion xmmpsf zashift zbabs zdust zigm zmshift zredden Absorption due to the ISM including molecules and grains UV reddening Photoelectric absorption with variable abundances Photoelectric absorption Morrison amp McCammon Photoelectric absorption with low energy window The reflected spectrum from a photo ionized accretion disk XMM PSF model Redshift an additive model EUV ISM attenuation Extinction by dust grains Pei 1992 UV Optical attenuation by the intergalactic medium Redshift a multiplicative model Redshifted IR optical UV extinction from Cardelli et al 1989 170 Model Description zsmdust Extinction by dust grains in starburst galaxies zvfeabs Redshifted absorption with variable iron abundance zxipef Partial covering absorption by partially ionized material 6 2 Additive Model Components Sources This and the following sections contain information on specific installed XSPEC models The parameters are given as parl par2 and norm which is the normalization Additive models
127. T OFILE suzpsf Set filename to write mixing factors XMMPSF IMAGE xmmpsf Set image file to be used for surface brightness XMMPSF RA xmmpsf Set RA for center surface brightness map which is taken from the WMAP XMMPSF DEC xmmpsf Set Dec for center surface brightness map which is taken from the WMAP XMMPSF MIXFACT IFILE xmmpsf Set filename to read mixing factors XMMPSF MIXFACT OFILE xmmpsf Set filename to write mixing factors NSA FILE nsa Change filename used for model data NSAGRAV DIR nsagrav Change directory used for model data files NSMAX DIR nsmax Change directory used for model data files ZXIPCF_ DIR zxipcf Change directory used XSPEC Models 161 for model data files Examples XSPEC12 gt xset neivers 2 0 Set the NEIVERS variable to 2 0 XSPEC12 gt xset List the current string variables XSPEC12 gt xset apecroot foo bar apec v1 01 Set the APECROOT variable XSPEC12 gt xset seed 1515151 Re initialize the pseudo random number generator with the seed value 1515151 5 9 Tcl Scripts The following Tcl scripts are auto loaded when xspec starts up so can be used in the same ways as commands Entering the name of the script without arguments will produce a short summary The scripts themselves can be found in HEADAS spectral scripts and can be us
128. XSPEC does not have the capability to plot or store and manipulate the background subtracted data This is a feature under consideration for a future release If we had chosen a observation containing more than a single source the procedure would have been similar except that the sequence of model commands would be extended e g XSPEC12 gt data MyDataDir GCDE aug 03 pha 1 475 XSPEC12 gt model 1 1e1740 po XSPEC12 gt model 2 gxl 4 po XSPEC12 gt model 3 bkg spibkg lo 63 Here data from the Galactic Center deep exposure campaign were loaded and two sources are sought In this case a much larger number of spectra were loaded 475 spectra corresponds to one full 5x5 dither using all 19 detectors In this case the simple approach of applying constant background i e no detector to detector or pointing to pointing variation to the full data set is likely to be a poor approximation A more realistic approach would be to use the XSPEC grouping capability to handle such variations in the background solution This can be accomplished in the usual manner refer to the description of the grouping command in this document however it can become tedious in terms of the required command line inputs For example to establish a separate data group for each detector for a long e g 5x5 dither observations a sequence of commands such as this would be required XSPEC12 gt data Per MyDataDir rev0044 Crab pha fits 1 XSPEC12 gt
129. a multivariate Gaussian centered on the best fit parameters with sigmas from the covariance matrix This is only an approximation in the case that fit statistic space is not quadratic Examples The current data have significant response to data within to 18 keV XSPEC gt lumin 0 5 Calculate the current model luminosity over the default range for z 0 5 XSPEC gt lumin 6 4 7 0 Calculate the current luminosity over 6 4 to 7 keV 5 6 14 mdefine Define a simple model using an arithmetic expression Syntax mdefine name expression type emin emax where name the name of the model If name is a previously defined model with mdefine the current definition will overwrite the old one and the user is warned if it is a built in model however the user will be asked to use a different name expression a string of arithmetic expression Simple rules for expression 1 The energy term must be e or E in the expression Other words which are not numerical constants nor internal functions are assumed to be model parameters 2 If a convolution model varies with the location on the spectrum to be convolved the special variable e or E may be used to refer to the convolution point 3 The expression may contain spaces for better readability type user may optionally specify the type of the model the valid types are add mul con Mix models are not yet implemented as of v12 5 0 Please note
130. abel top Simulated Spectrum label file Chandra ACIS S LT gt label y counts s u 1 d keV u 1 d Note the change in the y axis label is to remove the string normalized The normalization referred to is almost always unity so this label can generally be changed To get help on a PLT command just type help followed by the name of the command Note that PLT commands can be abbreviated just like XSPEC commands To see the results of changing the viewport and the labels just enter the command plot The two changes we want to make next are to rescale the axes and to change the y axis to a logarithmic scale The commands for these changes also are straightforward the rescale command takes the minimum and maximum values as its arguments while the log command takes x or y as arguments P P P E LT gt LT gt LT gt LT gt rescale x 0 3 6 0 rescale y 1 0e 4 0 03 log y plot To revert to a linear scale use the command log off y The only remaining extra change is to reduce the size of the characters This is done using the csize command which takes the normalization as its argument One 1 will not change the size a number less than one will reduce it and a number bigger than one will increase it Figure J A simulated Chandra ACIS S spectrum produced to show how a plot can be modified by the user Simulated Spectrum Chandra ACIS S 57 0 01 counts s keV 10 10 0 5 1 2 5 Energy keV
131. absorption 246 6 3 19 phabs vphabs zphabs zvphabs photoelectric absorption 247 6 3 20 plabs power law absorption cccecceseeseeeeeeeeeeeeeeeeeeseeneeeeeeeeeenenss 247 6 3 21 pwab power law distribution of neutral absorbers 0 248 6 3 22 recorn change correction norm for a Spectrum ccceeeeeeeeeeeeeeeeee 248 6 3 23 redden interstellar Extinction 2 sseeesseeeseeeseeeseeeseeeseeeeeeeees 248 6 3 24 smedge smeared CAGEC sseeeeeeeeeeeeesssseneeneneeeeeeeeeensesneneeeeeeeeenseess 249 6 3 25 spexpcut super exponential cutoff absorption 2 0 0 249 6 3 26 spline Spline modification ccceete te eeseeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeenenes 249 6 3 27 SSS ice Einstein SSS ice absorption eeeceeeeeeeeeeeeeeeeeeeeeeeeeeeees 250 viii 6 3 28 swind1 absorption by partially ionized material with large velocity a E E A A ATT 250 6 3 29 tbabs ztbabs tbgrain tbvarabs ISM grain absorption 250 6 3 30 uvred interstellar extinction Seaton Law cssseesseeeeeeeees 252 6 3 31 varabs zvarabs photoelectric absorption sesseeseeee 252 6 3 32 wabs zwabs photoelectric absorption Wisconsin cross sections 253 6 3 33 wndabs zwndabs photo electric absorption warm absorbet 253 6 3 34 xion reflected spectrum of photo ionized accretion disk ring 25
132. accretion onto the polar cap of a magnetized neutron star This model describes the spectral formation in the accretion column onto the polar cap of a magnetized neutron star with both thermal and bulk Comptonization processes taken into account The details for the method adopted for the numerical solution of the radiative transfer equation are reported in Farinelli et al 2012 A amp A 538 A67 This model can be used for spectral fitting of both accreting X ray pulsars and Supergiant Fast X ray Trasients parl kTpp temperature of the seed blackbody spectrum keV par2 kT electron temperature of the accretion column keV par3 T vertical optical depth of the accretion column with electron cross section equal to 10 of the Thomson cross section par4 n index of the velocity profile when the accretion velocity increases towards the neutron star valid when par8 1 pars Bo terminal velocity of the accreting matter at the neutron star surface valid when par8 1 par6 ro radius of the accretion column in units of the neutron star Schwarzschild radius par7 A albedo at the neutron star surface par8 Flag for setting the velocity profile of the accretion column if 1 B Z A Z Z where A Bo Zo Zs if 2 B t aTt norm R km D 10 Where Rkm and Djo are the accretion column radius in km and the source distance in units of 10 kpc respectively 6 2 18 compPS Comptonization Poutanen amp Svenson Comptonization spec
133. ading data into the program or replacing spectra or their ancillary detector background correction or efficiency auxiliary response arrays Additionally data commands control the channels under analysis The fit commands invoke the fitting routines modify their behavior by interchanging fitting algorithms or statistics in use fixing parameters or perform statistical testing The Model commands create or manipulate the model adding or editing components modifying parameters or alternatively performing analytical calculations from a model The Plot commands deal with all aspects of plotting The scripts are auto loaded Tcl scripts that can be used in the same ways as commands Finally the Setting commands sets variables that affect theoretical models Command Category Description abund SETTING Set the abundance table addcomp MODEL Add a component to the model addline MODEL Add lines to a model arf DATA Read an auxiliary response file autosave CONTROL Periodically save the XSPEC status DATA Reset the files to be used for background backgrnd subtraction bayes FIT Set up for Bayesian inference chain FIT Run a Monte Carlo Markov Chain chatter CONTROL Control the verbosity of XSPEC DATA Reset the files to be used for background corfile correction DATA Reset the normalization to be used in cornorm correcting the background cosmo SETTING Set Ho qo and A 68 Command Category Description cpd PLOT Alias for setplo
134. again we obtain Figure F The black body fit is obviously not a good one Not only is y large but the best fitting Ny is indeterminate Inspection of the residuals confirms this the pronounced wave like shape is indicative of a bad choice of overall continuum Let s try thermal bremsstrahlung next XSPEC12 gt mo pha br Input parameter value delta min bot top and max values for 1 0 001 0 01 0 0 100000 le 06 1 phabs nH gt data and folded model normalized counts s keV normalized counts s keV Energy keV Figure F As for Figure D but the model is the best fitting absorbed black body Note the wave like shape of the residuals which indicates how poor the fit is i e that the continuum is obviously not a black body Model phabs lt 1 gt bremss lt 2 gt Source No 1 Active On Model Model Component Parameter Unit Value par comp 1 1 phabs nH 10 22 1 00000 0 0 2 2 bremss kT keV 7 00000 0 0 3 2 b remss norm 1 00000 0 0 Fit statistic Chi Squared 4 534834e 07 using 45 PHA bins Test statistic Chi Squared 4 534834e 07 using 45 PHA bins Reduced chi squared 1 079722e 06 for 42 degrees of freedom Null hypothesis probability 0 000000e 00 Current data and model not fit yet XSPEC12 gt fit Parameters Chi Squared beta N Lvl 1 nH 2 kT 3 norm 156 921 6 92228e 11 3 1 00000 7 00000 0 00863005 106 765 24 2507 4 0 264912 6 25747 0 00718902 40 0331 190 876 0 8 46112
135. age provides a number of programs and subroutine libraries to manipulate the FITS files used by XSPEC A description of most tasks can be obtained by typing help taskname or to get a complete list fhelp ftools FTLIST DMPRMF FPARKEY GRPPHA RBNPHA MATHPHA CMPPHA RBNMF CMPRMF ADDARF ADDRMF MARFRMF GENRSP HEAsoft reading tasks Prints the contents of a FITS file to the screen or to a file Prints the contents of a FITS RMF file to the screen or to a file This tool prints the RMF file in a more legible fashion than FTLIST HEAsoft manipulation tasks Changes the value of a keyword in a FITS extension header Defines or redefines and or displays the grouping and quality flags the important keywords and the fractional systematic errors Compresses a FITS PHA file to a user defined number of channels The output is a new file containing the revised PHA extension plus a direct copy of any other extensions in the original file Performs arithmetical operations on PHA files Convert a type II pha file to a type I pha file Bins a FITS RMF file the detector response matrix in channel or energy space Compress an RMF by removing all response below a threshold value Adds together ARFs Adds together RMFs Multiplies an RMF file by an ARF file A generic spectral response generator HEAsoft subroutines A 302 The directory ftools callib src gen in the HEAsoft distribution contains a number of subro
136. ake install from the heasoft ver Xspec src tools initpackage directory To make sure the linker pulls in the library on Mac OS X Further edit the xspackage tmpl file by adding a 1 flag for the library e g lgsl in the HD_SHLIB LIBS settings Then reinstall xspackage tmpl as mentioned above On Linux Unix The XSPEC executable itself should be relinked with the new library included So edit the file heasoft ver Xspec src main Makefile by adding a l flag for the library to the HD_CXXLIBS setting Then from the same directory do rm xspec hmake local hmake publish hmake install After these modifications you should be able to use initpackage and Imod in the normal way to build and load your local models library C 5 Writing new mixing models Mixing models are fundamentally different from the other kinds of models since they apply a transformation to a set of modeled fluxes as enumerated by the spectra in the fit rather than modify the flux designed to fit a single spectrum The need to store temporary results as well as the requirements of the model calculation lead to many workspace arrays further the transformations applied are often fixed during a fit or can be split to avoid redundant calculations into parts that are fixed and parts that change during iteration in order XSPEC s internal organization data structures can be mapped straightforwardly to the requirements of these models so to implement them effi
137. akeit with an exposure of lt time gt and writes the results to lt outfile gt Before running this procedure you have read in one and only one dataset along with its response and optional background and arf files You must also have defined the model The output file is a FITS binary table with the columns being the value fit for each parameter in each iteration The final column is the statistic value for that iteration Note that if an error occurs during the fit of a faked spectrum then 999 is written for all parameters and the statistic value for that iteration 5 9 3 rescalecov rescale the covariance matrix Tcl script to rescale the entire covariance matrix used in the proposal chain command Syntax rescalecov lt scale gt Rescales the chain proposal distribution covariance matrix by the factor input as lt scale gt 5 9 4 simftest estimate the F test probability for adding a component Tcl script to generate simulated datasets and use these to estimate the F test probability for adding a model component Syntax simftest lt model_ comp gt lt niter gt lt filename gt This script runs lt niter gt sets of simulated datasets to estimate the F test probability for adding the additional model component number lt model_comp gt If lt filename gt is specified then passes this to Irt tcl to save likelihood ratio simulation information The first line of the file written contains the results for the data the other line
138. al COVEFING seeeeeeeeeeeseeeeessseneeneeeeeeeensnseeeeeeeeonseeeess 263 6 4 10 rdblur convolve with the diskline model shape cceeeesseeees 264 6 4 11 reflect reflection from neutral material ssseeeseeeeeeeeeeeees 264 6 4 12 simpl comptonization of a seed spectrum esseeeeeeeeeeeees 265 6 4 13 Zashift Redshift an additive model 0 ssseeeseeeeeeeeeeeeeeeees 265 6 4 14 Zmshift Redshift a multiplicative model cc ccssseeeeeeeeeeeeeeeeeeeees 266 6 5 Pile Up Model Components esseeseeeseeeeeeeeeeeeeeeeeeees 266 6 5 1 pileup CCD pile up model for Chandra cccccsssessseeeeeeeeeeeneeeees 266 6 6 Mixing Model Components sesseseseseeteeeeeseeeeeeeeeeees 267 6 6 1 ascac ASCA surface brightness model ccssseeeeesseeeeeeeeseeeeeeeees 267 6 6 2 projct project 3 D ellipsoidal shells onto 2 D elliptical annuli 268 6 6 3 suzpsf suzaku surface brightness model ccccccsseeeeeeeeeeeeeeeeeeeees 269 6 6 4 xmmpsf xmm surface brightness model cccccsesseeeeeeeeeteeeeeeneenees 270 Appendices fis sissies siesandesceneesnasssensecesenstcnesanssauesesasndsuusancssuaseundoeusGeueannneds 272 Appendix A The User Interface cccsseescseeeeeeeeeeeeeeeeeeeeeeeeeeseeeeeeeeenes 272 Appendix B Statistics in XSPEC ccccssssssseeeeeeeeeeeeeeseeeeeeeeeeeeeeeeeeees 281 Appendix C
139. alization of one of the additive models must be fixed to a non zero value It is also important to ensure that the energy range over which the model is calculated which is determined by the response matrix in use covers the energy range for which the photon flux is calculated If the model to which the cpflux is applied integrates to zero then a divide by zero error will occur resulting in NaN values for the fit statistic Parameters are parl Emin Minimum energy over which photon flux is calculated par2 Emax Maximum energy over which photon flux is calculated par3 Flux Photon flux in ph cm s 6 4 3 gsmooth gaussian smoothing Gaussian smoothing with a variable width Z E which varies as the par2 power of the energy The width at 6 keV is set with par1 Note that the energy binning must be uniform If the response energies are not uniformly spaced then the energies command should be used to set uniform energy binning 1 1 E XY dC E A X dX a 2nX E ao a X E o E 6 where parl o gaussian sigma at 6 keV 261 par2 a power of energy for sigma variation 6 4 4 ireflect reflection from ionized material Convolution model for reflection from ionized material according to the method of Magdziarz amp Zdziarski 1995 MNRAS 273 837 This is a generalization of the pexriv and bexriv models Ionization and opacities of the reflecting medium is computed as in the absori model The reflection component alo
140. ameter 3 from 1 0 10 0 in 5 logarithmic bins XSPEC12 gt margin 2 10 0 100 0 10 nolog 4 20 30 10 Now calculate for parameter 2 in 10 log bins and parameter 4 in 10 linear bins 5 5 9 renorm renormalize model to minimize statistic with current parameters Renormalize model or change renorm conditions Syntax renorm AUTO NONE PREFIT The renorm command will adjust the normalizations of the model by a single multiplication factor which is chosen to minimize the fit statistic Such a renorm will be performed explicitly whenever the command is used without a key word or during certain XSPEC commands as determined by the following key words AUTO Renormalize after a model or newpar command and at the beginning of a fit PREFIT Renormalize only at the beginning of a fit NONE Perform no automatic renormalizations i e only perform them when a renorm command is given explicitly 5 5 10 steppar generate the statistic surface for 1 or more parameters Perform a fit while stepping the value of a parameter through a given range Useful for determining confidence ranges in situations where greater control is needed than given with the error command Syntax steppar lt current best gt lt step spec gt lt step spec gt where lt step spec gt lt log nolog gt lt modelName gt lt param index gt lt low value gt lt high value gt lt steps gt or lt
141. ameters parl ny equivalent hydrogen column in units of 10 atoms cm par2 z Redshift The variants vphabs zvphabs allow the user to set fixed abundance parameters with respect to the solar composition as defined by the abund command For vphabs rest frame the parameters are parl ny equivalent hydrogen column in units of 10 atoms cm par2 parl8 abundances for He C N O Ne Na Mg Al Si S Cl Ar Ca Cr Fe Co Ni wrt to Solar While the corresponding redshifted variant zvphabs has parameters parl ny equivalent hydrogen column in units of 10 atoms cm par2 parl8 abundances for He C N O Ne Na Mg Al Si S Cl Ar Ca Cr Fe Co Ni wrt to Solar defined by the abund command parl9 z redshift 6 3 20 plabs power law absorption Absorption as a power law in energy Useful for things like dust 248 M E KE parl a index par2 K coefficient 6 3 21 pwab power law distribution of neutral absorbers An extension of partial covering fraction absorption into a power law distribution of covering fraction as a function of column density built from the wabs code See Done amp Magdziarz 1998 MNRAS 298 737 for details parl minimum equivalent hydrogen column in units of 10 22 atoms cm 2 par2 maximum equivalent hydrogen column in units of 10 22 atoms cm 2 par3 power law index for covering fraction 6 3 22 recorn change correction norm for a spectrum This model is a repla
142. ameters 4 5 and 6 are frozen 5 5 6 ftest calculate the F statistic from two chi square values Calculate the F statistic and its probability given new and old values of and number of degrees of freedom DOF Syntax ftest chisq2 dof2 chisq dofl 111 The new 2 and DOF chisq2 and dof2 should come from adding an extra model component to or thawing a frozen parameter of the model which gave chisq and dof If the F test probability is low then it is reasonable to add the extra model component WARNING it is not correct to use the F test statistic to test for the presence of a line see Protassov et al 2002 ApJ 571 545 WARNING this command can only be used if the extra model component is additive this does not give the correct result if the component is multiplicative see Orlandini et al 2012 ApJ 748 86 5 5 7 goodness perform a goodness of fit Monte Carlo simulation Perform a Monte Carlo calculation of the goodness of fit Syntax goodness lt of realizations gt sim nosim This command simulates lt of realizations gt spectra based on the model and writes out the percentage of these simulations with the fit statistic less than that for the data If the observed spectrum was produced by the model then this number should be around 50 This command only works if the sole source of variance in the data is counting statistics The sim nosim switch determines whether each simulation will use parameter values dra
143. an h for the function signatures FNINIT Initializes data directory locations needed by the models See below for a fuller description FGABND Get an element abundance A 304 FGCHAT Get current chatter level setting for model functions output verbosity FPCHAT Set the chatter level Default is 10 higher chatter levels produce more output FGDATD Get the model dat files path FPDATD Set the model dat files path FGMODF Get the model ion data path FGMSTR Get a model string value see XSPEC xset command FPMSTR Set a model string value FPSLFL Load values of a file solar abundance table see abund command FGSOLR Get the solar abundance table setting FPSOLR Set the solar abundance table FGXSCT Get the cross section table setting FPXSCT Set the cross section table RFLABD Read abundance data from a file then load and set this to be the current abundance table Essentially this combines a file read with the FPSLFL and FPSOLR functions csmgh0 Get the cosmology HO setting see the cosmo command csmph0O Set HO csmgl0 Get AO csmpl0 Set AO csmgq0 Get q0 csmpq0 Put q0 fzsq Computes the luminosity distance c H0 fzsq The function is valid for small values of q0 z for the case of no cosmological constant and uses the approximation of Pen 1999 ApJS 120 49 for the case of a cosmological A 305
144. and may be modified using an equivalent set of commands to those used for regular model parameters The command names are the same except prefixed by the letter r XSPEC commands for Equivalent commands for editing viewing model gain or response parameters parameters newpar rmewpar freeze rfreeze thaw rthaw untie runtie error rerror model rmodel show par show par show rpar For example after assigning gain fit parameters to source 1 of spectrum 1 with gain fit 1 XSPEC12 gt rfreeze 1 XSPEC12 gt rnewpar 2 05 XSPEC12 gt show rpar 126 Response parameters defined Source No 1 Rpar Spectrum Rmodel Rpar_ name Unit Value 1 1 gain slope 1 00000 frozen 2 1 gain offset 5 00000E 02 0 0 Rnewpar can also link gain parameters to one another and can adjust the hard and soft parameter limits as newpar does for model parameters The default gain parameter hard limits are hardcoded in XSPEC but these can be overridden by setting GSLOP_MIN GSLOP_ MAX GOFFS_MIN and GOFFS_MAX keywords in the matrix extension of your response file The gain operation itself belongs to the category of response functions which in future versions of XSPEC may be defined with rmodel just as regular XSPEC model functions are defined with model Though gain is currently the only available response function the following command will work Apply gain to the response belonging to
145. arameter values will be drawn The resulting equivalent widths are ordered and the central lt level gt percent selected to give the error range You can get the full array of simulated equivalent width values by calling tclout eqwidth with the errsims option see tclout command 123 When Monte Carlo Markov Chains are loaded see chain command they will provide the distribution of parameter values for the error estimate Otherwise the parameter values distribution is assumed to be a multivariate Gaussian centered on the best fit parameters with sigmas from the covariance matrix This is only an approximation in the case that fit statistic space is not quadratic Examples The current model is assumed to be M A A2 A3 A4 M A5 where the M models are multiplicative and the A models are additive XSPEC12 gt eqwidth 3 Calculate the total flux of component M A the third component of the model with its multiplicative pre factor and find its peak energy E The continuum flux is found by the integral flux of M A A3 A M2 As using the range of 0 95E to 1 05E to estimate the flux XSPEC12 gt eqwidth range 1 3 As before but now the continuum is estimated from its behavior over the range 0 9E to 1 1E XSPEC12 gt eqwidth range 0 3 Now the continuum at the single energy range E will be used XSPEC12 gt eqwidth range 05 2 Now the component M A is used as the feature and M1 Aj
146. arating multiplicative models and parentheses to show which additive models the multiplicative models act on The need not be included next to parentheses where it is redundant Also if only one additive model is being modified by one or more multiplicative models the 135 required brackets may be replaced by a In this case the additive model must be the last component in the grouping Thus M1 A A M gt M3 A3 My Ag As is a valid model where the M s signify multiplicative models and the A s additive models The old style syntax for entering models versions 9 02 and earlier is not supported in version 12 and will return a syntax error XSPEC12 s recursive lexical analyzer and expression parser allows in principle infinite nesting depth It has been tested to 3 levels of parentheses although it should be said that this new behavior is a by product of the design rather than fulfilling an important need Thus expressions such as M A A2 A3 M2 M3 Ag A7 Cy As A9 A10 Mz Ao are supported The model expression is analyzed on entry and syntax errors or undefined models will return control to the prompt with an error message XSPEC12 s model definition algorithm treats expressions delimited by signs that are not within parentheses as separate Component Groups The Component Group comprises a list of components of the different types and these are in turn calculated and then combined to
147. are distinguished by name which is a character string assigned by the user The purpose of this is to allow an intuitive syntax for creating multiple models simultaneously fit to data assigned to a corresponding number of sources The familiar XSPEC11 syntax is however fully supported by assigning an internal symbol name For example INTEGRAL SPI data is modeled using 2 or more sources one assigned to the background and one or more assigned to objects resolved by the coded mask XSPEC12 gt data rev_001234 1 19 XSPEC12 gt model 1 sourcel phabs cutoffpl XSPEC12 gt model 2 source2 phabs powerlaw XSPEC12 gt model 3 bkg spibk Note that a source number must precede the name to avoid confusion with model expressions The normal case fitting to a single source corresponds to source 1 115 When the fit command is given the parameters of the model will be labeled source1 1 source 2 source2 1 source2 2 bkg 1 bkg 2 etc Another use for multiple models is to name a model fit with it and then mark it as inactive i e not fit to data A second model may then be defined and fit to the data and afterward be interchanged This is designed to allow the user to compare the fits from competing models without recalculation Apart from the removal of the pre XSPEC10 model expression format which was previously declared deprecated and is now no longer recognized this new functionality provides a
148. ata chi XSPEC12 gt plot ufspec XSPEC12 gt plot efficiency XSPEC12 gt cpd none Will produce 3 plots in the file dataplot ps Note in contrast that the hardcopy command will print only the plot that is currently in a graphics frame 5 7 2 hardcopy print plot Spool the current plot to the printer Syntax hardcopy lt filename gt mono color This command takes whatever is the current display in you plot window writes it to a postscript file and then sends it to a printer using the unix lpr command It will thus be printed on whatever printer lpr uses as your default printer If a filename is specified the postscript file will be saved e g hardcopy dataplot ps color will produce a color plot saved in the file dataplot ps If mono or color is not given the hardcopy will be monochrome 5 7 3 iplot make a plot and leave XSPEC in interactive plotting mode Interactive plotting on the current plot device iplot lt plot type gt This command works like the plot command see the plot command description but allows the user to change the plot and to add text to the plot interactively using the PLT package See the Overview of PLT in the Appendices for more information 5 7 4 plot make a plot Make one or more plots to the current plot device see setplot device Syntax plot lt plot type gt lt plot type gt lt plot type gt lt plot type gt is a keyword describing the various plots allowed Up to six plot
149. atistical Challenges in Modern Astronomy eds Feigelson E D and Babu G J pp 275 297 Siemiginowska A 2011 In Handbook of X ray Astronomy eds Arnaud K A Smith R K and Siemiginowska A Cambridge University Press Cambridge Vaughan S 2010 A Bayesian test for periodic signals in red noise MNRAS 402 307 A 290 Appendix C Adding models to XSPEC XSPEC includes a large collection of standard models that can be fit to data However sometimes these are not enough and a new model might be required In order of increasing complexity the ways to do this are use the mdefine command create a table model load a model function created by someone else create and load your own model function The mdefine command can be used for a model which can be described using a simple formula and is documented under the commands section of the manual so we do not discuss it further This appendix describes the other three methods then finishes with a note about the more complex issue of mixing models C 1 Table models A very simple way of fitting with user defined models is available for a particular class of models These are models that can be defined by a grid of spectra with the elements of the grid covering the range of values of the parameters of the model For instance for a one parameter model a set of model spectra can be tabulated for different values of the parameter P1 P2 P3 etc The correct model spectrum fo
150. atter correctly taking into account Compton scattering The model can be used for radial column densities up to 5x10 cm The valid energy range for which data can be modeled is between 10 and 18 5 keV depending on the column density Details of the physics of the model the approximations used and further details on the regimes of validity can be found in Yaqoob 1997 ApJ 479 184 In this particular incarnation the initial spectrum is a power law modified by a high energy exponential cut off above a certain threshold energy Also to improve the speed a FAST option is available in which a full integration over the input spectrum is replaced by a simple mean energy shift for each bin This option is obtained by setting parameter 9 to a value of 1 or greater and cannot be made variable Further for single scattering albedos less than ACRIT i e par8 energy shifts are neglected altogether The recommended value is ACRIT 0 1 which corresponds to about 4 keV for cosmic abundances and is more than adequate for ASCA data Note that for column densities in the range 10 10 cm the maximum number of scatterings which need be considered for convergence of the spectrum of better than 1 is between 1 and 5 For column densities as high as 5x10 cm the maximum number of scatterings which need be considered for the same level of convergence is 12 This parameter cannot be made variable parl Column density in units 10 cm pa
151. ave reasonable values Optional pairs of extra keywords eg XFLT0004 5 XFLT0006 7 etc can be used to specify start and end angles for a partial annulus These angles should be given relative to the same zero as the position angle The user reads in the spectra as separate datagroups and sets model parameters for each datagroup The model for datagroup J will be the model in the shell whose outer boundary is a prolate ellipsoid of semi major and semi minor axes given by the semi major and semi minor axes in the XFLT keywords for dataset J The projct model sums up the appropriate fractions of each ellipsoid model to make the projected spectrum For example suppose we extract spectrum from three elliptical regions defined by 1 0 5 0 2 1 0 3 1 5 0 That is the first region is in an ellipse of semi major axis 1 and semi minor axis 0 5 The second region is an elliptical annulus whose inner boundary has semi major axis 1 and semi minor axes 0 5 and whose outer boundary has semi major axis 2 and semi minor axis 1 The third region is defined similarly The model fit has a temperature of 2 keV for the first datagroup 3 keV for the second and 4 keV for the third The actual model fit to the first dataset has contributions from all three temperatures the second only from the 3 and 4 keV components and the third only from the 4 keV component The weighting is the fraction of the ellipsoidal volume intersected 269 by the elliptical annular c
152. avoided as much as possible To speed things up it is possible to save the mixing factor array to a FITS file and re use it during a later calculation To save a mixing factor calculation prior to loading the mixing model using the model command use xset to set the variable XMMPSF MIXFACT OFILEn to the name of the output FITS file and where n is an integer corresponding to the XSPI XSP XSP part par2 par3 par4 observation number EC12 gt xset XMMPSF MIXFACT OFILE1 fact_obsl fits Conversely a saved factor array can be read in by setting XMMPSF MIXFACT IFILEn EC12 gt xset XMMPSF MIXFACT IFILE1 fact_obsl fits Multiple observations can be fit simultaneously In this case the observations should be read in each datagroup in the same order e g EC12 gt data 1 1 obslregl 1 2 obs2regl 1 3 obs3regl 2 4 obslreg2 2 5 obs2reg2 Alpha not used if Switch 0 Beta Core arcmin Switch 0 beta model 1 2 power law A 272 Appendices Appendix A The User Interface A 1 Introduction All communication with the user in XSPEC is performed through the tcl user interface When XSPEC starts a tcl interpreter is initialized and the XSPEC commands are added to it so that the tcl interpreter understands them The XSPEC commands which are C functions define the syntax through a new built in library of utility functions The parser used in earlier versions of XSPEC has been discontinued how
153. aw emissivity function corresponds to emission measure weighted by the inverse of the bolometric luminosity at that temperature The model assumes H 50 and q 0 The abundance ratios are set by the abund command parl par2 index for power law emissivity function low temperature keV 184 par3 high temperature keV par4 abundance relative Solar pars redshift z norm Mass accretion rate solar mass yr 6 2 15 compbb Comptonization black body Comptonized blackbody model by Nishimura Mitsuda and Itoh 1986 PASJ 38 819 The electron temperature should normally be kept fixed since the Compton y parameter is the product of the electron temperature and optical depth parl blackbody temperature keV par2 electron temperature of the hot plasma keV par3 optical depth of the plasma norm 2 Lao Dy where L39 is the source luminosity in units of 10 ergs and Dyo is the distance to the source in units of 10 kpc the same definition used for the bbodyrad model 6 2 16 compLS Comptonization Lamb amp Sanford A Comptonization spectrum after Lamb and Sanford 1979 M N R A S 288 555 This model calculates the self Comptonization of a bremsstrahlung emission from an optically thick spherical plasma cloud with a given optical depth and temperature It was popular for Sco X 1 parl temperature in keV par2 optical depth norm normalization 185 6 2 17 compmag Thermal and bulk Comptonization for cylindrical
154. be adjusted with the newpar command and they correspond to the quantities min and max associated with the parameter values The command eqwidth takes the component number as its argument The upper limit on the equivalent width of a 6 4 keV emission line is high 784 eV 4 3 Simultaneous Fitting XSPEC has the very useful facility of allowing models to be fitted simultaneously to more than one data file It is even possible to group files together and to fit different models simultaneously Reasons for fitting in this manner include 46 The same target is observed at several epochs but although the source stays constant the response matrix has changed When this happens the data files cannot be added together they have to be fitted separately Fitting the data files simultaneously yields tighter constraints The same target is observed with different instruments All the instruments on Suzaku for example observe in the same direction simultaneously As far as XSPEC is concerned this is just like the previous case two data files with two responses fitted simultaneously with the same model Different targets are observed but the user wants to fit the same model to each data file with some parameters shared and some allowed to vary separately For example if we have a series of spectra from a variable AGN we might want to fit them simultaneously with a model that has the same common photon index but separately vary the normalization
155. be given for the adopted ionization balance Arnaud M and Rothenflug M 1985 A amp AS 60 425 Arnaud M and Raymond J 1992 ApJ 398 394 6 2 50 mekal vmekal emission hot diffuse gas Mewe Kaastra Liedahl An emission spectrum from hot diffuse gas based on the model calculations of Mewe and Kaastra with Fe L calculations by Liedahl The model includes line emissions from several elements The switch parameter determines whether the mekal code will be 211 run to calculate the model spectrum for each temperature or whether the model spectrum will be interpolated from a pre calculated table The former is slower but more accurate Relative abundances are set by the abund command for the mekal model The vmekal variant allows the user to set the individual abundances for the model parl plasma temperature in keV par2 H density cm par3 Metal abundance He fixed at cosmic The elements included are C N O Ne Na Mg Al Si S Ar Ca Fe Ni par4 fixed redshift 0 calculate Par5 1 interpolate 2 interpolate using APEC model norm 107 4z D 1 z to the source cm and ne ny cm are the electron and hydrogen densities respectively F JngnaV where D4 is the angular diameter distance Parameters for the vmekal variant are parl plasma temperature in keV par2 H density cm par3 parl6 Abundances for He C N O Ne Na Mg Al Si S Ar Ca Fe Ni wrt Solar given by the Anders amp G
156. bsorption edges Convolution and mixing models can then perform sophisticated operations on the result Models are defined in algebraic notation For example the following expression phabs power phabs bbody defines an absorbed blackbody phabs bbody added to a power law power The result then is modified by another absorption component phabs For a list of available models see Chapter 6 Fits and Confidence Intervals Once data have been read in and a model defined XSPEC uses a fitting algorithm to find the best fit values of the model parameter The default is a modified Levenberg Marquardt algorithm based on CURFIT from Bevington 1969 The algorithm used is local rather than global so be aware that it is possible for the fitting process to get stuck in a local minimum and not find the global best fit The process also goes much faster and is more likely to find the true minimum if the initial model parameters are set to sensible values The Levenberg Marquardt algorithm relies on XSPEC calculating the 2 derivatives of the fit statistic with respect to the model parameters By default these are calculated analytically with the assumption that the 2 derivatives of the model itself may be ignored This can be changed by setting the USE NUMERICAL DIFFERENTIATION flag to true in the Xspec init initialization file in which case XSPEC will perform numerical calculations of the derivatives which are slower
157. bug output Examples XSPEC12 gt cha Set the terminal chattiness to 10 same as the initial value XSPEC12 gt chatter 0 tter 10 ia Set the chattiness for the log file to very low g This setting essentially disables the log file output XSPEC12 gt chatter 5 Make XSPEC very quiet XSPEC12 gt chatter 10 25 Restore the terminal chattiness to the initial level while in the log file XSPEC will tell all particularly when new data files are read in 5 3 3 exit quit exit program The command to end the current XSPEC run Syntax exit After an exit the current plot files are closed An lt EOF gt will have an identical result 5 3 4 help display manual or help for a specific command theoretical model component Obtain help on the XSPEC commands their syntax and examples of their use Syntax help lt topic list gt On the first invocation of the help command an instance of a pdf file reader by default Adobe Acrobat Reader is started a shortly delay may ensue or the XSPEC manual is accessed online Please see the subsection Customizing XSPEC in the XSPEC Overview section for details on how to control this behavior The Acrobat reader must be in the user s path If this default is used then subsequent calls to help will use this instance to display other help pages help without arguments displays the XSPEC manual with a bookmark index that allows
158. by Magdziarz amp Zdziarski See also Zdziarski et al 1995 ApJ 438 L63 Photoionization rates are from Reilman amp Manson 1979 ApJS 40 815 who employ the Hartree Slater approximation accurate to about 5 and recombination rates are from Shull amp Steenburg 1982 ApJS 48 95 The cross sections are extrapolated with 3 above 5 keV The abundances are set up by the command abund Send questions or comments to aaz camk edu pl parl power law photon index par2 Hydrogen column in units of 1022cm 2 par3 Absorber temperature in K par4 Absorber ionization state L nR2 see Done et al 1992 pars 2 redshift par6 Iron abundance relative to that defined by the command abund 6 3 2 acisabs Chandra ACIS q e decay This model accounts for the decay in the ACIS quantum efficiency most likely caused by molecular contamination of the ACIS filters The user needs to supply the number of days between Chandra launch and observation The acisabs parameters related to the composition of the hydrocarbon and the rate of decay should be frozen and not modified The present version of acisabs is to be used for the analysis of bare ACIS I and ACIS S data For the present version of acisabs one must use the standard qe file vN0003 instead of the optional vN0004 file Because of the present large uncertainty in the ACIS gain at energies below 350eV we recommend that events in the 0 350eV range be ignored in the spectral analysis until t
159. c statement to load into Python XSPEC can now be run from object oriented Python scripts or interactively from a Python shell prompt Detailed instructions can be found in PyXspec pdf While most features of standard XSPEC are already supported in this beta release some still remain to be implemented Please let us know if any missing feature is of particular importance to you or if you have suggestions and ideas for improvement Other new features New models cplinear Piecewise linear non physical background model for low count spectra developed for Chandra by Patrick Broos eqpair eqtherm compth Paolo Coppi s hybrid hot plasma emission models vvapec bvvapec APEC models allowing all 30 elemental abundances to vary for use with AtomDB 2 0 zigm Multiplicative model computes the mean attenuation of the optical UV spectrum by the intergalactic medium zashift zmshift Convolution models for applying redshifts to additive and multiplicative models respectively Also note that the default APEC model data files have been updated to AtomDB 2 0 This version of AtomDB includes contributions from more elements than earlier versions When using the apec and vapec models these extra elements have Solar abundance by default To change this use xset APEC_TRACE ABUND The statistic command may now be applied to individual spectra This makes it possible to simultaneously fit spectra which require different fit statistics A
160. c energy steps 0 0 channel offset and 0 0 channel width The default values of the first 5 parameters will be modified each time the parameter is explicitly entered The channel width parameter however always defaults to 0 0 which indicates mode 2 operation described below In addition to the 6 optional parameters allowed for versions 11 x and earlier a seventh optional parameter has been added allowing the user to apply the dummy response to just one particular source of a spectrum It consists of two integers for 1 based source number and spectrum number separated by a colon Either both integers should be entered or they should be left out entirely ie A dummy response is either made for EVERY source in every spectrum or just 1 source in 1 spectrum This parameter always defaults to all sources and all spectra For mode 1 usage simply enter a non zero value for the channel width In this instance one has a spectrum for which typically no response matrix is currently available This command will create a diagonal response matrix with perfect efficiency allowing for the differences in binning between the photon energies and the detector channel energies see example below The response matrix will range in energy from lt low Energy gt to lt high Energy gt using lt of ranges gt as the number of steps into which the range is logarithmically or linearly divided The detector channels are assigned to have widths of energy lt channel wid
161. cation function udmget have been removed from the Fortran models in XSPEC s models library The relevant code has been converted to C Ifa user s local models library still requires the udmget code they ll need to run initpackage with the new udmget option Additional enhancements previously released as patches to 12 5 0 e Setplot wave x axis units can be toggled from Hz to angstroms through WAVE PLOT_UNITS entry in Xspec init file e New tclout gain and sigma options e Newxs_getVersion function available for those linking their own programs to the XSPEC models library e The show parameters option can now take a range of parameters for displaying subsets All bug fixes to v12 5 0 released as patches a an are included in v12 5 1 In addition the following problems have been corrected e After running the ARF command any gain previously applied to the associated RMF will be removed Previously it was erroneously applying the gain to the new ARF A 320 e Additional header file inclusions needed in code files to compile with gt 4 4 0 e Extra line feed characters removed from Ascii text files in the modelData directory These were causing problems on Solaris 10 w f90 e The nthcomp model s internal arrays were hardcoded to a maximum size of 5000 energy bins The size is now dynamically allocated This also affects the diskir model e A Levenberg Marquardt fit now immediately stops if the fit statistic becomes NaN du
162. cement for and improvement on the old xspec command recornrm If a correction file is in use for a spectrum then its normalization can be fitted for using this model The first parameter which is not variable is the spectrum number and the second the correction file normalization The starting value of the second parameter should be set to the current value of the correction file norm this can be independently set using the cornorm command Note that in order to fit the cornorm parameter the USE NUMERICAL DIFFERENTIATION setting in the user s Xspec init start up file must be set to true This causes XSPEC to use a slower full numerical differentiation algorithm when calculating parameter derivatives during a fit and therefore is not recommended for general usage parl specnum spectrum number par2 cornorm correction file normalization 6 3 23 redden interstellar extinction IR optical UV extinction from Cardelli et al 1989 ApJ 345 245 The transmission is set to unity shortward of the Lyman limit This is incorrect physically but does allow the model to be used in combination with an X ray photoelectric absorption model such as phabs 249 parl E B V 6 3 24 smedge smeared edge A smeared edge Ebisawa PhD thesis implemented by Frank Marshall l E lt E M E exp f E E 1 exp E E W EzE where parl E the threshold energy keV par2 f the maximum absorption factor at threshold par3 a index for phot
163. ch the quantities listed below are IN inner rim of the projected annular sector Mpc OUT outer rim of the projected annular sector Mpc WID width of the projected annular sector deg EVOL emitting volume within the integration radius cutoff Mpc EINT emission integral within the integration radius cutoff Mpc cm 6 If nH cc is frozen to 1 the actual EI is obtaned by multiplying this figure by the square root of the model normalisation 6 2 75 srcut synchrotron spectrum cutoff power law srcut describes the synchrotron spectrum from an exponentially cut off power law distribution of electrons in a homogeneous magnetic field This spectrum is itself a power law rolling off more slowly than exponential in photon energies Though more realistic than a power law it is highly oversimplified but does give the maximally curved physically plausible spectrum and can be used to set limits on maximum accelerated electron energies even in remnants whose X rays are thermal See Reynolds S P amp Keohane J W 1999 ApJ 525 368 and Reynolds S P 1998 ApJ 493 357 Note that the radio spectral index and flux can be obtained from Green s Catalogue at http www mrao cam ac uk surveys snrs for galactic SNRs 238 parl alpha radio spectral index par2 break Hz approximately the frequency at which the flux has dropped by a factor of 10 from a straight power law norm 1 GHz flux Jy 6 2 76 sresc synchrotron spectrum cut off by particl
164. ches that change the mode in which a theoretical component is calculated i e it may be interpolated or analytically calculated scale or switch parameters cannot be linked to any other type of parameter but only to other scale or switch parameters Details of parameter types are explained in more detail in Appendix C The syntax for linking parameters is XSPEC12 gt newpar lt par gt f par where fis a polynomial in the other parameters with real coefficients N B Integers appearing in f that are within the range of existing parameter numbers will be interpreted as parameters to avoid confusion if a real number is intended it should include a decimal point Integers larger than the last parameter number will be interpreted as integers Parameters of named models must have their index numbers prefixed by mode1Name If there are multiple data groups present then the parameters of models associated with datagroups greater than 1 secondary models are coupled by default to their primary counterparts For example if there are 5 parameters in the model and 3 datagroups present then the model command will prompt for 15 parameters If the user types XSPEC12 gt model lt expression gt XSPEC12 gt 139 Then parameters 1 5 will be set to their values specified in the initialization model dat file Parameters 6 15 will be linked to their counterparts i e as if the user had typed XSPEC
165. ciently and handle memory allocation we recommend that mixing models be written in C or C At present only a C implementation is available Users considering adding new mixing model types should contact the developers of XSPEC at xspec12 athena gsfc nasa gov A 296 A 297 Appendix D Overview of PLT As in previous versions the initial release of XSPEC12 uses the PLT library which is in turn based on PGPLOT to implement its plotting capabilities Future versions will be able to offer other plotting library options Extensive documentation for the PLT graphics routine is available in the The QDP PLT Users s Guide and from PLT s interactive help This appendix is intended to provide information to assist in using PLT from within the XSPEC program Within XSPEC it is possible to set your graphics device using the CPD command Any PGPLOT device supported by your local version of PGPLOT is accepted The CPD command can also be used to display a list of all PGPLOT devices If you fail to enter a device name you will be prompted for a PGPLOT device every time you generate a new plot From XSPEC there are two ways to call the PLT routine Both have the same syntax which is described in the corresponding manual section e The plot lt plot mode gt command will produce a graph and control will return immediately to XSPEC e The iplot lt plot mode gt command will put XSPEC into interactive plot mode The PLT gt prompt will appear
166. cision wrapper function name will be the original C function name appended with a f_ prefix while the double precision wrapper will have a C_ prefix For example XSPEC s model dat entry for the power law model lists the function name C_powerLaw This shows that the actual function name is powerLaw and the C_ indicates it has a C interface inside XSPEC funcWrappers cxx defines the following 2 wrappers void f powerLaw const float energy int nFlux const float params int spectrumNumber float flux float fluxError void C_powerLaw const double energy int nFlux const double params int spectrumNumber double flux double fluxError const char initStr The second function is intended to be called from C programs while Fortran programs may call either funcWrappers cxx also includes CERN lt cfortran h gt definitions to make these accessible to Fortran F 2 Interface Routines XSPEC also provides a set of functions for accessing some of the model functions internal data The C functions are listed in the file FunctionUtility h in the XSUtil FunctionUtils directory For C and Fortran access equivalent wrapper functions are listed in the same directory in xsFortran h The wrapper functions have C style function declarations and are also made available to Fortran calling routines via the CERN lt cfortan h gt interface The currently provided C Fortran wrapper functions are see xsFortr
167. ctually required this will leave the current model in use The new command variants have the following uses model lt name gt none removes the model of name lt name gt if given Without the lt name gt argument the command removes the unnamed default model which is of course the XSPEC11 behavior model clear removes all models model lt name gt unnamed activelinactive makes the model named lt name gt active fit to data or inactive Inactive models are tied to a dummy unit diagonal response Making a model assigned to a given source active makes any previous model assigned to that source inactive Note that to make the default unnamed model active or inactive refer to it by the string unnamed See the commands delcomp addcomp and editmod for details on how to modify the current model without having to enter a completely new model rmodel lt source num gt lt spec num gt lt response function gt none assigns or removes a response function to the response belonging to lt source num gt of spectrum lt spec num gt Currently the only available lt response function gt in XSPEC is gain which makes rmodel redundant with the gain command usage gain fit lt source num gt lt spec num gt The rmodel none option removes the response function and restores the response to its initial state Syntax Rules Model components are combined in the obvious algebraic way with separating additive models sep
168. curred if tclout notice energies was performed on a spectrum containing only a dummy response with no channels The 5 redundant xset options those which merely duplicate other existing XSPEC commands weren t passing their arguments to the command handlers correctly Fit error messages were misleading for the case where the data was missing a suitable response or when the only existing models were inactive A fatal error could occur in fakeit when attempting to generate a background file while only a dummy was used for the response The bayes command handler was not properly handling the case where the prior type option string was abbreviated A crash occurred when flux was run in error mode and the specified energy was entirely outside the range of one or more spectra v12 6 0 March 2010 The main improvements in version 12 6 0 are to XSPEC s plotting capabilities Multi panel plotting is now supported for all combinations except contour plots For example plot data model resid ratio will produce a 4 panel plot on a single page Up to 6 panels can be plotted in this manner There are many choices for axis units These can be selected using the setplot energy and setplot wave commands For example setplot energy GeV uses GeV on the x and y axes setplot wave also has a new perhz option for displaying the Y axis in 1 Hz units The setplot command has a new redshift lt z gt option for shifting display
169. custom energy binned model flux array needs to be multiplied by a response matrix xspec will temporarily rebin the flux array to match up with the response energy binning This is done by simply scaling the flux by the fractional overlap between the custom and response bins If there is no overlap between the custom and response energies then the response will be multiplied by zero The energies command saves the most recently entered range and extension specifiers to be used as default values the next time it is called The initial default range specifier is 1 range with lt low E gt 122 1 lt high E gt 10 lt nBins gt 1000 and 1in The initial default extension specifier is high with lt energy gt 100 lt nBins gt 200 and log Examples XSPEC12 gt energies 50 log Creates an array from 1 to 50 of 1000 logarithmic bins XSPEC12 gt energies 100 5 lin Modifies previous array by adding 5 linear bins from 50 to 100 XSPEC12 gt energies 200 The 2 range is now 50 to 200 in 5 linear bins XSPEC12 gt energies 1 100 Array is now just 1 range 1 to 50 in 100 logarithmic bins XSPEC12 gt energies myFile txt Array is replaced with values stored in myFile txt XSPEC12 gt energies extend 75 lin Models will go back to using respons nergies but with an extension of the high end to 75 keV in 100 additional linear bins XSPEC12 gt energies extend low 01 Add a low end extensio
170. d and responses Input one or more spectra together with their associated background response files Syntax data lt file specl gt lt file spec2 gt data none data lt spectrum gt none where the file specification is lt filespec gt lt data group gt lt spectrum gt lt filename gt ranges If a particular file is not found or cannot be opened for input for some reason then the user is prompted for a replacement file name An lt EOF gt at this point is equivalent to typing none The default extension for all files is pha so all other extensions e g fak must be entered explicitly The default directory is the current user directory when XSPEC is invoked When a new file is input by default all its PHA channels are considered good channels for fitting and plotting purposes see the ignore and notice commands XSPEC s native data format is the OGIP standard The standard specifies the representation of spectrum and all related datasets XSPEC12 is explicitly designed to be able to work with other data formats as required for example the Integral SPI spectral data format although based on OGIP Typell deviates slightly This was necessary because 3 response arf pairs are required per spectrum XSPEC12 has the ability to specify how response and other data are stored on disk composed and combined within the spectral fitting problem by adding new data modules at run time In XS
171. d by the command fit As the fit proceeds the screen displays the status of the fit for each iteration until either the fit converges to the minimum y or we are asked whether the fit is to go through another set of iterations to find the minimum The default number of iterations before prompting is ten XSPEC12 gt fit Chi Squared beta N Lvl 1 nH 2 PhoIndex 3 norm 121 3533 1 01892e 10 3 1 00000 1 00000 0 00242602 471 551 150 854 4 0 152441 1 67440 0 00415548 367 421 60807 7 3 0 308661 2 31822 0 00958061 53 6787 25662 3 4 0 503525 2 14501 0 0121712 43 8123 4706 76 5 0 549824 2 23901 0 0130837 43 802 118 915 6 0 538696 2 23676 0 0130385 43 802 0 422329 7 0 537843 2 23646 0 0130320 Variances and Principal Axes 1 2 3 4 7883E 08 0 0025 0 0151 0 9999 8 6821E 02 0 9153 0 4026 0 0084 2 2915E 03 0 4027 0 9153 0 0128 Covariance Matrix 1 2 3 7 312e 02 3 115e 02 6 564e 04 3 115e 02 1 599e 02 3 207e 04 6 564e 04 3 207e 04 6 561e 06 Model phabs lt 1 gt powerlaw lt 2 gt Source No 1 Active On Model Model Component Parameter Unit Value par comp L 1 phabs nH 10 22 0 537843 0 270399 2 2 powerlaw PhoIndex 2 23646 0 126455 3 2 powerlaw norm 1 30320E 02 2 56146E 03 Fit statistic Chi Squared 43 80 using 45 PHA bins Test statistic Chi Squared Reduced chi squared Null hypothesis probability 43 80 using 45 PHA bins 1 043 for 42 degrees of freedom 3 949507e 01 The
172. d in one command Several datasets may be stored in a single file and accessed separately A particular dataset in use may be replaced by another or dropped entirely The input data file contains pointers to background redistribution and auxiliary response files but these pointers may be overridden by the backgrnd response and arf commands All these commands have the same syntax as data An auxiliary background file called the correction file an absolute subtraction with zero variance also can be included using the corfile command Its use is described in the section on fitting The current response can be replaced by a diagonal version using diagrsp A dummy response for testing purposes can be defined using dummyrsp 3 7 2 Controlling channels being fitted PHA channels may be left out of fitting using the ignore command and included again using the notice command These commands have a syntax allowing the same channels to be specified for more than one input file The ignored and noticed ranges can be specified either as channels or as energies If the command setplot wave has been entered real ranges are interpreted as wavelengths 3 7 3 Simulations The fakeit command is used to generate simulated data The current response matrix and model a model must be defined prior to using the fakeit command are used to create fake data The user is prompted for various options To make fake data when only a response matrix is available give th
173. dded the pgstat option to the statistic command This is similar to using cstat with a background file except that the background is assumed to have Gaussian statistics not Poisson read from a STAT_ERR and optionally SYS_ERR column Modified the pileup model for consistency with Sherpa and ISIS A new parameter fracexpo is added which should be set to the FRACEXPO keyword value in the ARF It is now possible to choose proportional or fixed fit deltas from the startup Xspec init file The initial default setting is now proportional deltas rather than fixed deltas Improvements made to the output generated during a fit The parameter names are listed at the top of columns not just their numbers Column alignment has been improved and is no longer limited to a maximum width of 5 columns Added reporting of the Bayesian contribution if any to the fit statistic output Enhancements previously released as patches to 12 6 0 A 317 Initpackage now recognizes and builds files with f03 extensions for Fortran 2003 and f90 extensions for Fortran 90 Added a new fakeit option for setting the fake background exposure time Added a new tclout version option for returning the XSPEC version string Improved XSPEC s internal update mechanism to reduce the number of model calculations All bug fixes to v12 6 0 released as patches a ab are included in v12 7 0 In addition the following problems have been corrected A crash oc
174. default suffix for xspec scripts is xcm The save command writes the current XSPEC status to a command file which later can be run to reset XSPEC to the same configuration XSPEC has a mechanism to save the current status automatically This is controlled through the autosave command This command is very useful when reading a large number of data sets and or fitting complicated models If autosaving is operating the default then the equivalent of XSPEC12 gt save all xautosav xcm is run after each command so if a disaster occurs it is possible to recover 3 6 3 Miscellaneous Information on the current XSPEC status can be printed out using the show command The time command writes out system timing information and the version command writes out the version number and the build time and date Finally XSPEC can be terminated with the exit or quit commands 17 3 7 Data Commands XSPEC is designed to allow complicated multi instrument analysis so most commands can take arguments specifying more than one data set Arguments in XSPEC are separated by either blanks or commas A single argument can define a range The ranges are delimited by a dash A colon is used to separate ranges e g the phrase 1 2 11 24 refers to channels 11 24 in files 1 and 2 3 7 1 Reading data and modifying calibration and auxiliary files XSPEC reads in spectra from spectral files using the data command Several datasets may be specifie
175. del 2 eeseeeeeeeeeeeeeeeees 117 5 6 3 delcomp delete a model component eeeeeeeeeeeeeeeteeeeeeeeeeneeees 117 5 6 4 dummyrsp create and assign GUMMY reSPONSE eeeeeeeeeeeeees 118 5 6 5 editmod edit a Model COMPONENM sseeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeneess 120 5 6 6 energies specify new energy binning for model fluxes 120 5 6 7 eqwidth determine equivalent width ceecessseeeeeeeeeeeeeeeeeneeees 122 5 6 8 flux calculate flUXeS nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn nnmnnn 123 5 6 9 gain Modify a response file QaiN ces sseeeseeeeee ee eeeeeeeeeeeceeeeeeeeenneees 124 5 6 10 identify identify Spectral lines 0 00 ccc ssseeeeeneeeeeeeeeeeeeeeseeeeeeeeeeeeenees 127 5 6 11 initpackage initialize a package of local MOdelS ccceeeseeeees 128 5 6 12 Imod localmodel load a package of local models cccccessesees 129 5 6 13 lumin calculate luminosities 2 2 eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeneeeees 129 5 6 14 mdefine Define a simple model using an arithmetic expression 130 5 6 15 model define a theoretical model 2 ss eesseeeseeeseeeeeeeeeeeees 132 5 6 16 modid write out possible IDs for lines in the model 137 5 6 17 newpar change parameter ValUCS cc sseseseeeeeeeeeeeeeeeeeeeneeeeeeeeenenees 137 5 6 18 systematic add a model dependent sy
176. del will be presented in Nayakshin et al 2001 currently available at http adsabs harvard edu cgi bin nph 255 bib_query bibcode 2001ApJ 546 406N amp amp db_key AST amp amp data_type HT ML amp amp format amp high 4230b2429423803 parl par2 par3 par4 pars par6 par7 par8 par9 par10 parl1 parl2 par13 height of the source above the disk in Schwarzschild radii ratio of the X ray source luminosity to that of the disk accretion rate in Eddington units COS the inclination angle 1 face on inner radius of the disk in Schwarzschild radii outer radius of the disk in Schwarzschild radii photon index of the source redshift z Fe abundance relative to Solar which is defined as 3 16 10 by number relative to H Exponential high energy cut off energy for the source 1 gt reflected direct direct 2 gt reflected incident incident 3 gt reflected incident 2 gt no relativistic smearing 4 gt relativistic smearing 1 gt lamppost 2 gt central hot sphere with outer cold disk 3 magnetic flares above a cold disk Note that setting par13 to 2 gives a central hot sphere with 2 p l0y luminosity law dL dR 4aR R The inner radius of the sphere is 3 Schwarzschild radii and the outer radius is equal to parl Only the case with par5 2 parl has been tested so far 256 6 3 35 zbabs EUV ISM attenuation The ISM attenuation due to neutral H neutral He and once ionized He This is a
177. determined from the last use of the data command An optional lt source num gt may be specified to attach additional responses to a spectrum and should be paired with lt spectrum num gt separated by a This allows the user to assign multiple models each with their own response file to a particular spectrum See the model command for more information Ifno lt source num gt is specified it always defaults to 1 Source numbers do not need to be assigned consecutively to a spectrum and gaps in numbering are allowed The additional response may be removed with a response lt source num gt lt spectrum num gt none command Both the show data and show response commands will display current information regarding the response s to spectrum assignments A file name none indicates that no response is to be used for that spectrum This situation means that any incident spectrum will produce no counts for those particular channels If a file is not found or cannot be opened for input then the user is prompted for a replacement response file An lt EOF gt at this point is equivalent to using none as the response See the data command for ways to totally remove the spectrum from consideration The user is also prompted for a replacement if the response file has a different number of PHA channels than the associated spectrum A warning will be printed out if the response detector ID is different from the associated spectrum s The current ignore s
178. disk as a function of radius is assumed to be T r T_ r 3 4 201 1 r 1 2 4 1 4 where r R R_in and T_ f 3 GM Mdot 8 pi R_in 3 sigma 1 4 The maximum temperature in the disk is given by T_max 0 488 T _ This model is an alternative to diskbb which assumes a non zero torque at the inner edge and a temperature profile T r T_ r 3 4 and it should be used to fit spectra of disks when the zero torque inner boundary condition is appropriate For details see Zimmerman et al 2004 astro ph 0408209 parl maximum temperature in the disk keV par2 1 f 4 R_in D 2 cos i where R_in is the inner radius of the disk in km D is the distance to the source in units of 10 kpc i is the inclination and fis the color to effective temperature ratio 6 2 37 gadem vgadem plasma emission multi temperature with gaussian distribution of emission measure A multi temperature plasma emission model built on top of the apec or mekal codes The emission measure distribution is a gaussian with mean and sigma given by the first two model parameters The switch parameter determines whether the apec or mekal codes will be used For the mekal code there are also the options to run the code for each temperature or interpolate from a pre calculated table The former is slower but more accurate See the documentation on the apec model for additional information on using different AtomDB versions or applying thermal or velocity broadenin
179. drawn Without the string argument the current label for Top X or Y is set to the empty string Hardcopy PGPLOT plot device Create a file that can later be printed Since it redraws the graph and sends it to a file it does not reproduce what currently is visible on the graphics display but rather what you would see if you re issued the Plot command With the optional argument Hardcopy returns the current hardcopy plotting device This can be overridden with Hardcopy PGPLOT device name EXit return control to XSPEC Any changes you have made to the plot will be lost D 2 PLT Command summary CLear Immediately clear the graphics device COlor Change the default colour index CONtour Produce a contour plot CPD Change the plotting device CQuit Clear the graphics device and return control to XSPEC CSize Change the default character size Error Control whether errors are displayed and used in fitting EXit Exit PLT and return control to XSPEC Fit Fit the PLT model to the data FNy FOnt Freeze GAp Grid Hardcopy HEIp Imodel LAbel LIne LOg LStyle LWidth MArker MOdel Newpar PLot PRompt Rescale SCr SHow SKip STatistics THaw Time A 299 Evaluate the model at the specified location Change the default text font Freeze a parameter value Change the default gap size between the data and the edge Control the location of the major and minor tic marks Make a file that can later be printed Obtain help on a
180. dshift z 10 4n D z distance to the source cm ne and ny are the electron and H densities cm i Jn n aV where D4 is the angular diameter For the vapec variant the parameters are as follows parl par2 parl4 plasma temperature keV Abundances for He C N O Ne Mg Al Si S Ar Ca Fe Ni wrt Solar defined by the abund command The trace element abundances are from xset APEC TRACE ABUND the default is 1 0 parl5 norm 172 redshift z 10 Rea manga where Dy is the angular diameter A distance to the source cm ne and ny are the electron and H densities cm For the vvapec variant the parameters are as follows Parl par2 par31 Par32 norm plasma temperature keV Abundances for H He Li Be B C N O F Ne Na Mg Al Si P S Cl Ar K Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn wrt Solar defined by the abund command redshift z 10 4x D 1 z J nNydV Where D is the angular diameter A distance to the source cm ne and ny are the electron and H densities cm 6 2 2 atable tabulated additive model An additive table model component The filename to be used must be given immediately after atable in the model command For example model atable mymod mod uses mymod mod as the input for the model For specifications of the table model file see the OGIP memo 92 009 on the FITS file format for table model files available on the WWW or by
181. dual components These components may be either additive multiplicative mixing or convolution Multiplicative components simply multiply the model by an energy dependent factor Convolutions apply a transformation to the model component they operated on whereby the output can be affected by a range of input energies such as in smoothing operations Mixing components are two dimensional and designed to transform fluxes between different spatial regions such as in projection Multiplicative and convolution components can act on individual components on groups of components or on the entire model whereas mixing transformations apply to the whole model The model command defines the model to be used and prompts for the starting values of its parameters The user also can set the allowed ranges of the parameter Parameters can be linked to an algebraic function of the other parameters and unlinked using the untie command The value of an individual parameter can be changed with the command newpar and the current setting queried with newpar 0 Parameters can be fixed at their current value with the freeze command and allowed to vary freely with the thaw command Individual components can be added or subtracted from the model using addcomp delcomp and editmod The plasma emission and photoelectric absorption models require an assumption about relative elemental abundances The flux command calculates the flux from the current model in the given
182. e and their sum 4 3 bbody kT kev 2 00000 frozen 5 3 bbody norm 2 29697E 04 2 04095E 05 Fit statistic Chi Squared 69 53 using 45 PHA bins The fit is better than the one with just a power law and the fixed Galactic column but it is still not good Thawing the black body temperature and fitting does of course improve the fit but the powerl law index becomes even steeper Looking at this odd model with the command XSPEC12 gt plot model We see in Figure H that the black body and the power law have changed places in that the power law provides the soft photons required by the high absorption while the black body provides the harder photons We could continue to search for a plausible well fitting model but the data with their limited signal to noise and energy resolution probably don t warrant it the original investigators published only the power law fit There is however one final useful thing to do with the data derive an upper limit to the presence of a fluorescent iron emission line First we delete the black body component using 45 delcomp then thaw Ny and refit to recover our original best fit Now we add a gaussian emission line of fixed energy and width then fit to get Model phabs lt 1 gt powerlaw lt 2 gt gaussian lt 3 gt Source No 1 Active On Model Model Component Parameter Unit Value par comp 1 1 phabs nH 10 22 0 753989 0 320344 2 2 powerlaw PhoIndex 2 38165 0 1669
183. e keV par2 Metal abundances He fixed at cosmic The elements included are C N O Ne Mg Si S Ar Ca Fe Ni Abundances are defined by the abund command par3 redshift 10 nn dV Ar D 1 2 J H where D4 is the angular diameter norm distance to the source cm ne is the electron density cm and ny is the hydrogen density cm 200 For the vequil model the parameters are parl plasma temperature keV par2 parl13 Abundances for He C N O Ne Mg Si S Ar Ca Fe Ni wrt Solar defined by the abund command parl4 Redshift z 14 2 fnna where Dy is the angular diameter z 4x D 1 z i orm distance to the source cm ne is the electron density em and ny is the hydrogen density cm The references for this model are as follows Borkowski Lyerly amp Reynolds 2001 ApJ 548 820 Hamilton A J S Sarazin C L amp Chevalier R A 1983 ApJS 51 115 Borkowski K J Sarazin C L amp Blondin J M 1994 ApJ 429 710 Liedahl D A Osterheld A L Goldstein W H 1995 ApJ 438 L11 6 2 35 expdec exponential decay An exponential decay A E exp KE where parl K exponential factor 6 2 36 ezdiskbb multiple blackbody disk model with zero torque inner boundary A multi temperature blackbody model for a thin steady state Newtonian accretion disk assuming zero torque at the inner boundary for the disk at radius R_in The temperature of the
184. e 05 5 28741 0 00831314 40 41 Variances and Principal Axes 1 2 3 1 9514E 08 0 0016 0 0007 1 0000 1 1574E 02 0 9738 0 2272 0 0014 5 3111E 01 0 2272 0 9738 0 0011 Covariance Matrix 1 2 3 3 839e 02 1 150e 01 1 427e 04 1 150e 01 5 043e 01 5 396e 04 1 427e 04 5 396e 04 6 287e 07 Model phabs lt 1 gt bremss lt 2 gt Source No 1 Active On Model Model Component Parameter Unit Value par comp 1 1 phabs nH 10 22 8 46112E 05 0 195940 2 2 bremss kT keV 5 28741 0 710133 3 2 bremss norm 8 31314E 03 7 92890E 04 Fit statistic Chi Squared 40 03 using 45 PHA bins Test statistic Chi Squared 40 03 using 45 PHA bins Reduced chi squared 0 9532 for 42 degrees of freedom Null hypothesis probability 5 576222e 01 Bremsstrahlung is a better fit than the black body and is as good as the power law although it shares the low Ny With two good fits the power law and the bremsstrahlung it s time to scrutinize their parameters in more detail First we reset our fit to the powerlaw output omitted XSPEC12 gt mo pha po From the EXOSAT database on HEASARC we know that the target in question 1E1048 1 5937 has a Galactic latitude of 24 i e almost on the plane of the Galaxy In fact the database also provides the value of the Galactic Ny based on 21 cm radio observations At 4x10 cm it is higher than the 90 percent confidence upper limit from the po
185. e command XSPEC12 gt fakeit none XSPEC will prompt the user for the response and ancillary filenames from which to build the simulated data It is important to note that a model must be defined prior to issuing this command 3 7 4 Data groups The most common use of XSPEC is to fit one or more data sets with responses to a particular model However it is often useful to be able to fit simultaneously several data sets with a model whose parameters can be different for each data set A simple example would be a number of data sets that we expect to have the same model spectrum shape but different normalizations XSPEC caters to this need through the use of data 18 groups When files are read in they can be labeled as belonging to a particular data group When a model is defined a set of model parameters is allocated for each data group These parameters can all vary freely or they can be linked together across data groups as required To set up data groups the data command should be given as in the following example XSPEC12 gt data 1 1 filel 1 2 file2 2 3 file3 which sets up two data groups The first data group comprises data sets from file1 and file2 and the second data group takes the data set from file3 Now when a model is defined XSPEC will give two sets of model parameters one for the first datagroup and one for the second 3 8 Model Commands XSPEC allows users to fit data with models constructed from indivi
186. e escape The synchrotron spectrum from an electron distribution limited by particle escape above some energy The electrons are shock accelerated in a Sedov blast wave encountering a constant density medium containing a uniform magnetic field The model includes variations in electron acceleration efficiency with shock obliquity and post shock radiative and adiabatic losses as described in Reynolds S P ApJ 493 357 1998 This is a highly specific detailed model for a fairly narrow set of conditions See also Reynolds S P ApJL 459 L13 1996 Note that the radio spectral index and flux can be obtained from Green s Catalogue at http www mrao cam ac uk surveys snrs for galactic SNRs parl alpha radio spectral index flux proportional to frequency f par2 break Hz approximately the frequency at which the flux has dropped by a factor of 6 below a straight power law extrapolation from radio frequencies This frequency is 5 3 times the peak frequency radiated by electrons with energy Em3 in a magnetic field of 48 in the notation of Reynolds 1998 Eq 19 norm 1 GHz flux Jy 6 2 77 step step function convolved with gaussian A step function convolved with a gaussian o se parl E start energy keV par2 o gaussian sigma keV norm K step amplitude 239 6 3 Multiplicative Model Components 6 3 1 absori ionized absorber An ionized absorber based on that of Done et al 1992 ApJ 395 275 and developed
187. e g by XSPEC12 gt xmodel wa po peg pl p2 A 280 Note that the model string which contains spaces needs to be entered in or double quotes Note also that tcl understands a single string argument args as in proc tclscript args to mean a variable number of arguments to a procedure it is supplied as a tcl list which can be split within the procedure into separate strings for digestion by xspec if present A 17 Script Example In the directory HEADAS spectral session isa script file called tclex xcm This script gives an example of how one might use the power of tcl s scripting language in an XSPEC session This script should be executed with XSPEC12 gt tclex This script gives an example of how one might use the power of tcl s scripting language in an XSPEC session In this example XSPEC loops thru 3 data files filel file2 and file3 and fits them each to the same model wabs potga After the fit the value of parameter 4 the line energy for the gaussian for each data set is saved to a file Keep going until fit converges query yes Open the file to put the results in set fileid open fit _result dat w for set i 1 Si lt 4 incr i Set up the model model wabs potga amp Get the file data fileSi Fit it to the model frt Get the values specified for parameter 4 tclout param 4 set par4 string trim xspec_tclout Turn i
188. e options for prior types are as follows Prior type Log prior cons 0 exp par hpar1 log hpar1 jeffreys log par gauss 0 5log 2ahpar2 0 5 hpar1 2 2 par hpar2 Where par is the parameter value and hpar the hyperparameter values jeff is an abbreviation for the Jeffreys prior which is 1 x for an assumed Gaussian distribution of the parameter 103 5 5 2 chain run a Monte Carlo Markov Chain Syntax chain burn lt length gt clear filetype fits ascii info length lt length gt load lt filename gt proposal lt distr gt lt source gt lt user defined gt rand on off run gt lt filename gt stat lt par num gt temperature lt value gt type mh gw unload lt range gt walkers lt value gt If the proposal source is set to use the fit correlation matrix the default you must perform a fit before running any chains When chains are loaded and their parameters correspond to the currently loaded model they will be used by the various XSPEC commands that require distributions of parameter values such as eqwidth or flux when calculating error estimations The error command itself will also use the loaded chains determining the error range from a central percentage of the sorted chain values This is likely to be faster than the error command s standard algorithm when not using chains burn lt length gt Specifies that the first lt length gt steps should
189. e parameter Optically thick accretion disk around a Kerr black hole 167 Model Description kerrdisk Accretion disk line emission with BH spin as free parameter laor Line from accretion disk around a black hole laor2 Line from accretion disk with broken power law emissivity around a black hole logpar Log parabolic blazar model lorentz Lorentzian line profile Ismooth Lorentzian smoothing with an energy dependent sigma lyman Voigt absorption profiles for H I or He II Lyman series meka vmeka mekal vmekal mkcflow vmcflow mtable nei vnei notch npshock vnpshock nsa nsagrav nsatmos nsmax nteea nthcomp optxagnf optxagn partcov pcfabs zpcfabs Mewe Gronenschild Kaastra thermal plasma 1992 Mewe Kaastra Liedahl thermal plasma 1995 Cooling flow model based on mekal Multiplicative table model Simple nonequilibrium ionization plasma model Notch line absorption Plane parallel shock with ion and electron temperatures Neutron star with hydrogen atmosphere Neutron star with hydrogen atmosphere for different g Neutron star H atmosphere with e conduction and self irradiation Neutron star magnetic atmosphere Pair plasma model Thermally comptonized continuum Colour temperature corrected disc and energetically coupled Comptonisation model for AGN Convert absorption model into a partial covering absorption Partial covering fraction absorption 168 Model Description peg
190. e parameters Entering lt return gt or in response to a prompt uses the default values We could also have set all parameters to their default values by entering at the first prompt As well as the parameter values themselves users also may specify step sizes and ranges lt value gt lt delta gt lt min gt lt bot gt lt top gt and lt max values gt but here we ll enter the defaults XSPEC12 gt mo pha po Input parameter value delta min bot top and max values for 1 0 001 0 01 0 0 100000 1E 06 30 1 phabs nH gt Model phabs lt 1 gt powerlaw lt 2 gt Source No 1 Active On Model Model Component Parameter Unit Value par comp 1 1 phabs nH 10 22 1 00000 0 0 2 2 powerlaw PhoIndex 1 00000 0 0 3 2 powerlaw norm 1 00000 0 0 Fit statistic Chi Squared 4 864244e 08 using 125 PHA bins Test statistic Chi Squared 4 864244e 08 using 125 PHA bins Reduced chi squared 3 987085e 06 for 122 degrees of freedom Null hypothesis probability 0 000000e 00 Current data and model not fit yet The current statistic is y and is huge for the initial default values mostly because the power law normalization is two orders of magnitude too large This is easily fixed using the renorm command XSPEC12 gt renorm Fit statistic Chi Squared 852 19 using 125 PHA bins Test statistic Chi Squared 852 19 using 125 PHA bins Reduced chi squared 6 9852 for 122 degrees of freedom
191. e same arguments as steppar The results can be plotted in 1 or 2 D using plot margin however this is not quite as useful as it might be because what is plotted is the probability not the probability within some region If MCMC chains are in use then the error command will use them to estimate the parameter uncertainty B 4 Goodness of fit Parameter values and confidence regions only mean anything if the model actual fits the data The standard way of assessing this is to perform a test to reject the null hypothesis that the observed data are drawn from the model Thus we calculate some statistic T and if Tobs gt Teriticat then we reject the model at the confidence level corresponding to Teritical Ideally Triticat is independent of the model so all that is required to evaluate the test is a table giving Teritica Values for different confidence levels This is the case for X which is one of the reasons why it is used so widely However for other test statistics this may not be true and the distribution of T must be estimated for the model in use then the observed value compared to that distribution This is done in XSPEC using the goodness command The model is simulated many times and a value of T calculated for each fake dataset These are then ordered and a distribution constructed This distribution can be plotted using plot goodness Now suppose that To s exceeds 90 of the simulated T values we can reject the model at 90 confidence
192. e that the APECROOT value gives the complete directory path e g XSPEC12 gt xset APECROOT foo bar apec v1 2 0 will use the input files foo bar apec_v1 2 0_coco fits foo bar apec v1 2 0_line fits The bapec model uses abundances set by the abund command The bvapec and bwvapec variants allow the user to set the abundance using additional parameters For bapec and bvapec the abundances of the trace elements ie Li Be B F Na P Cl K Sc Ti V Cr Mn Co Cu Zn can be set using xset APEC_TRACE ABUND These trace element abundances can be set either to the abundance of one of the main elements or to a numerical value relative to Solar For instance XSPEC12 gt xset APEC TRACE ABUND Fe sets trace element abundances to that of iron while XSPEC12 gt xset APEC TRACE ABUND 1 0 sets them to Solar For the vapec model the parameters are parl Plasma temperature keV par2 par3 par4 norm 174 Metal abundances He fixed at cosmic The elements included are C N O Ne Mg Al Si S Ar Ca Fe Ni Relative abundances are set by the abund command Redshift z Gaussian sigma for velocity broadening km s 10 4x D 2 to the source cm ne and ny are the electron and H densities cm Jn ny aV where Dy is the angular diameter distance For the bvapec variant the parameters are as follows parl par2 par14 parl5 parl6 norm
193. e to an erroneous model calculation e C style comments have been removed from xsFortran h for the benefit of users compiling their own C programs with the models library e Plotting fix for case where setplot area is selected and no models are currently loaded e Model parsing fix for case of nested parentheses with no operator ie A B C D v12 5 0 Nov 2008 Two of the remaining unimplemented v1 1 commands have now been added mdefine allows dynamic definition of models that can be expressed algebraicly recornrm has been replaced by the recorn model This allows the correction norm to be treated as a fit parameter a better solution than the v11 recornrm command The complete HTML help files are included in a tar file These can be made available on a local machine if remote access is now available and selected in the Xspec init file Convolution components can now operate on multiplicative components For example in the model CM A the convolution component acts on only the multiplicative component Previously this would have been treated the same as C MA The partcov partial covering model takes advantage of this new capability There is a new simple way of estimating fluxes and their errors from parts of the model Apply the cflux convolution model to the component s for which the flux is required The following models have been added as standard diskir irradiated disk e kerrdisk broad iron line fro
194. e to power the entire SED is L eff Mdot c where the efficiency is set by black hole spin assuming Novikov Thorne emissivity There are two versions of the model Optxagnf is the one recommended for most purposes and has the colour temperature correction calculated for each temperature from the approximations given in Done et al 2011 Optxagn instead allows the user to define their own colour temperature correction fcol which is then applied to annuli with effective temperature gt Tscatt In both models the flux is set by the physical parameters of mass L Lrgq spin and distance hence the model normalisations MUST be frozen at unity Parameters in Optxagnf parl mass Black hole mass in solar masses par2 dist Comoving proper distance in Mpc par3 logL Ledd Eddington ratio par4 astar Dimensionless black hole spin par5 rcor Coronal radius in R GM c marking the transition from colour temperature corrected blackbody emission to a Comptonised spectrum If this parameter is negative then only the blackbody component is used par6 logrout Log of the outer radius of the disc in units of R if this is ve the code will use the self gravity radius as calculated from Laor amp Netzer 1989 par7 kT_e par8 tau par9 Gamma parl0 fpl parl1 Redshift norm K Parameters in Optxagn parl mass par2 dist par3 logL Ledd par4 astar par5 rcor par6 logrout par7 kT_e par8
195. e various additive components are also plotted If using a named model the model name should be given as an additional argument emodel plots Ef E or if 146 plotting wavelength Af X eemodel plots E f E or if plotting wavelength ARA The E or 2 used in the multiplicative factor is taken to be the geometric mean of the lower and upper energies of the plot bin ratio Plot the data divided by the folded model residuals Plot the data minus the folded model sensitvty Plot the sensitivity of the current spectrum to changes in the incident spectra experimental sum A pretty plot of the data and residuals against both channels and energy ufspec eufspec eeufspec Plot the unfolded spectrum and the model The contributions to the model of the various additive components also are plotted WARNING This plot is not model independent and your unfolded model points will move if the model is changed The data points plotted are calculated by D unfolded model folded model where D is the observed data unfolded model is the theoretical model integrated over the plot bin and folded model is the model times the response as seen in the standard plot data eufspec plots the unfolded spectrum and model in Ef E or if plotting wavelength Af A eeufspec plots the unfolded spectrum and model in E f E or if plotting wavelength f A The E or A used in the multiplicative factor is taken to be the geometric mean of the lowe
196. ear why this happens although binning to ensure that every bin contains at least one count often seems to fix the problem In the limit of large numbers of counts per spectrum bin a second order Taylor expansion shows that W tends to x S t m ST B ST 2 t m f j tf which is distributed as x with N M degrees of freedom where the model m has M parameters include the normalization For Poisson data with Gaussian background pgstat Another possible background option is if the background spectrum is not Poisson For instance it may have been generated by some model based on correlations between the background counts and spacecraft orbital position In this case there may be an uncertainty associated with the background which is assumed to be Gaussian In this case the same technique as above can be used to derive a profile likelihood statistic N PG 29 t m f S ln t m 1 5 B nf S 1 InS oO i l i where t 07 1 B t m d w and 2 d dro t B tom 4t tom S0 1 B m There is a special case for any bin with S equal to zero P t m B t t 0 50 t This is what is used for the statistic pgstat option Bayesian analysis of Poisson data with Poisson background Istat An alternative approach to fitting Poisson data with background is to use Bayesian methods In this case instead of solving for the background rate parameters we marginalize o
197. eavsastiuazece vindicate viacuacatdeacegavininanabenael 19 iii 3 9 1 What to do when you have Poisson data nnsnnnnnnnnnnnnnnnnnnnnnnnnnne 20 3 9 2 Binning and Grouping data cecccceesseeeeeeeeeeeeseeeeeeeeeseneeeeeeeeneeeeeeees 20 3 10 Plotting CommandS nssssssunnnnnnennnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn nnmnnn 20 3 11 Setting Command S in nuien stevinciaietaacnadetinnaintiann saccade 21 3 12 Breaking With Ctrl C aaansnnesssnnnnnnnnennnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn nnna 22 3 13 GUSTOMIZING XSPEC eo siiicccissscscewedcsacewesessnescteneraseteruaneueaceseeseaenasaueidens 22 3 13 1 Customizing system wide csscccceseeeeeeeeeeeeeeeeseseeeeeeseseeneessseeneeeeees 25 Walks thr ugh XSPEC rninha aa aaco SENN a 26 4 1 IMMFOGUGCTION cic isieicisccccictecssnsedsccdscetecccscntesctevececededsdndesessdecccecedaascersterece 26 4 1 1 Brief Discussion Of XSPEC Files csssessseeeeeeeeseeeeeeeeeeeeeeeeeeenennees 26 4 2 Fitting Models to Data An Old Example from EXOSAT 26 4 3 SIMUMANEOUS FING siisvcisisiccdstuicccdndcancncadwdecnesavenadaaucedwicaddadvenaniadues 45 4 4 Multiple Models a Background Modeling Example 0 49 4 5 Using XSPEC to Simulate Data an Example for Chandra 51 4 6 Producing Plots Modifying the Defaults eens 54 4 7 INTEGRAL SP srciccscsaciccsecececenecaseusneatawanevstowsnewstowsnewsousnewssousewctawsneus
198. ec gt is the same as for the backgrnd command The correction file can be associated with a spectrum to further adjust the count rates It is a PHA file whose count rate is multiplied by the current associated correction norm see the cornorm and recornrm command and then subtracted from the input uncorrected data The correction norm is not changed by running the corfile command Default values for the correction file and norm are included in the data PHA file Unlike the background file the correction data does NOT contribute to the measurement error A file name of none 89 is equivalent to no correction file used If an input file can not be opened or found an error message is printed and the user prompted for a replacement As with the backgrnd command the correction file is checked against the associated spectrum for number of channels grouping status and detector ID The current ignore status for channels is not affected by the corfile command Note that correction files have the same format as the PHA files used by the data command Examples It is assumed that there are currently three spectra XSPEC12 gt corfile a b c New correction files are used for all three spectra gt XSPEC12 gt corfile 2 none No correction will be done for the second spectrum XSPEC12 gt corfile d The 2nd file now uses d pha as its correction XSPEC12 gt corfile 2 e 4 5 Rows 4 and 5 of Type II file e pha becom the correction files f
199. ectory gt To load the new proposal s into XSPEC XSPEC12 gt lmod lt name gt lt directory gt where lt name gt is the name you choose for the package collection of proposal classes It will also become the library file name The only differences from the local models case are that here the initializer file MUST be named randomize dat and that the directory path to the proposal classes either relative or absolute must be provided on the command line If this is left off XSPEC will default to looking in the directory set by LOCAL MODEL _ DIRECTORY and these classes should NOT be stored in the same directory as local models If the building and loading has successfully completed you should see the proposal name the same name string that was passed to the RandomizerBase constructor appear in the chain proposal list displayed by typing chain proposal with no other arguments A 310 Appendix H Changes between v11 and v12 In 1998 we decided to re engineer XSPEC using modern computer science methods so it could continue fulfilling its role as a mission independent X ray spectral fitting program The program s internal design layout and data structures have largely been rewritten in ANSI C using object oriented design techniques generic programming techniques and design patterns The thoroughgoing reanalysis has also allowed a number of improvements in overall design and at robustness as well as maintainability without changi
200. ectra numbered 3 or higher XSPEC12 gt data 3 none removes only spectrum 3 and renumbers the rest The data command determines the current total number Nr of spectra either Nr spectra are implied by the command line or the highest spectrum number added after XSPEC has made corrections as mentioned above is Nr This is true UNLESS a character terminates the data command If the line is terminated by a slash then the current number of spectra is the previous total number of datsets N or the number as determined from the command line whichever is greater The command XSPEC12 gt data by itself prints the one line help summary as does XSPEC12 gt data data groups XSPEC allows the user to specify separate data groups for different spectra Each data group has its own set of parameters for the defined model These parameters can be either independent from data group to data group or they can be linked across data groups using the standard XSPEC syntax see the newpar command This facility can be used for say analyzing extended sources Note that the data group number precedes the spectrum number in the example XSPEC12 gt data 2 3 spectrum4 93 which assumes that at least two spectra are already present the data group number is 2 and the spectrum number is 3 XSPEC will not allow the data group number to exceed the spectrum number for example XSPEC12 gt data 3 2 spectrum4 is invalid XSPEC will correct
201. ed energies to the source frame Other new features New models ireflect is a convolution model based on the pexriv code sirf is a multiblackbody self irradiated funnel The normalizations on all power law models ie powerlaw bknpow bkn2pow cutoffpl can be changed to a flux over an energy range by setting POW_EMIN A 318 and POW_EMAX keywords in xset The powerlaw model then becomes equivalent to the pegpwlw model The Compton reflection models b p exr a i v and i reflect have been restructured to use adaptive Gauss Kronrod quadrature for the Greens function integrals The precision to which the integrals are calculated can be set allowing a trade off between speed and precision The wrapper functions additiveTable and multiplicativeTable give external C models access to XSPEC s table model interpolation routines equivalent to the xsatbl and xsmtbl functions for Fortran models The display of link expressions has been simplified to show only the parameter numbers and not the extraneous component information Also show model will now only display the model components and not the individual parameters The parameters can be seen with show par Additional enhancements previously released as patches to 12 5 1 Added the solar abundance data set of Asplund Grevesse and Sauval 2006 to the list of available tables accessed with the abund command New tclout nchan option for returning the number of channels in a s
202. ed as the starting point for more complicated scripting of xspec 5 9 1 Irt likelihood ratio test between two models Tcl script to perform a likelihood ratio test between two models Syntax Irt lt niter gt lt model0 name gt lt modell name gt lt filename gt Runs lt niter gt simulations of datasets based on lt model0_name gt calculates the likelihood ratio for lt modell_name gt relative to lt model0 name gt calculated by the statistic for lt model0_ name gt minus the statistic for lt modell_ name gt and outputs the fraction of iterations with the likelihood ratio smaller than that for the data If the optional filename is given then the simulation results are written to the file The first line of the file contains the results for the data the other lines the simulations Each line comprises the statistic values for lt model0_name gt the statistic value for lt modell_name gt and the difference Before running this procedure you must have created command files called lt model0_name gt xcm and lt modell_name gt xcm which define the two models A good way to do this is to set up the model then use save model to make the command file 5 9 2 multifake perform multiple fakeit iterations and save to file Tcl script to perform many iterations of fakeit and save the results in a FITS file Syntax multifake lt time gt lt niter gt lt outfile gt XSPEC Models 162 This script runs lt niter gt iterations of f
203. ed medium 2 0sseeeeeee 226 6 2 65 plcabs powerlaw observed through dense cold matter 227 6 2 66 POSM positronium CONTINUUM cccccccessseeeeneeneeeeeeeeeeeeseeceeeeeeeeeennes 228 6 2 67 powerlaw zpowerlw power law photon spectrum 2 000 228 6 2 68 pshock vpshock plane parallel shocked plasma constant TOMPCLatUle ecccccccceeccneecneeeeesceeseeesseesenoeseoecneeseeeceoeceeeseeeecnoeceeecneeseeeenos 229 6 2 69 raymond vraymond emission hot diffuse gas Raymond Smith 230 6 2 70 redge emission recombination edge s eeeccessseeeeneeeeeteeeeenneees 231 6 2 71 refsch reflected power law from ionized accretion disk 232 6 2 72 sedov vsedov sedov model separate ion electron temperature 233 6 2 73 sirf self irradiated funnel 2 c eeseeeseeeseeeseeeseeeeeeeeeeeeneeeeeeees 234 6 2 74 smaug optically thin spherically symmetric thermal plasma 235 6 2 75 srcut synchrotron spectrum Cutoff power laW c eseeeeeeeeees 237 6 2 76 sresc synchrotron spectrum cut off by particle escape 238 6 2 77 step step function convolved with gaussian 0sseseeee 238 6 3 Multiplicative Model Components sseeeeeeeeeeeeeeees 239 6 3 1 absori ionized abSOrbe 2 s eeseeeeseeeseeeseeeseeeseeeseeeeneeeseeeeeeees 239 6 3 2 acisabs Chandra ACIS q e A CAay csecccseeeeee
204. ed to an accuracy of 0 01 i e 1 This can be changed using e g xset NTEEA PRECISION 0 05 The abundances are set up by the command abund Send questions or comments to aaz camk edu pl parl nonthermal electron compactness par2 blackbody compactness par3 scaling factor for reflection 1 for isotropic source above disk par4 blackbody temperature in eV par5 the maximum Lorentz factor par6 thermal compactness 0 for pure nonthermal plasma par7 Thomson optical depth of ionization electrons e g 0 par8 electron injection index 0 for monoenergetic injection ard minimum Lorentz factor of the power law injection not used for P monoenergetic injection parl0 minimum Lorentz factor for nonthermal reprocessing lt Par10 lt par9 parl1 radius in cm for Coulomb bremsstrahlung only parl2 pair escape rate in c 0 1 see Zdziarski 1985 ApJ 289 514 par13 cosine of inclination angle parl4 iron abundance relative to that defined by abund parl5 redshift z photon flux of the direct component w o reflection at 1 keV in the norm observer s frame 221 6 2 59 Nthcomp Thermally comptonized continuum Nthcomp is a much better description of the continuum shape from thermal comptonisation than an exponentially cutoff power law but is not that much more complicated in terms of parameters The high energy cutoff is sharper than an exponential and is parameterized by the electron temperature kT_e VERY roughly an exponential rollover ener
205. eeeeeeeeeeeeeeeeeeeeees 14 Sel SYM D AA A A 14 3 2 Howto return to the XSPEC gt prompt cccceeeeeeeeeeeeeeeeeeeeeeeeeseneeees 14 3 3 Getting Help nsssssnnnnnnnennnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn nnmnnn nnmnnn 14 3 4 Command S wactccccteccsccccscacacctwctsccccscacatitaciaciaassnaataeasieacaessneataeseacataanaces 14 3 5 ISSUING COMMANAS vi seis cciseedecciiecisccdiesdesndsendendientvendsendeederedsesdusndeneen 15 3 6 Control ComMmmandS ssssssssssssnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn nnmnnn 15 3 6 1 Query chatter and shutting XSPEC up somewhat ccceeeeeeseeee 16 3 6 2 Scripts and the Save command cccceeeceseeeeeeeeeeeeeeeeeeneeeeeesesseeneeeees 16 3 6 3 Miscellaneous dtesiccecsvascsecs coaducensnsvarrcassecersisara cceaduustenaswndanianave duteateteaeratee 16 3 7 Data COMMANGS arara ea aaaea aaa aaea aaa aaaea aa ara naaa araida aiaiai 17 3 7 1 Reading data and modifying calibration and auxiliary files 17 3 7 2 Controlling channels being fitted ccccceeeeceeeeeeeeeeeeeeeeeeeeseneeneeeees 17 AT Ae ees ULES Le aE T ne ner OTe ye 17 3 7 4 Data QIOUP Ss tieicccesiedersutessecsuiteicviscutincteddiadcuutuniuledoueddiivaddnsldcuidddntandan 17 3 8 Model CommandS s sssssssssssnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn nnmnnn nnna 18 3 8 1 Models with multiple responses and background models 19 3 9 Fitting CommandS basic iecdustetdusvecavt
206. eeeeeeeeeeneeenees 77 5 3 10 show output Current program State seeeeeeeeeeeeeeeseeeeeeeeeeeeneeenees 77 5 3 11 syscall execute a Shell command eeeeeeeee ee eeeeeeeeeeeeeeeeeeeeeeennnnees 78 5 3 12 tclout create tcl variables from Current State sceeeeeeeeeeeeneeeeeee 80 5 3 13 tcloutr tclout With return ValUC cccecessseeeeneeeeeeeeeeeeeeeeeeeeeeeeeeeeenenees 85 5 3 14 time print EXECUTION TIIMEC ceeeeeeeeeeeeeneeneneeeeneeeeeeeeeeeeeeneneeeeeeeeennenees 86 5 3 15 undo undo the previous command ee 86 5 3 16 version print the version String cccccccssseeesneeeeeeeeeeeeeeseeneeeeeeeeenenneees 86 5 4 BEE olalar lae a A A A A A T A AA 87 iv 5 4 1 arf change the efficiency file for a given reSPONSE ccceeeeeeeeees 87 5 4 2 backgrnd change the background file for a given spectrum 87 5 4 3 corfile change the correction file for a given spectrum 00 88 5 4 4 cornorm change the normalization of the correction file 89 5 4 5 data read data background and responses eee 90 5 4 6 diagrsp set a perfect response for a spectrum 0seeeeee 94 5 4 7 fakeit simulate observations of theoretical MOdelS cccssseeees 94 5 4 8 ignore ignore detector Channel s cccccssseeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeneneees 98 5 4 9 notice notice data channels ce iin 99 5 4 10 r
207. efault postscript driver will be used The default postscript driver produces a monochrome plot in landscape orientation The filename argument can be followed by a that specifies a particular postscript driver variant Allowable variants are cps color postscript vps monochrome portrait orientation and veps color portrait orientation as well as the default ps Set the device used for plots PGPLOT devices A number of plot device types are supported in XSPEC PGPLOT devices available on Unix machines are GIF Graphics Interchange Format file landscape orientation VGIF Graphics Interchange Format file portrait orientation NULL Null device no output PPM Portable Pixel Map file landscape orientation VPPM Portable Pixel Map file portrait orientation PS PostScript file landscape orientation VPS PostScript file portrait orientation CPS Colour PostScript file landscape orientation VCPS Colour PostScript file portrait orientation TEK4010 Tektronix 4010 terminal GE GraphOn Tek terminal emulator RETRO Retrographics VT640 Tek emulator GTERM Color gterm terminal emulator XTERM XTERM Tek terminal emulator ZSTEM ZSTEM Tek terminal emulator V603 Visual 603 terminal 149 KRM3 Kermit 3 IBM PC terminal emulator TK4100 Tektronix 4100 terminals VT125DEC VT125 and other REGIS terminals XDISP pgdisp or figdisp server XWINDOW X window window
208. egration required for the Compton reflection calculation is performed to an accuracy of 0 01 i e 1 This can be changed using e g xset COMPPS PRECISION 0 05 The model parameters are as follows parl Te electron temperature in keV par2 p electron power law index N gamma gamma p par3 gmin minimum Lorentz factor gamma par4 gmax maximum Lorentz factor gamma a if any of gmin or gmax lt 1 then Maxwellian electron distribution with parameter Te b if Te 0 then power law electrons with parameters p gmin gmax c if both gmin gmax gt 1 but gmax lt gmin then cutoff Maxwellian with Te p gmin cutoff Lorentz factor as parameters d if Te ne 0 gmin gmax gt 1 then hybrid electron distribution with parameters Te p gmin gmax parS Tbb temperature of soft photons Tbb gt 0 blackbody Tbb lt 0 multicolor disk with inner disk temperature Tbb par6 if gt 0 tau vertical optical depth of the corona if lt 0 y 4 Theta tau limits for the slab geometry tau lt 1 if say tau 2 increase MAXTAU to 50 for sphere tau lt 3 par7 geom 0 approximate treatment of radiative transfer using escape probability for a sphere very fast method 1 slab 2 cylinder 3 hemisphere 4 5 sphere input photons at the bottom of the slab cylinder hemisphere or center of the sphere or from the central plane of the slab 188 if cov_fact not 1 if lt 0 then geometry defined by geom and sources of incident photons
209. el is given in Heinke et al 2006 ApJ in press astro ph 0506563 see also McClintock et al 2004 ApJ 615 402 219 parl Log Terr unredshifted effective temperature par2 Mss neutron star gravitational mass in units of Solar mass par3 Rss true neutron star radius km par4 dist distance to the neutron star in kpc K fraction of the neutron star surface emitting 6 2 57 nsmax Neutron Star Magnetic Atmosphere This model interpolates from a grid of neutron star NS atmosphere spectra to produce a final spectrum that depends on the parameters listed below The atmosphere spectra are obtained using the latest equation of state and opacity results for a partially ionized strongly magnetized hydrogen or mid Z element plasma The models are constructed by solving the coupled radiative transfer equations for the two photon polarization modes in a magnetized medium and the atmosphere is in radiative and hydrostatic equilibrium The atmosphere models mainly depend on the surface effective temperature T and magnetic field strength B and inclination Og there is also a dependence on the surface gravity g 1 z GMIR where 1 z 1 2GM R is the gravitational redshift and M and R are the NS mass and radius respectively Two sets of models are given one set with a single surface B and Tefrand a set which is constructed with B and T varying across the surface according to the magnetic dipole model for the latter Om is the ang
210. en response Read in one or more auxiliary response files ARF An ARF gives area versus energy and is used to modify the response matrix for a spectrum The file must be in the OGIP standard format Syntax arf lt filespec gt where lt filespec gt source lt spectrum num gt lt filename gt ranges and where lt spectrum num gt is the spectrum number for the first lt filename gt specified lt spectrum num gt plus one is the spectrum number for the next file or next entry in ranges specifier for Type II multi ARF files and so on lt filename gt is the name of the auxiliary response file to be used with the associated spectrum The optional source number defaults to 1 and for ARFs stored in OGIP Type II files ranges specifies the row numbers of the desired ARF s See the data command for allowed range specification Ifno lt spectrum num gt is given in the first lt filespec gt it is assumed to be 1 If no file specifications are entered then none of the spectrum responses are modified An error message is printed if the spectrum number is greater than the current number of spectra as determined from the last use of the data command A file name none indicates that no auxiliary response is to be used for that spectrum If a file is not found or cannot be opened for input then the user is prompted for a replacement auxiliary response file An lt EOF gt at this point is equivalent to none See the data com
211. ened to the fit statistic during the run XSPEC12 gt plot chain 0 The result is shown in Figure K which plots the statistic value against the chain step It is clear that after about 2000 steps the chain reached a steady state We would usually have told XSPEC to discard the first few thousand steps but included them for illustrative purposes Let us do this again but specifying a burn in phase that will not be stored XSPEC12 gt chain burn 5000 XSPEC12 gt chain run testl fits The output chain now comprises 10 000 steady state samples of the parameter probability distribution Repeating plot chain 0 will confirm that the chain is in a steady state The other parameter values can be plotted either singly using eg plot chain 2 for the power law index or in pairs eg plot chain 1 2 giving a scatter plot as shown in Figure L Using the error command at this point will generate errors based on the chain values XSPEC12 gt error 1 2 3 Errors calculated from chains Figure L The scatter plot from a 10 000 step MCMC run 59 Parameter Confidence Range 2 706 1 0 264971 0 919546 2 2 1134 2 41307 3 0 0107304 0 0171814 The 90 confidence ranges are determined by ordering the parameter values in the chain then finding the center 90 4 7 INTEGRAL SPI 4 7 1 A Walk Through Example Consider an observation of the Crab for which a standard 5 x5 dithering observation strategy was employed Since the Crab pulsar and nebula
212. ensity temperature and metal abundance determined by a simultaneous fit of the spectra The cosmological parameters can be set using the cosmo command part par2 par3 par4 pard par6 par7 par8 par9 par10 par11 par12 par13 par14 par15 par16 par17 par18 par19 par20 par21 236 central temperature keV max difference of temperature keV exponent of the inner temperature radius of the inner temperature Mpc exponent of the middle temperature radius of the middle temperature Mpc exponent of the outer temperature radius of the outer temperature Mpc central hydrogen density cm 3 fraction of nH cc relative to the 1st beta component exponent of the first beta component radius of the 1st beta component Mpc exponent of the 2nd beta component radius of the 2nd beta component Mpc central metallicity solar units exponent of the metal distribution radius of the metal distribution Mpc redshift of the source number of mesh points of the dem summation grid cutoff radius for the calculation Mpc mode of spectral evaluation 0 calculate 1 interpolate 2 APEC interpolate 237 par22 type of plasma emission code 1 Raymond Smith 2 Mekal 3 Meka 4 APEC K model normalisation nH cc squared cm 6 Ho Hubble constant km s Mpc qo deceleration parameter Lo cosmological constant DA source angular distance Mpc DSET dataset no to whi
213. ent a mixing component which operates on the model pre multiplied by the effective area This is similar to the pile up model type but allows for a models which require mixing between multiple spectra Table model files can now have interpolated and additional parameters intermixed provided that additional parameters are indicated by METHOD 1 in the PARAMETERS extension Enhancements previously released as patches to 12 7 1 The plot chain has a new thin option for thinning the display of chain points Added a tclout ignore option for easy retrieval of currently ignored channels Similar capability added to PyXspec s Spectrum class All bug fixes to v12 7 1 released as patches are included in v12 8 0 In addition the following problems have been corrected The eqpair model used wrongly sized arrays when multiple spectra were used with RMFs having varying numbers of photon energy bins Eqpair plus eqtherm and compth also needed a new default value for its optical depth parameter which fixes the problem if parameter 4 is zero A fit parameter which started close to the minimum maximum could under some circumstances be incorrectly pegged at the maximum minimum When the error command was run on a model with soft limits ie soft limits for some parameters set to a narrower range than hard limits and the best fit value fell within the soft limit region the displayed differences in parentheses were not consistent with the rep
214. er lies The answer to this question is the confidence interval for the parameter The confidence interval for a given parameter is computed by varying the parameter value until the X increases by a particular amount above the minimum or best fit value The amount that the Z is allowed to increase also referred to as the critical AY depends on the confidence level one requires and on the number of parameters whose confidence space is being calculated The critical AZ for common cases are given in the following table from Avni 1976 Confidence Parameters 1 2 3 0 68 1 00 2 30 3 50 0 90 2 71 4 61 6 25 0 99 6 63 9 21 11 30 2 3 The XSPEC implementation To summarize the preceding section the main components of spectral fitting are as follows e A set of one or more observed spectra D 1 with background measurements B I where available e The corresponding instrumental responses 7 E e A set of model spectra M e These components are used in the following manner e Choose a parameterized model which is thought to represent the actual spectrum of the source e Choose values for the model parameters e Based on the parameter values given predict the count spectrum that would be detected by the spectrometer in a given channel for such a model e Compare the predicted spectrum to the spectrum actually obtained by the instrument e Manipulate the values of t
215. ere D is the angular diameter distance to the source cm and ne ny em are the electron and hydrogen densities respectively For vnpshock the parameters are 216 parl Mean shock temperature keV par2 electron temperature immediately behind the shock front keV par3 H density in cm par4 parl5 Abundances for He C N O Ne Mg Si S Ar Ca Fe Ni wrt Solar given by the Anders amp Grevesse mixture parl6 Lower limit on ionization timescale in units of s cm parl7 Upper limit on ionization timescale in units of s cm par18 redshift z norm 107 n n dV l l ir DiS zf J H where Dy is the angular diameter distance to the source cm and ne ny cm are the electron and hydrogen densities respectively 6 2 54 nsa neutron star atmosphere This model provides the spectra in the X ray range 0 05 10 keV emitted from a hydrogen atmosphere of a neutron star There are three options nonmagnetized B lt 10 10 G with a uniform surface effective temperature in the range of log T K 5 0 7 0 a field B 10 G with a uniform surface effective temperature in the range of log 7 K 5 5 6 8 a field B 10 G with a uniform surface effective temperature in the range of log T K 5 5 6 8 The atmosphere is in radiative and hydrostatic equilibrium sources of heat are well below the atmosphere The Comptonization effects significant at 7 gt 3x10 K are taken i
216. ergies minimize an objective function S of C R 1 E M E using a fitting algorithm i e S S C gt Mj oR In the default case this reduces to the specific expression for X fitting of a single source S C R M where i runs over all of the channels in all of the spectra being fitted and using the Levenberg Marquadt algorithm to perform the fitting This differs from the previous formulation in that the operations that control the fitting process make fewer assumptions about how the data are formatted what function is being minimized and which algorithm is being employed At the calculation level XSPEC requires spectra backgrounds responses and models but places fewer constraints as to how they are represented on disk and how they are combined to compute 10 the objective function statistic This has immediate implications for the extension of XSPEC analysis to future missions New data formats can be implemented independently of the existing code so that they may be loaded during program execution The data format includes the specification not only of the files on disk but how they combine with models Multiple sources may be extracted from a spectrum For example it generalizes the fitting problem to minimizing in the case of the Y i statistic x lt gt R oM and j runs over one or more models This allows the analysis of coded aperture data where multiple sources may be spatially
217. ern CCD instruments If some other sort of noise is dominant then it is usually described by the Gaussian distribution A common example of this is detectors that require background to be modeled in some way rather than directly measured The uncertainty in the background modeling is assumed to be Gaussian In the limit of large numbers of counts the Poisson distribution can be well approximated by a Gaussian so the latter is often used for detectors with high counting rates In most cases this will cause no errors and does simplify the handling of background uncertainties however care should be exercised that no systematic offsets are introduced A fuller discussion of many of the issues discussed in this appendix can be found in Siemiginowska 2011 B 2 Parameter Estimation The standard statistic used in parameter estimation is the maximum likelihood This is based on the intuitive idea that the best values of the parameters are those that maximize the probability of the observed data given the model The likelihood is defined as the total probability of observing the data given the model and current parameters In practice the statistic used is twice the negative log likelihood For Gaussian data chi The likelihood for Gaussian data is A 282 where y are the observed data rates o their errors and m the values of the predicted data rates based on the model with current parameters and instrumental response Taking twice the ne
218. error command uses one of two algorithms If Monte Carlo Markov Chains are loaded see chain command the error range is determined by sorting the chain values and then taking a 108 central percentage of the values corresponding to the confidence level as indicated by lt delta fit statistic gt This is likely to be the faster of the two algorithms When chains are not loaded error s algorithm is as follows Each indicated parameter is varied within its allowed hard limits until the value of the fit statistic minimized by allowing all the other non frozen parameters to vary is equal to the last value of fit statistic determined by the fit command plus the indicated lt delta fit statistic gt to within an absolute not fractional tolerance of lt toler gt Note that before the error command is executed the data must be fitted The initial default values are the range 1 1 and the lt delta fit statistic gt of 2 706 equivalent to the 90 confidence region for a single interesting parameter The number of trials and the tolerance for determining when the critical fit statistic is reached can be modified by preceeding them with the stopat keyword Initially the values are 20 trials with a tolerance of 0 01 in fit statistic If a new minimum is found in the course of finding the error then the calculation is aborted and control returned to the user The maximum keyword ensures that error will not be run if the reduced chi squared of
219. es He fixed at cosmic The elements included are C N O Ne Mg Si S Ar Ca Fe Ni Abundances are defined by the abund command par3 Ionization timescale in units of s cm par4 Ionization timescale averaged plasma temperature keV pars fixed redshift 10 norn NNydV where D4 is the angular diameter 4n D 1 2 204 distance to the source cm ne and ny cm are the electron and hydrogen densities respectively For vgnei the parameters are parl plasma temperature keV par2 parl3 Fixed Abundances for He C N O Ne Mg Si S Ar Ca Fe Ni wrt Solar defined by the abund command parl4 Ionization timescale in units of s cm parl5 Ionization timescale averaged plasma temperature keV parl6 fixed redshift 107 f J MetnudV where Dy is the angular diameter Gai 4r D 1 z distance to the source cm and ne ny cm are the electron and hydrogen densities respectively 6 2 40 grad accretion disk Schwarzschild black hole General Relativistic Accretion Disk model around a Schwarzschild black hole Inner radius is fixed to be 3 Schwarzschild radii thus the energy conversion efficiency is 0 057 See Hanawa T 1989 ApJ 341 948 and Ebisawa K Mitsuda K and Hanawa T 1991 ApJ 367 213 Several bugs were found in the old GRAD model which was included in xspec 11 0 lae and before Due to these bugs it turned out that the mass obtained by fitting the old GRAD model to the observation was 1 4 tim
220. es over estimated These bugs were fixed and a new parameter par6 was added to make the distinction between the old and new codes clear parl par2 par3 par4 pars distance kpc disk inclination angle deg 0 for face on mass of the central object solar units mass accretion rate 10 gs spectral hardening factor Too1 Terr Should be greater than 1 0 and considered to be 1 5 1 9 for accretion disks around a stellar mass black hole See e g Shimura and Takahara 1995 ApJ 445 780 205 par6 A flag to switch on off the relativistic effects never allowed to be free If positive relativistic calculation if negative or zero Newtonian calculation the inner radius is still fixed at 3 Schwarzschild radii and the efficiency is 1 12 norm Should be fixed to 1 6 2 41 grbm gamma ray burst continuum A model for gamma ray burst continuum spectra developed by D Band et al 1993 ApJ 413 281 K E 100 exp E E E lt a E A E K E 100 100 exp a a E gt a E where is in units of keV parl a first power law index par2 a second power law index par3 E characteristic energy in keV norm K normalization constant 6 2 42 kerrbb multi temperature blackbody model for thin accretion disk around a Kerr black hole A multi temperature blackbody model for a thin steady state general relativistic accretion disk around a Kerr black hole The effect of self irradiat
221. es were ignored since the source flux becomes insignificant relative to the background Some results are illustrated below These plots were generated with the sequence of commands XSPEC12 gt setplot group 1 19 XSPEC12 gt plot ldata res 62 XSPEC12 gt plot ufspec Note that without the setplot group command XSPEC would plot 19 sets of spectral data models and residuals The can become confusing especially as the number of spectra included in an analysis becomes much larger than 19 On the other hand it can be useful to divide the data into subsets for plotting purposes e g setplot group 1 6 7 12 13 19 to get an idea of relative shadowing effects of the coded mask The left hand plot illustrates the source model the background model the total model i e source background and the data here in count rates per channel The right hand plot illustrates the unfolded model blue power law curve the summed model and the data as a photon flux A possible source of confusion is the similarity of the background model curves plotted in theses two separate representations The explanation is that the background which is dominated by instrumental contributions is modeled in detector count space i e the background response matrix has unit effective area Thus to be strictly correct the right hand plot is a hybrid of the photon source model and the detector rate background model We further note that at the present time
222. esponse change the detector response for a spectrum 101 5 5 Fit COMMANGS araa aarre aaaea an an aaar an aiaa iaaii 102 5 5 1 bayes set up for Bayesian inference snsnennnnnnrennnnnnnnnnnnnn nnmnnn 102 5 5 2 chain run a Monte Carlo Markov Chain aaasssssussnnnnnnnnnnnnnnnnennnnnnnn 103 5 5 3 error uncertain determine confidence intervals of a fit 107 5 5 4 gt fiti fit data ae mo iene eee Senor pen ene iiaa Eee Snr eee 109 5 5 5 freeze set parameters as fixed ccceccccessseeeeeneeeeeeeeeeeeeeeeeneeeeeeeeeenense 110 5 5 6 ftest calculate the F statistic from two chi square values 110 5 5 7 goodness perform a goodness of fit Monte Carlo simulation 111 5 5 8 margin MCMC probability distribution cccceeeeteseeeeeeeeeeeeeeeees 111 5 5 9 renorm renormalize model to minimize statistic with current Parameters siinccieeivedieidieni eceiedeendeneieataaainerteneiveniden tannin NAR oiTa 112 5 5 10 steppar generate the statistic surface for 1 or more parameters 112 5 5 11 thaw allow fixed parameters tO Vary sssseecereeeeeeeeeeseeeeeeeeeeeeenees 113 5 5 12 weight change weighting used in computing statistic 114 5 6 Modell COMMANGS sisssisccsesicsccrssteicarestriccrsaccdensacndaardacndenrdsauanavdaanaeds 114 5 6 1 addcomp add component to a MOdEl eeeceeeeeeeeeeeeeeeeeeeeeennnes 115 5 6 2 addline add spectral lines to a mo
223. ession ABS expr absolute value of a vector expression INT expr integer part of a vector expression ASIN expr ACOS expr II sin 1 of a vector expression in rad cos 1 of a vector expression in rad MEAN expr mean value of a vector expression DIM expr dimension of a vector expression SMIN expr minimum value of a vector expression SMAX expr maximum value of a vector expression Binary Functions 132 MAX exprl expr2 MIN exprl expr2 maximum of the two vector expressions minimum of the two vector expressions define a model named dplaw with parameters pl p2 f define a model named junk with parameters a b define a model named junk2 with parameter a the option ollowing says that it will be multiplicative model define a model named jJunk3 with parameter B options following says that this will be a ultiplicative model try to define a blackbody model ith name bb you get warning re defined model rent name for your model 6 283 A sqrt Gl con this defines a Gaussian convolution model with sigma varying with square root of energy delete junk2 display all user defined models Examples XSPEC12 gt mdef dplaw E pl f E p2 3 XSPEC12 gt mdef junk a etb log e sin e 2 XSPEC12 gt mdef junk2 exp a e mul 1
224. esult of the last ftest command For gain fit parameters value delta min low high max for the slope or offset parameter belonging to the lt sourceNum gt lt specNum gt response For nonfit gain parameters only the value is returned The percentage of realizations from the last goodness command with statistic value less than the best fit statistic using the data If optional sims keyword is specified this will instead give the full array of simulation values from the last goodness command Possible line IDs within the range e d e d The range s of the ignored channels for spectrum lt n gt Last model luminosity calculated for spectrum n Same output format as flux option in units of 1 0x10 erg s The probability option returns the probability column respectively from the most recent margin command Otherwise the parameter column indicated by lt parNum gt is returned Note that for multi dimensional margin the returned parameter column will contain duplicate values in the same order as they originally appeared on the screen during the margin run Description of current model s modcomp lt mod gt modpar lt mod gt modval lt specNum gt lt mod nchan lt n gt noticed lt n gt noticed energy lt n gt nullhyp param lt mod gt n peakrsid n lo hi pinfo lt mod gt n plink lt mod gt n plot lt option gt lt array gt lt plot group n gt plotgrp
225. ethod which continues until a given estimated fractional precision is reached The precision can be changed by setting IREFLECT_PRECISION eg xset IREFLECT_ PRECISION 0 05 The default precision is 0 01 ie 1 parl reflection scaling factor 1 for isotropic source above disk par2 z redshift par3 abundance of elements heavier than He relative to the solar abundances par4 iron abundance relative to the above pars cos i the inclination angle pars disk temperature in K 262 par9 Toa disk ionization parameter 4r a where Fion is the 5eV 20keV irradiating flux n is the density of the reflector see Done et al 1992 ApJ 395 275 6 4 5 kdblur convolve with the laor model shape A convolution model to smooth a spectrum by relativistic effects from an accretion disk around a rotating black hole Uses Ari Laor s calculation including GR effects ApJ 376 90 Modified from laor model by Andy Fabian and Roderick Johnstone parl Index power law dependence of emissivity scales as R par2 inner radius units of GM c par3 outer radius units of GM c par4 inclination degrees 6 4 6 kdblur2 convolve with the laor2 model shape A convolution model to smooth a spectrum by relativistic effects from an accretion disk around a rotating black hole The accretion disk has a broken power law emissivity profile Uses Ari Laor s calculation including GR effects ApJ 376 90 Modified from laor2 model by Andy Fabian and
226. ever the syntax understood by XSPEC12 is much the same as before A 2 XSPEC and tcl tk Because tcl is a full scripting language users can write complex scripts with loops branching etc which utilize XSPEC commands Here we describe how to use those features of tcl necessary to give the user similar functionality to that available in previous versions of XSPEC and to give information on the details of our tcl implementation that may be useful to experienced tcl users For a description of tcl see for example Practical Programming in Tcl and Tk B Welch 1997 Prentice Hall Tk tcl s companion graphical user interface GUI toolkit is also loaded by XSPEC on startup It is planned that future versions of XSPEC will provide an optional GUI side by side with the command line interface CLI Although XSPEC does not currently use tk its presence allows users to write XSPEC scripts with graphical interfaces using Tk commands A 3 A note on command processing To emulate the performance of the former XSPEC parser the command functions are programmed to react similarly to some of its features The sign is used for comments in tcl but may appear only at the beginning of a command tcl and XSPEC both ignore carriage returns on a new line but XSPEC also ignores the skip character The character sequence entered during a command exits that command sets any responses to the default response and returns the user to the
227. f are also described below x NOTE Backwards incompatible syntax change Beginning with XSPEC 12 5 1 gain parameters must be specified as lt sourceNum gt lt specNum gt and NOT lt specNum gt lt sourceNum gt This reversal was made so that the gain command conforms to the lt sourceNum gt lt specNum gt usage in other XSPEC commands such as response and arf 5 6 10 identify identify spectral lines List possible lines in the specified energy range 128 Syntax identify lt energy gt lt delta_energy gt lt redshift gt lt line list gt The energy range searched is lt energy gt A lt energy gt keV in the rest frame of the source If working in wavelength mode as set by the setplot command then the lt energy gt and lt delta energy gt parameters should be entered as wavelengths in Angstroms lt line list gt specifies the list of lines to be searched The options are bearden which searches the Bearden compilation of fluorescence lines Bearden J A 1967 Rev Mod Phys 39 78 mekal which uses the lines from the mekal model q v and apec which uses the APEC http cxc harvard edu atomdb line list The apec option takes an additional two arguments the temperature of the plasma keV and a minimum emissivity of lines to be shown If the command xset has been used to set APECROOT then identify uses the APECROOT value to define the new atomic physics data files See the help on the apec mode
228. f iterations and critical delta chi squared XSPEC12 gt fit 60 Fit with 60 as the number of iterations XSPEC12 gt fit 50 1 e 3 Fit with 1 e 3 as the critical delta XSPEC12 gt fit 50 1 e 3 20 Same fit but will now use beta N 20 0 as another stopping criterion in addition to that of the critical delta XSPEC12 gt fit delay Same fit but will now use delayed gratification 110 5 5 5 freeze set parameters as fixed Do not allow indicated model parameters to vary See also thaw Syntax freeze lt param range gt where lt param range modelName lt param gt lt param gt lt param gt For response parameters see gain command rfreeze lt param range gt where lt param range source number lt param gt lt param gt lt param gt The indicated model parameter or range of model parameters will be marked so they cannot be varied by the fit command By default the range will be the last range input by either a freeze or thaw command Examples Currently there are six parameters initially all unfrozen XSPEC12 gt freeze 2 Parameter 2 is frozen XSPEC12 gt freeze 4 6 Parameters 4 5 and 6 are frozen XSPEC12 gt thaw 2 3 5 Parameters 2 4 and 5 are thawed parameter 3 is unaffected XSPEC12 gt freeze Parameters 3 4 5 are frozen the last range input by a freeze or thaw command XSPEC12 gt rfreeze 4 6 Response par
229. f possible actual values 4 6 Producing Plots Modifying the Defaults The final results of using XSPEC are usually one or more tables containing confidence ranges and fit statistics and one or more plots showing the fits themselves So far the plots shown have generally used the default settings but it is possible to edit plots to improve their appearance The plotting package used by XSPEC is PGPLOT which is comprised of a library of low level tasks At a higher level is QDP PLT the interactive program that forms the interface between 55 the XSPEC user and PGPLOT QDP PLT has its own manual it also comes with on line help Here we show how to make some of the most common modifications to plots In this example we ll take the simulated Chandra spectrum and make a better plot Figure I shows the basic data and folded model plot The only additional changes we have made to this plot are to increase the line widths to make them print better We made this plot as follows XSPEC12 gt setplot energy XSPEC12 gt iplot data PLT gt lwidth 3 PLT gt lwidth 3 on 1 2 PLT gt time off PLT gt hard figi ps ps The first lwidth command increases the line widths on the frame while the second increases it on the data and model The time off command just removes a username and time stamp from the bottom right of the plot The hard command makes a hardcopy in this case a PostScript file Before looking at other PLT commands we can use to
230. factor z is the spectral 190 6 2 20 comptb Thermal and bulk Comptonization of a seed blackbody like spectrum This model describes the Comptonization spectrum of soft photons off electrons which are either purely thermal or additionally subjected to an inward bulk motion It consists of two components one is the direct seed photon spectrum and the other one is the Comptonizated spectrum The latter is obtained as a self consistent convolution of the seed photon spectrum with the system Green s function The model is not specific to bulk Comptonization but it includes in a coherent way different spectral shapes such as simple blackbody i e neither thermal nor bulk Comptonization thermal Comptonization equivalent to compTT and thermal plus bulk Comptonization In the latter case it can be considered a completion and update of the BMC model as it includes the cut off term in the spectrum All mathematical details of the model and its validity limits for applications are reported in Farinelli et al 2008 ApJ 680 602 parl kT temperature of the seed photons keV par2 gamma index of the seed photon spectrum default gamma 3 par3 alpha energy index of the Comptonization spectrum par4 delta bulk parameter efficiency of bulk over thermal Comptonization par5 kT temperature of the electrons keV par6 log A log of the illuminating factor parameter A norm Normalization of the seed photon spectrum defined in t
231. filename specified is assigned to 1 If spectra have already been loaded at this point they will be replaced deleted or added to depending on the command For example if there are 3 spectra loaded N 3 and the user types XSPEC12 gt data multidatafile 1 2 then spectra 1 and 2 will be replaced and 3 deleted The command XSPEC12 gt data multidatafile 1 4 will replace all three spectra and add the fourth If the user specifies a load point i e the first spectrum number to be created by the new command i e XSPEC12 gt data 3 multidatafile 1 4 For OGIP files any FITS NULL values will be converted to the value 1 E 32 This should have no practical effect because any channels with NULL values will presumably be marked as bad or otherwise ignored 92 then that load point may not exceed N 1 If it does XSPEC will correct the number and issue a warning A skipped over argument can be effected by a comma for example XSPEC12 gt data 3 spectrum spectrum2 indicates that the spectrum for that position as input in an earlier invocation of data will continue to be used in this example spectrum 3 is replaced 4 is left untouched and 5 is either replaced or added Any spectra with numbers great than 5 are removed If the filename input is none that spectrum is removed and so are any higher number spectra unless none is terminated with a character For example XSPEC12 gt data 3 none removes all sp
232. files 26 4 Walks through XSPEC 4 1 Introduction This chapter demonstrates the use of XSPEC The brief discussion of data and response files is followed by fully worked examples using real data that include all the screen input and output with a variety of plots The topics covered are as follows defining models fitting data determining errors fitting more than one set of data simultaneously simulating data and producing plots 4 1 1 Brief Discussion of XSPEC Files At least two files are necessary for use with XSPEC a data file and a response file In some cases a file containing background may also be used and in rare cases a correction file is needed to adjust the background during fitting If the response is split between an rmf and an arf then an ancillary response file is also required However most of the time the user need only specify the data file as the names and locations of the correct response and background files should be written in the header of the data file by whatever program created the files 4 2 Fitting Models to Data An Old Example from EXOSAT Our first example uses very old data which is much simpler than more modern observations and so can be used to better illustrate the basics of XSPEC analysis The 6s X ray pulsar 1E1048 1 5937 was observed by EXOSAT in June 1985 for 20 ks In this example we ll conduct a general investigation of the spectrum from the Medium Energy ME instrument i e follow
233. following XSPEC12 gt model wa potpha pegtedge diskt bbod const pla posthr step not gau Applying multiple models Assume 3 spectra are loaded each with a single response source 1 by default XSPEC12 gt model wa po The unnamed model wa po will apply to all 3 spectra accordingly multiplied by each spectrum s response XSPEC12 gt response 2 2 new_resp pha 2 3 another new _resp pha Additional responses assigned to source number 2 for spectra 2 and 3 XSPEC12 gt model 2 second_mod ga The model second_mod will now apply to source 2 and is therefore multiplied by new_resp pha and another new_resp pha for spectra 2 and 3 respectively XSPEC12 gt model second_mod inactive second_mod will no longer apply to spectra 2 and 3 though they retain responses for source 2 OR XSPEC12 gt response 2 2 none XSPEC12 gt response 2 3 none No responses exist for source number 2 second_mod is rendered inactive 137 5 6 16 modid write out possible IDs for lines in the model Tcl script to write out possible IDs for gaussian or lorentzian lines in the current model Syntax modid lt delta gt conf This script runs the identify command for every gaussian or lorentzian line included in the current model If a number is given as an argument then that is used as the delta energy for identify If the string conf is given as the argument then the last calculated conf
234. for 1 0 001 0 01 0 0 100000 le 06 1l phabs nH gt 0 08 1 0 001 0 01 0 0 100000 1le 06 2 zphabs nH gt 1 0 0 0 01 0 01 0 999 0 999 10 10 3 zphabs Redshift gt 5 1 52 0 01 0 01 3 2 9 10 4 zpowerlw PhoIndex gt 1 7 0 0 01 0 01 0 999 0 9 99 10 10 5 zpowerlw Redshift gt 5 1 1 0 01 0 01 0 0 let 24 le 24 6 zpowerlw norm gt Model phabs lt 1 gt zphabs lt 2 gt zpowerlw lt 3 gt Source No 1 Active Off Model Model Component Parameter Unit Value par comp 1 1 phabs nH 10 22 8 00000E 02 0 0 2 2 zphabs nH 10 22 1 00000 0 0 3 2 zphabs Redshift 5 10000 frozen 4 3 zpowerlw PhoIndex 1 70000 0 0 5 3 zZpowerlw Redshift 5 10000 frozen 6 3 zpowerlw norm 1 00000 0 0 Now suppose that we know that the observed 0 5 2 5 keV flux is 1 1x10 ergs em s We now can derive the correct normalization by using the commands energies flux and newpar That is we ll determine the flux of the model with the normalization of unity We then work out the new normalization and reset it XSPEC12 gt energies 0 5 2 5 1000 XSPEC12 gt flux 0 5 2 5 Model Flux 0 052736 photons 1 0017e 10 ergs cm 2 s range 0 50000 2 5000 keV XSPEC12 gt newpar 6 1 1le 3 3 variable fit parameters XSPEC12 gt flux Model Flux 2 6368e 05 photons 5 0086e 14 ergs cm 2 s range 0 50000 2 5000 keV Here we have changed the value of the n
235. ful for putting constraints on M and R from spectral fits to thermal emission detected from neutron stars provided the quality of the observational data are good enough to warrant a detailed analysis The parameters M and R can be fixed at specific values or allowed to vary within a reasonable range see the note above For example one can run spectral fits on a M R grid using the steppar command within the allowed parameter domain see above Please send your comments questions if any to Slava Zavlin vyacheslav zavlin msfc nasa gov and or George Pavlov pavlov astro psu edu If you publish results obtained using this model please reference Zavlin et al 1996 A amp A 315 141 parl Log Tere unredshifted effective temperature par2 Mss neutron star gravitational mass in units of Solar mass par3 Rss true neutron star radius km K 1 D where D is the distance to the object in pc 6 2 56 nsatmos NS Hydrogen Atmosphere model with electron conduction and self irradiation This model interpolates from a grid of NS atmosphere calculations provided by George Rybicki and Ramesh Narayan to output a NS atmosphere spectrum The model grids cover a wide range of surface gravity and effective temperature and incorporate thermal electron conduction and self irradiation by photons from the compact object This code assumes negligible less than 10 9 G magnetic fields and a pure hydrogen atmosphere A detailed description of the mod
236. g For the gadem version the abundance ratios are set by the abund command The vgadem variant allows the user to define the abundances See the documentation on the apec model for information on using additional elements included in AtomDB v2 The parameters for gadem are parl mean temperature for gaussian emission measure distribution par2 sigma temperature for gaussian emission measure distribution par3 ny cm par4 abundance relative to solar par5 redshift z 0 calculate using MEKAL model par6 1 interpolate using MEKAL model 2 interpolate using APEC model norm Normalization 202 For the vgadem variant the parameters are parl mean temperature for gaussian emission measure distribution par2 sigma temperature for gaussian emission measure distribution 3 par3 ny cm par4 abundance relative to solar Abundances for He C N O Ne Na Mg 17 Al Si S Ar Ca Fe Ni wrt Solar defined by the abund command parl8 redshift z 0 calculate using MEKAL model parl9 1 gt interpolate using APEC model 2 interpolate using APEC model norm Normalization 6 2 38 gauss zgauss gaussian line profile A simple gaussian line profile If the width is lt 0 then itis treated as a delta function The zgauss variant computes a redshifted gaussian 2s l E E AE K a where parl E line energy in keV par2 o line width in keV Norm K total photons cm s in the line For zgauss the corresponding f
237. g 45 PHA bins Test statistic Chi Squared 823 34 using 45 PHA bins Reduced chi squared 19 148 for 43 degrees of freedom Null hypothesis probability 6 151383e 145 Current data and model not fit yet The same result can be obtained by putting everything onto the command line i e newpar 1 4 0 or by issuing the two commands newpar 1 4 followed by freeze 1 Now if we fit and plot again we get the following model Fig G XSPEC12 gt fit Model phabs lt 1 gt powerlaw lt 2 gt Source No 1 Active On Model Model Component Parameter Unit Value 43 par comp 1 1 phabs nH 10322 4 00000 frozen 2 2 powerlaw PhoIndex 3 59784 6 76670E 02 3 2 powerlaw norm 0 116579 9 43208E 03 Fit statistic Chi Squared 136 04 using 45 PHA bins The fit is not good In Figure G we can see why there appears to be a surplus of softer photons perhaps indicating a second continuum component To investigate this possibility we can add a component to our model The editmod command lets us do this without having to respecify the model from scratch Here we ll add a black body component XSPEC12 gt editmod pha potbb Input parameter value delta min bot top and max values for 3 0 01 0 03 0 0001 0 01 100 200 4 bbody kT gt 2 0 1 0 01 0 01 0 0 let 24 let 24 5 bbody norm gt le 5 Fit statistic Chi Squared 132 76 using 45 PHA bins Test statistic Chi Squared 132 76 using 45 PHA bins Reduced chi squa
238. gative natural log of L and ignoring terms which depend only on the data and will thus not change as parameters are varied gives the familiar statistic N T 2 S 5O m i l O L commonly referred to as y and used for the statistic chi option For Gaussian data with background chi The previous section assumed that the only contribution to the observed data was from the model In practice there is usually background This can either be included in the model or taken from another spectrum file read in using the back command In the latter case the y become observed data rates from the source spectrum subtracted by the background spectrum and the o are the source and background errors added in quadrature Since the difference of two Gaussians variables is another Gaussian variable the S statistic can still be used in this case For Poisson data cstat The likelihood for Poisson distributed data is TIn exp tm S where S are the observed counts t the exposure time and m the predicted count rates based on the current model and instrumental response The maximum likelihood based statistic for Poisson data given in Cash 1979 is N C 2 tm S In tm 1nS i 1 Castor priv comm has pointed out that modifying this by a quantity that depends only on the data and hence makes no difference to the best fit parameters to give C 2 _ tm S S In S In zm provides a statistic which asympt
239. ged in future The input energies are set by the response matrices of the detectors in use IFL is an integer which specifies to which response and therefore which spectrum these energies correspond It exists to allow multi dimensional models where the function might also depend on eg pulse phase in a variable source The output flux array should not be assumed to have any A 295 particular values on input It is assumed to contain previously calculated values only by convolution pileup models which have the nature of operators The output flux error array allows the function to return model variances The C and C call types allow one extra argument which is a character string that can be appended to the top line of the model component description This string is read on initialization and available to the model during execution An example of its use might be the name of a file with specific data used in the model calculation this allows different models to be implemented the same way except for different input data by specifying different names and input strings C 4 Third Party Libraries In Local Models Build The Makefile that initpackage creates for building your local models library is based on the template file heasoft ver Xspec src tools initpackage xspackage tmpl If you need to add a path to a third party library s header files add I path to your 3rdParty library include to the HD_CXXFLAGS setting Then type hmake and hm
240. good fit The null hypothesis probability can be calculated analytically for x but not for some other test statistics so XSPEC provides another way of determining the meaning of the statistic value The goodness command performs simulations of the data based on the current model and parameters and compares the statistic values calculated with that for the real data If the observed statistic is larger than the values for the simulated data this implies that the real data do not come from the model To see how this works we will use the command for this case where it is not necessary XSPEC12 gt goodness 1000 47 40 of realizations are lt best fit statistic 43 80 nosim XSPEC12 gt plot goodness Approximately half of the simulations give a statistic value less than that observed consistent with this being a good fit Figure C shows a histogram of the y values from the simulations with the observed value shown by the vertical dotted line So the statistic implies the fit is good but it is still always a good idea to look at the data and residuals to check for any systematic differences that may not be caught by the test To see the fit and the residuals we produce figure D using the command XSPEC12 gt plot data resid Histogram fram goodness command 34 0 1 5 Fe a 0 05 0 30 40 50 60 70 r Figure C The result of the command plot goodness The histogram shows the fraction of simulations with a given value
241. gt Ifno lt spectrum range gt is given then the previous range is used the initial default range is file one 1 only The form of lt spectrum range gt is lt spectrum range gt lt init spectrum gt lt last spectrum gt lt spectrum gt where lt init spectrum gt lt last spectrum gt and lt spectrum gt are spectrum numbers in the order that they were input with the data command The form of channel range is lt channel range gt lt initial channel gt lt last channel gt lt channel gt If lt channel range gt are integers then channels will be used or if reals then energies or wavelengths if setplot wave has been specified Energy and wavelength units are determined by the setplot energy and wave settings If only the last channel is indicated then a default value of 1 is used for the initial channel Channels remain noticed until they are explicitly ignored with the ignore command When a spectrum is replaced by another spectrum all input channels automatically are noticed XSPEC12 gt notice all resets all the channels to noticed Examples Assume that 4 spectra have been read in the first 2 having 100 channels and the last 2 having 50 channels Assume also that channels 1 10 of all four spectra are ignored and that channels 80 100 of spectra 1 and 2 are ignored In XSPEC12 notice does not force the detector response to be reread see RESPONSE DESCRIPTION XSPEC12 gt notice
242. gt flux Calculate the current model flux over the default range XSPEC12 gt flux 6 4 7 0 Calculate the current flux over 6 4 to 7 keV XSPEC12 gt flux 1 10 The flux is calculated from 1 5 keV the lower limit of the current response s sensitivity to 10 kev 5 6 9 gain modify a response file gain Modify a response file gain in a particularly simple way CAUTION This command is to be used with extreme care for investigation of the response properties To properly fit data the response matrix should be recalculated explicitly outside of XSPEC using any modified gain information derived The gain command shifts the energies on which the response matrix is defined and shifts the effective area curve to match The effective area curve stored by XSPEC is either the ARF if one was in use or is calculated from the RSP file as the total area in each energy range This means that if there are sharp features in the response then these will only be handled correctly by the gain command if they are in the ARF or if no ARF is input The new energy is calculated by E E lt slope gt lt intercept gt where lt intercept gt is in units of keV Syntax gain lt sourceNum gt lt specNum gt lt slope gt lt intercept gt gain fit lt sourceNum gt lt specNum gt gain nofit lt sourceNum gt lt specNum gt all 125 gain off The first variant of the gain command shown above will apply the
243. gy E_c 2 3kT_e but the shape is very different so it impacts on the reflected fraction as well Another major effect especially for X ray binaries is that it incorporates the low energy rollover The hot electrons Compton UPscatter seed photons so there are few photons in the scattered spectrum at energies below the typical seed photon energies making it significantly different to a power law below this energy Typically the physical picture is that these seed photons are quasi blackbody eg neutron star boundary layer or disk blackbody in shape Either of these shapes can be selected input type both being parameterized by a seed photon temperature kT_bb Between the low and high energy rollovers the shape of the spectrum is set by the combination of electron scattering optical depth and electron temperature It is not necessarily a power law but can be parameterized by an asymptotic power law index Gamma Details of this are given in Zycki Done amp Smith 1999 including a self consistent reflection component which is NOT released here as it was written using non FITS standard files so has significant issues with portability This is the thermally comptonized continuum model of Zdziarski Johnson amp Magdziarz 1996 MNRAS 283 193 as extended by Zycki Done amp Smith 1999 MNRAS 309 561 Please reference these papers if you use it parl Gamma asymptotic power law photon index par2 kT e electron temperature high energy ro
244. h are proportional to the current parameter value rather than fixed For example XSPEC12 gt xset delta 15 will set each parameter fit delta to 15 parVal To turn proportional deltas off and restore the original fixed deltas set delta to a negative value or 0 0 The current proportional delta setting can be seen with show control The lt string name gt option can be used to pass string values to models XSPEC maintains a database of lt string name gt lt string value gt pairs created using this command Individual model functions can then access this database Note that xset does no checking on whether the lt string_ name gt is used by any model so spelling errors will not be trapped To access the lt string name gt lt string_ value gt database from within a model function use the fortran function fgmstr This is defined as character 128 and takes a single argument the string name as a character 128 Ifthe lt string name gt has not been set then a blank string will be returned The current lt string name gt options models to which they apply and brief descriptions are given in the following table APECROOT apec vapec bapec bvapec Switch from default equil vequil npshock APEC input files vnpshock pshock vpshock sedov vsedov c6mekl c6vmekl c6pmekl c6pvmekl cemkl cevmkl mekal vmekal mkcflow vmclow XSPEC Models APECTHERMAL apec vapec bapec bvapec equil vequil np
245. h a delta fit statistic 1 contour counts Plot the data with the folded model if defined with the y axis being numbers of counts in each bin data Plot the data with the folded model if defined delchi Plot the residuals in terms of sigmas with error bars of size one dem Plot the relative contributions of plasma at different temperatures for multi temperature models This is not very clever at the moment and only plots the last model calculated 145 eemodel See model eeufspec See ufspec efficien Plot the total response efficiency versus incident photon energy emodel See model eufspec See ufspec goodness Plot a histogram of the statistics calculated for each simulation of the most recent goodness command run icounts Integrated counts and folded model The integrated counts are normalized to unity insensitv Plot the insensitivity of the current spectrum to changes in the incident spectra experimental Icounts Plot the data with the folded model if defined with a logarithmic y axis indicating the count spectrum Idata Plot the data with the folded model if defined with a logarithmic y axis margin Plot the probability distribution from the results of the most recently run margin command Must be a 1 D or 2 D distribution model emodel eemodel Plot the current incident model spectrum Note This is NOT the same as an unfolded spectrum The contributions of th
246. he same way as the bbody model 6 2 21 compTT Comptonization Titarchuk This is an analytic model describing Comptonization of soft photons in a hot plasma developed by L Titarchuk see ApJ 434 313 This replaces the Sunyaev Titarchuk Comptonization model in the sense that the theory is extended to include relativistic effects Also the approximations used in the model work well for both the optically thin and thick regimes The Comptonized spectrum is determined completely by the plasma temperature and the so called B parameter which is independent of geometry The optical depth is then determined as a function of B for a given 191 geometry Thus par5 switches between spherical and disk geometries so that B is not a direct input here This parameter MUST be frozen If par5 20 f is obtained from the optical depth using analytic approximation e g Titarchuk 1994 If par5 lt 0 and 0 1 lt t lt 10 B is obtained by interpolation from a set of accurately calculated pairs of B and t from Sunyaev amp Titarchuk 1985 A amp A 143 374 In this incarnation of the model the soft photon input spectrum is a Wien law x e photons because this lends itself to a particularly simple analytical form of the model For present X ray detectors this should be adequate Note that in energy flux space the peak of the Wien law occurs at 3kT as opposed to 2 8kT for a blackbody The plasma temperature may range from 2 500 keV but the model is n
247. he beta test site for new releases The initial development of XSPEC was funded by a Royal Society grant to Prof Andy Fabian and subsequent development was partially funded by the European Space Agency s EXOSAT project and is now funded by the HEASARC at NASA GSFC 1 5 References Arnaud K A 1996 Astronomical Data Analysis Software and Systems V eds G Jacoby and J Barnes p17 ASP Conf Series volume 101 Dorman B and Arnaud K A 2001 Astronomical Data Analysis Software and Systems X eds F R Harnden Jr F A Primini and H E Payne vol 238 p 415 Dorman B Arnaud K A and Gordon C A XSPEC12 Object Oriented X Ray Data Analysis AAS HEAD meeting No 35 22 10 2 Spectral Fitting and XSPEC 2 1 Introduction This chapter comprises a brief description of the basics of spectral fitting their application in XSPEC and some helpful hints on how to approach particular problems We then provide more details on the way XSPEC provides flexibility in its approach to the minimization problem We also describe the data formats accepted 2 2 The Basics of Spectral Fitting Although we use a spectrometer to measure the spectrum of a source what the spectrometer obtains is not the actual spectrum but rather photon counts C within specific instrument channels I This observed spectrum is related to the actual spectrum of the source f E by CU f E RU EME Where R I E is the instrumental response and is pr
248. he data statement in the above example will be executed as if the following had been entered data 1 1 eso103 sO 20 data 2 2 esol04 sl 20 The tcl info command can be used to show which procedures have been defined XSPEC12 gt info commands lt procedure name gt This will return lt procedure name gt if that procedure has been compiled source d already or is a built in command or nothing if it has not yet been invoked or defined A 16 Scripting commands that prompt the user The commands model editmod addmod newpar and fakeit may prompt the user for more information when used interactively In order to write scripts that use these commands one must know how to force XSPEC to enter the information that would be prompted for The technique is exemplified as follows Suppose we defined a procedure xmodel that makes a model with certain predefined parameter values set pl 1 5 0 001 0 0 1 E05 1 E06 set p2 1 0 001 0 0 1 E05 1 E06 proc xmodel modelString paraml param2 args model SmodelString amp Sparaml amp param2 amp Here the amp character is taken by XSPEC as a carriage return delimiting the model string and parameter arguments into separate input lines The procedure xmodel may be compiled with the command XSPEC12 gt source xmodel tcl This creates xmodel as a command with two arguments which sets subsequent parameters to their default values It can be invoked
249. he full energy ranges of the Swift UVOT and XMM Newton OM detectors The transmission is set to unity shortward of 912 Angstroms in the rest frame of the dust This is incorrect physically but does allow the model to be used in combination with an X ray photoelectric absorption model such as phabs The extinction curve contains no spectral features and is characterized by a powerlaw slope over spectral wavelength This model has been justified by e g Savaglio amp Fall 2004 ApJ 614 293 because the apparent low metallicities within GRB hosts result in no significant spectral features within the extinction curve unlike those found in local galaxies The extinction at V A V E B V x Rv Standard values for Rv are Milky Way 3 08 LMC 3 16 and SMC 2 93 from table 2 of Pei 1992 ApJ 395 130 although these may not be applicable to more distant dusty sources parl E B V color excess par2 ExtIndex spectral index of the extinction curve par3 Rv ratio of total to selective extinction par4 z redshift 258 6 3 40 zvfeabs photoelectric absorption with free Fe edge energy Redshifted photoelectric absorption with all abundances tied to Solar except for iron The Fe K edge energy is a free parameter parl equivalent hydrogen column in units of 10 atoms cm par2 abundance relative to Solar par3 iron abundance relative to Solar par4 Fe K edge energy pars redshift z 6 3 41 zxipcf partial covering absorption by partially io
250. he gain issue is resolved acisabs calculates the mass absorption coefficients of the contaminant from atomic scattering factor files provided at http henke lbl gov optical_constants asf html 240 parl Days between Chandra launch and ACIS observation par2 Slope of linear quantum efficiency decay par3 Offset of linear quantum efficiency decay par4 Number of carbon atoms in hydrocarbon par5 Number of hydrogen atoms in hydrocarbon par6 Number of oxygen atoms in hydrocarbon par7 Number of nitrogen atoms in hydrocarbon 6 3 3 cabs Optically thin Compton scattering Optically thin Compton scattering M E exp n o E where or E is the Thomson cross section with Klein Nishina corrections at high energies Note that this model does not do frequency downshifting so is only valid for scattering out of the beam parl 4 hydrogen column in units of 10 atoms cm 6 3 4 constant energy independent factor An energy independent multiplicative factor par1 factor 6 3 5 cyclabs absorption line cyclotron A cyclotron absorption line as used in pulsar spectra See Mihara et al Nature 1990 or Makishima et al PASJ 1990 2 2 W E Ese 4D W E 2E ya PORSE uV We 2h E 2E Wr Cc C M E exp D parl Dr depth of the fundamental 241 par2 Ey cyclotron energy par3 Wr width of the fundamental par4 Dz depth 2nd harmonic par5 Wy width of the 2nd harmonic 6 3 6 dust dust
251. he parameters of the model until the best fit between the theoretical model and the observed data is found Then calculate the goodness of the fit to determine how well the model explains the observed data and calculate the confidence intervals for the model s parameters This section describes how XSPEC performs these tasks C I The Observed Spectrum To obtain each observed spectrum C 1 XSPEC uses two files the data spectrum file containing D I and the background file containing B 1 The data file tells XSPEC how many total photon counts were detected by the instrument in a given channel XSPEC then uses the background file to derive the set of background subtracted spectra C I in units of counts per second The background subtracted count rate is given by for each spectrum ca 2D bro BY adto bgo aste where D I and B T are the counts in the data and background files and t are the exposure times in the data and background files bp and bza apg and apg are D the background and area scaling values from the spectrum and background respectively which together refer the background flux to the same area as the observation as necessary When this is done XSPEC has an observed spectrum to which the model spectrum can be fit R E The Instrumental Response Before XSPEC can take a set of parameter values and predict the spectrum that would be detected by a given instrument XSPEC must know the spec
252. he user to the XSPEC prompt while the iplot command leaves the user in the interactive plotting interface thus allowing the user to edit the plot A variety of different quantities may be plotted including the data and the current model the integrated counts the fit residuals the ratio of data to model the contributions to the fit statistic the theoretical model the unfolded incident spectrum the detector efficiency the results of the goodness command and the fit statistic contours All data plots can have an x axis of channels energy or wavelength which are specified with setplot channel setplot energy setplot wavelength respectively A number of different units are available for energy or 21 wavelength The plotting device to be used is set using setplot device or cpd Separate spectra may be added together and channels binned up for plotting purposes only using setplot group and ungrouped with setplot ungroup and setplot rebin There is an option to plot individual additive model components on data plots this option is enabled by setplot add and disabled by setplot noadd The effective area can be divided out of data plots using setplot area which option can be turned off using setplot noarea Line IDs can be plotted using setplot id and turned off by setplot noid A stack of PLT commands can be created and manipulated with setplot command setplot delete and setplot list This command stack then is applied to every plot
253. heir own responses The model will be referred to the channel space using a response corresponding to that source number To create a model for a source number higher than 1 a detector response must first exist for that number See the examples below and the response command for more information about using multiple sources This ability to assign multiple models both generalizes and replaces the XSPEC11 method of using b to specify background models After the model is loaded if there are data present the model is attached through the instrumental response to the spectra to be fitted as in XSPEC11 Unlike XSPEC11 however if there are no data loaded the model will be attached to a default diagonal dummy response The parameters of that dummy response energy range number of flux points linear logarithmic intervals can be set by the user in the Xspec init file using the DUMMY setting Thus any model can be plotted in energy or wavelength space as soon as it has been defined The model components are of various types depending on what they represent and how they combine with other models additive multiplicative convolution pile up and mixing models Each component may have one or more parameters that can be varied during the fit see the newpar command writeup e Additive model components are those directly associated with sources such as power laws thermal models emission lines etc The net effect of two independent additive mode
254. hen accelerated particles are electrons from parl0 thermal pool if 1 then accelerated particles are electrons and positrons parll cosIncl inclination of reflecting material wrt line of sight ar12 Refl fraction of scattering region s emission intercepted by P reflecting material par13 Fe_abund relative abundance of iron parl4 Ab gt He relative abundance of other metals 199 par15 Taisk temperature of reflecting disk parl6 amp ionization parameter of reflector parl7 B power law index with radius of disk reflection emissivity parl8 Rin inner radius of reflecting material GM c parl9 Rout outer radius of reflecting material GM c par20 Redshift z norm 6 2 34 equil vequil collisional plasma ionization equilibrium Ionization equilibrium collisional plasma model This is the equilibrium version of Kazik Borkowski s NEI models Several versions are available To switch between them use the xset neivers command xset neivers 1 0 gives the version from xspec v11 1 xset neivers 1 1 uses updated calculations of ionization fractions using dielectronic recombination rates from Mazzotta et al 1988 and xset neivers 2 0 uses the same ionization fractions as 1 1 but uses APED to calculate the resulting spectrum Note that versions 1 x have no emission from Ar The default is version 1 1 The vequil variant allows the user to set the abundances for the model For the equil model the parameters are parl plasma temperatur
255. here where parl E line energy keV par2 W line width keV par3 f covering fraction 6 3 18 pcfabs zpcfabs partial covering fraction absorption A partial covering fraction absorption The relative abundances are set by the abund command M E f exp n o E 1 f where o E is the photo electric cross section NOT including Thomson scattering see phabs and parl ny equivalent hydrogen column in units of 10 atoms cm par2 f covering fraction 0 lt par2 lt 1 dimensionless The redshifted variant zpcfabs is given by M E fexp n 0 E 1 z 1 f where o E is the photo electric cross section NOT including Thomson scattering see phabs Relative abundances are as for pefabs Parameters are parl ny equivalent hydrogen column in units of 10 atoms cm par2 f dimensionless covering fraction 0 lt f lt 1 par3 z redshift 247 6 3 19 phabs vphabs zphabs zvphabs photoelectric absorption A photoelectric absorption using cross sections set by the xsect command The relative abundances are set by the abund command M E exp n o E where o E is the photo electric cross section NOT including Thomson scattering Note that the default He cross section changed in v11 The old version can be recovered using the command xsect obcm parl ny equivalent hydrogen column in units of 10 atoms cm The redshifted variant zphabs uses the formula M E exp 2 0 E z and has par
256. his command is now also supported on Cygwin Syntax Imod lt name gt directory As for initpackage the lt name gt argument is the name of the model package being loaded and the lt directory gt is the its location defaulting to the setting of LOCAL MODEL DIRECTORY given in the user s Xspec init Imod performs the following tasks loads the library corresponding to the package named lt name gt reads the model description file supplied by the initpackage command for the library e adds the new model components to the list of models recognized by the model command Note that Imod requires that the user has write access to lt directory gt please see Appendix C for details 5 6 13 lumin calculate luminosities Calculate the luminosity of the current model for a given redshift and rest frame energy range Syntax lumin lt lowEnergy gt lt hiEnergy gt lt redshift gt err lt number gt lt level gt noerr where lt low Energy gt and lt hi Energy gt are the rest frame energies over which the luminosity is calculated and lt redshift gt is the source redshift Initial default values are 2 to 10 keV for 0 redshift The luminosity is given in units of ergs s The energy range redshifted to the observed range must be contained by the range covered by the current spectra which determine the range over which the model is evaluated Values outside this range will be automatically reset to the extremes
257. hotoelectric absorption A photoelectric absorption with variable abundances using cross sections set by the xsect command The column for each element is in units of the column in a solar abundance column of an equivalent hydrogen column density of 10cm The Solar abundance table used is set by the abund command These models differ from the models vphabs zvphabs only by the units in which the abundances are expressed vphabs zvphabs define these relative to the solar abundance not in terms of column density parl par18 equivalent columns for H He C N O Ne Na Mg Al Si S Cl Ar Ca Cr Fe Co Ni The zvarabs variant allows the user to specify a fixed redshift i e the parameters are parl parl8 equivalent columns for H He C N O Ne Na Mg Al Si S Cl Ar Ca Cr Fe Ni Co 253 parl9 redshift 6 3 32 wabs zwabs photoelectric absorption Wisconsin cross sections A photo electric absorption using Wisconsin Morrison and McCammon ApJ 270 119 cross sections M E exp n o E where o E is the photo electric cross section NOT including Thomson scattering Note that this model uses the Anders amp Ebihara relative abundances 1982 Geochimica et Cosmochimica Acta 46 2363 regardless of the abund command parl ny equivalent hydrogen column in units of 10 atoms cm The zwabs variant allows the user to specify a fixed redshift parameter and uses the corresponding formula M E
258. i squared 1 043 for 42 degrees of freedom Null hypothesis probability 3 949504e 01 Current data and model not fit yet 37 XSPEC12 gt flux 0 2 2 Model Flux 0 004352 photons 8 847e 12 ergs cm 2 s range 0 20000 2 0000 keV The energy flux at 8 8x10 ergs cm s is lower in this band but the photon flux is higher The model energies can be reset to the response energies using energies reset Calculating the flux is not usually enough we want its uncertainty as well The best way to do this is to use the cflux model Suppose further that what we really want is the flux without the absorption then we include the new cflux model by XSPEC12 gt editmod pha cflux pow Input parameter value delta min bot top and max values for 0 35 O 1 0 005 0 0 1e 06 1le 06 2 cflux Emin gt 0 2 10 Qi5 0 1 0 0 1le 06 1le 06 3 cflux Emax gt 2 0 12 0 01 0 12 100 100 100 100 4 cflux 1g10Flux gt 10 3 Fit statistic Chi Squared 3459 85 using 45 PHA bins Test statistic Chi Squared 3459 85 using 45 PHA bins Reduced chi squared 84 3867 for 41 degrees of freedom Null hypothesis probability 0 000000e 00 Current data and model not fit yet Model phabs lt 1 gt cflux lt 2 gt powerlaw lt 3 gt Source No 1 Active On Model Model Component Parameter Unit Value par comp 1 1 phabs nH 10 22 0 537843 0 270399 2 2 cflux Emin keV 0 200000 frozen 3 2 cflux Emax keV 2 00000 frozen 4 2 cfl
259. ial emission measure using Chebyshev representations with multi temperature mekal c6mekl is a multi temperature mekal model using sixth order Chebyshev polynomial for the differential emission measure The DEM is not constrained to be positive The switch parameter determines whether the mekal code will be run to calculate the model spectrum for each temperature or whether the model spectrum will be interpolated from a pre calculated table The former is slower but more accurate The reference for this model is Singh et al 1996 ApJ 456 766 c6pmekl differs by using the exponential of the 6 order Chebyshev polynomial c6mekl and c6pmekl use abundances relative to the Solar abundances set by the abund command The variants c6vmkl and c6pvmkl with polynomial and exponential polynomial respectively allow the user to specify 14 elemental abundance For c6mekl and c6pmk the parameters are par1 6 Chebyshev polynomial coefficients par7 H density cm par8 abundance wrt to Solar par9 Redshift parl0 0 calculate 1 gt interpolate norm 182 2 interpolate using APEC model Normalization While for c6vmkl and c6vpmkl the parameters are par1 6 Chebyshev polynomial coefficients par7 H density cm par8 21 Abundances of He C N O Ne Na Mg Al Si S Ar Ca Fe Ni wrt Solar defined by the abund command par22 Redshift 0 gt calculate par23 1 interpolate 2 interpolate using APEC model norm Normaliza
260. ich represent X Ray sources of different kinds After being convolved with the instrument response the components prescribe the number of counts per energy bin e g a bremsstrahlung continuum and multiplicative models components which represent phenomena that modify the observed X Radiation e g reddening or an absorption edge They apply an energy dependent multiplicative factor to the source radiation before the result is convolved with the instrumental response normalized counts 57 keV 2x10 6x10 4x10 Figure A The result of the command plot data when the data file in question is the EXOSAT ME spectrum of the 6s X ray pulsar 1E1048 1 5937 available from the HEASARC on line service More generally XSPEC allows three types of modifying components convolutions and mixing models in addition to the multiplicative type Since there must be a source there must be least one additive component in a model but there is no restriction on the number of modifying components To see what components are available just type model XSPEC12 gt model Additive Models apec bapec bbody bbodyrad bexrav bexriv bkn2pow bknpower bmc bremss bvapec bvvapec c6mekl copmekl copyvmk1l covmekl cemek1 cevmk1 cflow compLs compPS compST compTT compbb compmag comptb compth cplinear cutoffpl disk diskbb diskir diskline diskm disko diskpbb diskpn eplogpar eqpair eqtherm equil expdec ezdiskbb gadem gaussian gnei grad grbm kerrbb kerrd
261. idence regions are searched for possible line IDs If no argument is given then conf is assumed 5 6 17 newpar change parameter values Adjust one or more of the model parameters Syntax newpar modelName lt index range gt lt param spec list gt newpar modelName lt index gt lt coupling expression gt newpar 0 where lt param spec list gt lt param value gt lt delta gt lt param range spec gt lt param range spec gt lt hard min gt lt soft min gt lt soft max gt lt hard max gt For response parameters created with the gain or rmodel command rnewpar lt sourceNum gt lt idx range gt lt param spec list gt rnewpar lt sourceNum gt lt index gt lt coupling expression gt The model parameters are accessed through their model parameter indices For example the first parameter of the first model component generally is model parameter 1 etc The first command line argument lt index range gt gives the indices parameters to be modified by the newpar command The default value is the range from the previous invocation of newpar The remaining arguments can be used to update the parameter specification If the parameter specification is omitted from the command line then the user is explicitly prompted for it The first two arguments of the parameter specification are lt param value gt The trial value of the parameter used initially in the fit The step size used in the numerical
262. ie command XSPEC12 gt SPIuntie bkg 475 19 1 untie bkg 52 Chi Squared 1 2030200E 04 using 1615 PHA bins Reduced chi squared 7 5852458E 00 for 1586 degrees of freedom Null hypothesis probability 0 0000000E 00 untie bkg 78 Chi Squared 1 2030200E 04 using 1615 PHA bins Reduced chi squared 7 5900314E 00 for 1585 degrees of freedom Null hypothesis probability 0 0000000E 00 untie bkg 104 renorm no renormalization necessary Chi Squared 1 2030200E 04 using 1615 PHA bins Reduced chi squared 7 5948231E 00 for 1584 degrees of freedom Null hypothesis probability 0 0000000E 00 One might then make a second pass at fitting the data hopefully leading to improved statistics Subsequently additional background model parameters could be untied using the 66 SPIuntie procedure as well For example to untie three additional parameters over the full data set the command syntax is XSPEC12 gt SPIuntie bkg 475 19 1 3 This will untie the first 3 parameters of the background model identified by bkg i e equivalent to issuing 475 1 x3 individual untie commands Note that you can always be reminded of the command line argument definitions by typing SPlIuntie h at the XSPEC prompt Suppose now that you are satisfied with the relative background normalization terms and wish to freeze them at their current values for subsequent fitting passes This could be accomplished us
263. ific characteristics of the instrument This information is known as the detector response Recall that for each spectrum the response R I E is proportional to the probability that an incoming photon of energy E will be detected in channel I As such the response is a continuous function of E This continuous function is converted to a discrete function by the creator of a response matrix who defines the energy ranges E such that ji RU E dE RJ pl J E E XSPEC reads both the energy ranges E and the response matrix R J from a response file in a compressed format that only stores non zero elements XSPEC also includes an option to use an auxiliary response file which contains an array A J that is multiplied into R I J as follows R UJ gt Rp UJ eApV This array is designed to represent the efficiency of the detector with the response file representing a normalized Redistribution Matrix Function or RMF Conventionally the response is in units of cm M E The Model Spectrum The model spectrum M is calculated within XSPEC using the energy ranges defined by the response file M J f M E dE Ej and is in units of photons em s XSPEC allows the construction of composite models consisting of additive components representing X ray sources e g power laws blackbodys and so forth multiplicative components which modify additive components by an energy dependent factor e g photoelectric a
264. ile is written and saved the user then can re run the same set of commands on other data by XSPEC12 gt source lt script file gt Examples XSPEC12 gt script Turn on the script file default xspec xcm XSPEC12 gt script none Close the script file XSPEC12 gt script myscript Open the script file myscript xcm 5 3 10 show output current program state List selected information to the user s terminal and the log file if open Syntax show lt selection gt where lt selection gt is a key word to select the information to be printed If omitted it is the information last asked for Initially the default selection is all Note to better integrate the usage of OGIP type II files much of the information given by show files in previous versions is now displayed by show data Selections are XSPEC12 gt show abund show current solar abundance table XSPEC12 gt show all All the information XSPEC12 gt show allfile All file information files noticed rates XSPEC12 gt show control XSPEC control information XSPEC12 gt show data 78 File names associated coefficients and net count rates displayed in order of spectrum number For higher chatter also displays grouping map XSPEC12 gt show free Free parameters XSPEC12 gt show files T Equivalent to show data but displayed in order of file name XS
265. ination angle deg 0 for face on par6 inner radius units of GM c 2 1 235 is the last stable orbit par7 outer radius units of GM c 2 K normalization factor should be fixed to 1 6 2 44 kerrdisk accretion disk line emission with BH spin as free parameter Model for an accretion disk broad emission line with the black hole spin allowed to be a free parameter A detailed description can be found in Brenneman amp Reynolds 2006ApJ 652 1028B This model is quite slow so is best used after models such as laor or diskline have been employed to get an estimate of the best fit parameters parl par2 par3 par4 par5 par6 par7 par8 par9 K 6 2 45 rest frame line energy keV emissivity index for the inner disk emissivity index for the outer disk break radius separating the inner and outer portions of the disk gravitational radii dimensionless black hole spin disk inclination angle to the line of sight degrees inner radius of the disk in units of the radius of marginal stability outer radius of the disk in units of the radius of marginal stability redshift z flux in line photons cm7 s laor accretion disk black hole emission line An emission line from an accreti on disk around a black hole Ari Laor s calculation including GR effects ApJ 376 90 parl Line energy in keV 208 par2 a power law dependence of emissivity scales as R par3 inner radius units of GM
266. ing the SPI freeze command script XSPEC12 gt SPIfreeze bkg 475 1 XSPEC12 gt SPIfreeze bkg 19 1 1 freeze bkg 52 1 Chi Squared 6 6232600E 05 using 1805 PHA bins Reduced chi squared 3 7589444E 02 for 1762 degrees of freedom Null hypothesis probability 0 0000000E 00 freeze bkg 78 Chi Squared 6 5791894E 05 using 1805 PHA bins Reduced chi squared 3 7318148E 02 for 1763 degrees of freedom Null hypothesis probability 0 0000000E 00 As with the SPIuntie command script typing SPIfreeze h at the XSPEC prompt will scroll the command line definitions to your screen 2 E Note that the current SPI background models which are documented elsewhere are designed so that the parameter list is hierarchically ordered in terms of decreasing criticality Thus freeing the first parameter is likely to have the most significant impact on the statistics the second parameter the next most significant and so on 67 5 XSPEC commands 5 1 Summary of Commands The following is a list of the commands available in XSPEC together with a brief description of the purpose of each The commands have been categorized under six headings Control Data Fit Model Plot Script and Setting The Control commands contain the interface with the operating system they cause commands to be executed or user input written to disk or control how much is output The Data commands manipulate the data being analyzed by re
267. ing with this but an inherited class may want to use this information in an overriden function In its simplest form a proposal class may be declared and defined as in the following example This doesn t actually do anything since the doRandomize function is empty and the parameterValues array is left unchanged MyProposal h ifndef MYPROPOSAL H define MYPROPOSAL H include lt xsTypes h gt include lt XSFit Randomizer RandomizerBase h gt class Fit only a forward declaration is required for Fit class MyProposal public RandomizerBase public MyProposal virtual MyProposal private virtual void doRandomize RealArray amp parameterValues const Fit fit A 309 MyProposal cxx include MyProposal h include lt XSFit Fit Fit h gt MyProposal MyProposal RandomizerBase myprop MyProposal MyProposal void MyProposal doRandomize RealArray amp parameterValues const Fit fit This is where the proposal algorithm should modify the variable model parameters in the parameterValues array G 3 Building and Loading the Proposal Class Library Once the randomize dat file and the class es have been written the library can be built and loaded during an XSPEC session using the same initpackage and Imod sequence that is used for local model libraries To create a Makefile and build the library XSPEC12 gt initpackage lt name gt randomize dat lt dir
268. internal exponential table model routines similar to what xsatbl and xsmtbl do for additive and multiplicative table models Bayes command is now supported for response parameters ie gain New show version option Improved error command output messaging The error results now have lower chatter level 5 than most of the warning messages 10 thus making it easier to filter out the warnings PyXspec beta version upgraded to v1 0 See the PyXspec release notes for details Enhancements previously released as patches to 12 7 0 New tclout options nullhyp rerror All bug fixes to v12 7 0 released as patches a u are included in v12 7 1 In addition the following problems have been corrected Program aborted when attempting to fit with gain parameters attched to dummy responses Program aborted when removing a spectrum with a response containing gain parameters AND while that response was temporarily replaced with a dummy response The save command did not add the default xcm extension for file names that included a path A crash could occur if the EBOUNDS array wasn t the right size It was not possible to plot 2 or more models in a multi panel plot model display v12 7 0 May 2011 A 316 The primary new feature of 12 7 0 is the addition of the Python module PyXspec v0 9 beta PyXspec is built and installed by defaulton most platforms along with the regular XSPEC build and simply requires an import xspe
269. ion g ranging from 1e13 to 1e15 cm s allowed by equations of state for the neutron star matter the nsa model gives the spectra calculated for g 2 43e14 cm s The uniform surface effective temperature is in the range of Log TeK 5 5 6 5 The atmosphere is in radiative and hydrostatic equilibrium sources of heat are well below the atmosphere The radiative force and electron heat conduction are included in the models but they are of no importance in the specified ranges of Te and g The model spectra are provided as seen by a distant observer with allowance for the GR effects The neutron star mass M and radius R determine the redshift parameter g 1 2 952 M R 218 and the gravitational acceleration at the surface g 1 33e16 M R7 g cm s where M is in units of solar mass and R is in km The allowed domain in the M R plane corresponds to g gt 1 3 and 1e13 lt g lt 1e15 cm s This domain is restricted by the solid curves in the figure If chosen M and R values correspond to g or and g values outside the allowed domain then the code sets the latter to be the closest limiting values e g if one chooses M 2 R 8 then the code will use g 3 0 578 instead of g 0 512 corresponding to the M and R chosen which would lead to unphysical results The values of the effective temperature and radius as measured by a distant observer values at infinity are T g Tg R R g The nsagrav model may be use
270. ion in Istat description of Appendix B Correction to par2 par9 and par10 description in optxagn model In chain command Goodman Weare is now the default Dec 2012 v12 8 0 release Major rewrite and expansion of the Walkthrough section including examples with features that are new for v12 8 0 New parallel command New models compmag and comptb New test option for the statistic command and new choices for statistics Enhanced the Poisson data subsection of the Overview New lt critical beta gt option for method and fit commands New options for the chain command type and walkers Added several sections in Appendix B for new statistics Added plot goodness and thin option to plot chain Note on grouped spectra added to fakeit xi Note on uniform binning added to gsmooth model Updated description for simpl convolution model New tclout options tclout ignore and tclout goodness sims Also added units to tclout lumin description Added to ftest a warning against using on a multiplicative component Added clarification on trace element abundances when using apec and vapec models Feb 2012 v12 7 1 release Compps eqpair and nteea models descriptions modified for change in handling Compton reflection Corrections made to the model strings table for the xset command Added RFLABD F
271. ion of coded aperture data One already mentioned is the source confusion issue there may be multiple sources in the FoV which are lead to different degrees of shadowing on different detectors Thus a separate instrumental response must be applied to a spectral model for each possible source for each detector This is further compounded by the fact that INTEGRAL s typical mode of observation is dithering A single observation may This is one of several possible analysis paths The most commonly used method involves the SPIROS utility in spectral extraction mode which leads to a effective area corrected background subtracted pseudo count spectra A single customized XSPEC RMF is then applied to approximate the photon to count redistribution for model fitting 12 consist of 10 s of individual exposures at raster points separated by 2 This further enumerates the number of individual response matrices required for the analysis If there are multiple sources in the FoV then additional spectral models can be applied to an additional set of response matrices enumerated as before over detector and dither pointing This capability to model more than one source at a time in a given Chi Square or alternative minimization procedure did not exist in previous versions of XSPEC For an observation with the INTEGRAL SPI instrument where the apparent detector efficiency is sensitive to the position of the source on the sky relative to the
272. ion of the disk is considered and the torque at the inner boundary of the disk is allowed to be non zero This model is intended as an extension to grad which assumes that the black hole is non rotating For details see Li et al ApJSuppl 157 335 2005 parl eta ratio of the disk power produced by a torque at the disk inner boundary to the disk power arising from accretion It must be gt 0 and 206 lt 1 When eta 0 the solution corresponds to that of a standard Keplerian disk with zero torque at the inner boundary par2 specific angular momentum of the black hole in units of the black hole mass M geometrized units G c 1 Should be gt 1 and lt 1 par3 disk s inclination angle the angle between the axis of the disk and the line of sight It is expressed in degrees 1 0 is for a face on accretion disk i should be lt 85 degree par4 the mass of the black hole in units of the solar mass par5 the effective mass accretion rate of the disk in units of 10 18 g sec When eta 0 zero torque at the inner boundary this is just the mass accretion rate of the disk When eta is nonzero the effective mass accretion rate 1 eta times the true mass accretion rate of the disk The total disk luminosity is then epsilon times the effective mass accretion rate times c 2 where epsilon is the radiation efficiency of a standard accretion disk around the Kerr black hole par6 the distance from the observer
273. iption of Syntax The individual commands are treated in alphabetical order in the following section The novice would be well served by reading the treatments of the data model newpar and fit commands in that order then the other commands as needed The write up for each command includes a brief description of the purpose an outline of the correct syntax a more detailed discussion of the command assumptions and purpose and a series of examples Some commands have one or more subcommands that are similarly described following the command In the command description the syntax uses the following conventions lt arg gt an argument to the command defines lt arg c gt as lt arga gt followed by lt arg c gt lt arg a gt lt arg b gt lt argb gt lt arg gt a repeated string of arguments of the same type lt arg gt is an optional argument indicates a choice between an argument lt arg a gt lt arg b gt 3 of lt arg a gt or lt arg b gt Exceptional responses to the command prompt are empty line or line containing nothing performed prompt repeated only spaces and tab characters any remaining arguments will have the values given on the last invocation of the command lt EOF gt Ctrl D on Unix same as quit skip input and return to prompt Defaults for prompted values will be used Print list of commands or summary help for a single command command command 5 3 Control Com
274. ipts directory 5 3 13 tcloutr tclout with return value Syntax tcoutr lt option gt lt parl gt lt par2 gt lt par3 gt gt tcloutr is identical to the tclout command except that it also provides what is stored in xspec_tclout as a return value Therefore it can be used in tcl scripts like this set varl tcloutr energies 1 tcloutr may produce quite a lot of unwanted screen output which can be avoided by using tclout 86 5 3 14 time print execution time Get some information about the program run time Syntax time The time command prints out elapses CPU time attributed to the user and to the system Two output lines are given one for user system time since the time command was last called and one for time elapsed since the program started 5 3 15 undo undo the previous command Undo the affects of the previously entered xspec command Syntax undo New for xspec version 12 the undo command will restore the state of the xspec session prior to the most recently entered command The current implementation does not allow restoration to more than one command back so calling undo repeatedly will have no effect Also a plot command cannot be undone 5 3 16 version print the version string Syntax version version prints out the information about version number and build date and time not current date time displayed when XSPEC is started 87 5 4 Data Commands 5 4 1 arf change the efficiency file for a giv
275. itten at NASA Goddard Space Flight Center for the OSO 8 HEAO 1 and EO missions The initial design was the fruit of many discussions between Rick Shafer and Andy Szymkowiak Rick Shafer subsequently joined the EXOSAT group where he enhanced the VAX VMS version in collaboration with Frank Haberl Meanwhile Keith Arnaud ported XSPEC to a Sun UNIX operating system The two implementations of XSPEC diverged for several years until a determined and coordinated effort was made to recover a single version The results of that effort was XSPECv6 described in the first edition of this manual Subsequent editions have covered later versions of the program In recent years XSPEC has become the de facto standard for X ray spectroscopic analysis for the ROSAT mission and the de jure standard for the BBXRT ASCA and RXTE missions It is now in extensive use for all current X ray and gamma ray missions An extensive re engineering effort was started in the fall of 1998 to improve long term maintainability allow significant new features to be added and support the analysis of spectra from coded mask instruments 1 4 Acknowledgements This project would not have been possible without ignoring the advice of far more people than can be mentioned here We would like to thank all our colleagues for their suggestions bug reports and especially source code The GSFC X ray astronomy group are particularly thanked for their patience exhibited while functioning as t
276. ive Example C C function definitions C style extern C void modelfunc const Real energy int Nflux const Real parameter int spectrum Real flux Real fluxError const char init Model code Do not allocate memory for flux and fluxError arrays XSPEC s C function wrapper will allocate arrays prior to calling the function and will free them afterwards C extern C void modelfunc const RealArray amp energy const RealArray amp parameter int spectrum RealArray amp flux RealArray amp fluxError const string amp init Model code Should resize flux RealArray to energy size 1 Do the same for fluxError array if calculating errors otherwise leave it at size 0 Note on type definitions for C and C XSPEC provides a typedef for Real in the xsTypes h header file The distributed code has typedef Real double i e all calculations are performed in double precision This is used for C models and C models with C style arguments The type RealArray is a dynamic resizeable array of Real XSPEC uses the std valarray template class to implement RealArray The internal details of XSPEC require that the RealArray typedef supports vectorized assignments and mathematical operations and indirect addressing see C documentation for details However we do not recommend using specific features of the std valarray class such as array slicing in case the typedef is chan
277. ive residuals and the Pearson Chi Square pchi statistic Pearson s original test statistic The basic Levenberg Marquardt fit algorithm has undergone a number of changes The most visible is an additional column in the output during the fit beta N is the norm of the vector of derivatives of the statistic with respect to the parameters divided by the number of parameters At the best fit this should be zero so provides another measure of how well the fit is converging beta N can also be used as the criterion to stop the fit instead of the statistic delta although this is still considered experimental Other internal changes to the fit algorithm are to treat the first iteration as a special case where only normalizations are allowed to change and to add the option of using delayed gratification which can speed up convergence New models compmag comptb rgsxsrc The latter is reinstated from it use in XSPEC v11 New plotting command plot goodness for plotting a histogram of the most recent goodness simulation New tclout option goodness sims Added the option of using the Goodman Weare algorithm instead of Metropolis Hastings when using the chains command to run MCMC Added the Whittle statistic for fitting models to power density spectra If a data file is read which has RESPFILE then the response extensions MATRIX EBOUNDS are read from the same file A 314 Added support for a new type of model compon
278. ive then only the hard Compton component is used parl1 fcol Colour temperature correction to apply to the disc blackbody emission for radii below rcor with effective temperature gt Tscatt par12 Tscatt Effective temperature criterion used as described above in K parl13 Redshift norm K Must be frozen 6 2 61 pegpwriw power law pegged normalization A power law with pegged normalization A E KE where parl a photon index of power law dimensionless par2 lower peg energy range par3 upper peg energy range norm flux in units of 107 erg cms over the energy par2 par3 If par2 par3 it is the flux in micro Jy at par2 6 2 62 pexmon neutral Compton reflection with self consistent Fe and Ni lines This model from Nandra et al 2007 MNRAS 382 194 combines pexrav with self consistently generated Fe Ka Fe KB Ni Ka and the Fe Ka Compton shoulder Line strengths are based on Monte Carlo calculations by George and Fabian 1991 MNRAS 249 352 which are parametrized for 1 1 lt y lt 2 5 by EW 9 66 EWo 77 0 56 with inclination dependence for for i lt 85 degrees EW EW 2 20 cos i 1 749 cos i 0 541 cos i 225 and abundance dependence log EW log EWo 0 0641 log Age 0 172 log Age The Fe KB and Ni Ka line fluxes are 11 3 and 5 respectively of that for Fe Ka The Fe Ka Compton shoulder is approximated as a gaussian with E 6 315 keV and o 0 035 keV The incli
279. ization fractions using dielectronic recombination rates from Mazzotta et al 1988 and xset neivers 2 0 uses the same ionization fractions as 1 1 but uses APED to calculate the resulting spectrum Note that versions 1 x have no emission from Ar The default is version 1 1 The sedov model has relative abundances determined by the solar Anders and Grevesse mixture while the vsedov variant allows the user to set the abundances Parameters for sedov are parl mean shock temperature keV par2 electron temperature immediately behind the shock front keV par3 Metal abundances He fixed at cosmic The elements included are C N O Ne Mg Si S Ar Ca Fe Ni Relative abundances are defined by the abund command par4 ionization age s cm of the remnant electron density immediately behind the shock front multiplied by the age of pars norm 234 the remnant redshift z 107 47 D z distance to the source cm and ne ny cm are the electron and hydrogen densities respectively i Jn n aV where Dy is the angular diameter For vsedov the parameters are parl mean shock temperature keV par2 electron temperature immediately behind the shock front keV par3 H density in cm par4 parl5 Abundances for He C N O Ne Mg Si S Ar Ca Fe Ni wrt Solar defined by the abund command par4 ionization age s cm of the remnant electron density immediately behind the shock front multiplied by the
280. k redshift z abundance of elements heavier than He relative to the solar abundances iron abundance relative to that defined by abund inclination angle degrees disk temperature in K F disk ionization parameter 4m where Fion is the 5eV 20keV n irradiating flux n is the density of the reflector see Done et al 1992 ApJ 395 275 power law dependence of emissivity the emissivity R 233 parl1 inner radius units of GM e parl2 outer radius units of GM c par13 internal model accuracy points of spectrum per energy decade norm photon flux at 1 keV photons keV lem s of the cutoff broken power law only no reflection in the observed frame 6 2 72 sedov vsedov sedov model separate ion electron temperature Sedov model with separate ion and electron temperatures This model is slow par1 provides a measure of the average energy per particle ions electrons and is constant throughout the postshock flow in plane shock models Borkowski et al 2001 ApJ 548 820 par2 should always be less than pari Ifpar2 exceeds par1 then their interpretations are switched ie the larger of par1 and par2 is always the mean temperature Additional references can be found under the help for the equil model Several versions are available To switch between them use the xset neivers command xset neivers 1 0 gives the version from xspec v11 1 xset neivers 1 1 uses updated calculations of ion
281. k for genetic plot options Number of plot groups query rate lt n all gt rerror lt sourceNumber gt n response n sigma lt modelName gt n simpars solab stat test statmethod test steppar statistic delstat lt modName gt lt parNum gt varpar version 84 The setting of the query option Count rate uncertainty and the model rate for the specified spectrum n or for the sum over all spectra Writes last confidence region calculated for response parameter n of model with optional source number and a string listing any errors that occurred during the calculation See the help above on the error option for a description of the string Response filename s for the spectrum n The sigma uncertainty value for parameter n Ifn is not a variable parameter or fit was unable to calculate sigma 1 0 is returned Creates a list of parameter values by drawing from a multivariate Normal distribution based on the covariance matrix from the last fit This is the same mechanism that is used to get the errors on fluxes and luminosities and to run the goodness command Solar abundance table values Value of statistic If optional test argument is given this outputs the test statistic rather than the fit Statistic The name of the fit stat method currently in use If optional test argument is given this will give the name of the test stat method The statistic and delsta
282. kerrdisk laor laor2 logpar lorentz meka mekal mkcflow nei npshock nsa nsagrav nsatmos nsmax nteea nthComp optxagn optxagnf pegpwrlw pexmon pexrav pexriv plcabs posm powerlaw pshock raymond redge refsch sedov sirf smaug srcut sresc step vapec vbremss vequil vgadem vgnei vmcflow vmeka vmekal vnei vnpshock vpshock vraymond vsedov vvapec zbbody zbremss zgauss zpowerlw Multiplicative Models SSS_ice TBabs TBgrain TBvarabs absori acisabs 28 29 cabs constant cyclabs dust edge expabs expfac gabs highecut hrefl notch pcfabs phabs plabs pwab recorn redden smedge spexpcut spline swindl uvred varabs vphabs wabs wndabs xion zTBabs zdust zedge zhighect zigm zpcfabs zphabs zredden zsmdust zvarabs zvfeabs zvphabs zwabs zwndabs zxipcf Convolution Models cflux gsmooth ireflect kdblur kdblur2 kerrconv lsmooth partcov rdblur reflect rgsxsrc simpl zashift zmshift Mixing Models ascac projct suzpsf xmmps f Pile up Models pileup Mixing pile up Models Additional models are available at legacy gsfc nasa gov docs xanadu xspec newmodels html For information about a specific component type help mode1 followed by the name of the component XSPEC12 gt help model apec Given the quality of our data as shown by the plot we ll choose an absorbed power law specified as follows XSPEC12 gt model phabs powerlaw Or abbreviating unambiguously XSPEC12 gt mo pha po The user is then prompted for the initial values of th
283. l C is sent while the spectra from my_data2 are loading the 50 spectra from my_datal will be retained while none will be from my_data2 XSPEC12 gt data my datal 1 50 mydata2 1 50 3 13 Customizing XSPEC The XSPEC environment can be customized using two separate files both of which are searched for in the directory HOME xspec The first file Xspec init contains a number of settings that control items in XSPEC An abridged version of this file is reproduced below HEE TE FE E EEE EE EEE EE EEE EH HH HEE EE EE EE EE EE EE EEE EH options and commands for displaying helpfiles USE ONLINE HELP true Recognized local help formats html pdf This is ignored when using online help XOCAL HELP FORMAT html Recommended command for Adobe Acrobat version 7 and later PDF COMMAND acroread openInNewWindow tempFileTitl Recommended command for Adobe Acrobat prior to version 7 PDF COMMAND acroread useFrontEndProgram tempFileTitl 23 Recommended command for Mac PDF viewing PDF COMMAND open Recommended command for Cygwin PDF viewing PDF COMMAND xpdf q Recommended command for Mac html HTML COMMAND open HTML COMMAND firefox HEHEHE E HE EEE HE EEE HE EEE EH HEHE HE EE HH EHH HF EH EF setting for GUI mode The code requires that the GUI setting starts with a t case insensitive otherwise GUI mode is false and the command
284. l for details 5 6 11 initpackage initialize a package of local models The initpackage command initializes a package of local models from their source code and from a model component description file in model dat format which defines the component s name type function call and its parameter names and initial settings Further details of the file format function and parameter specifications are given in Appendix C Adding Local Models To XSPEC Note initpackage is now also supported on Cygwin The former Cygwin only static_initpackage command has been removed Syntax initpackage lt name gt lt description file gt lt directory gt udmget The lt name gt argument names the package For internal reasons package names must be lowercase the initpackage command will force lower case and warn the user if the argument contains uppercase letters Also there should be no numerals in the package name The lt description file gt argument specifies the model component description file The third argument lt directory gt is optional and specifies the location of the source code If it is not given the value of the setting LOCAL MODEL DIRECTORY given in the user s Xspec init file will be used Finally the lt description file gt if not specified as an absolute pathname will be read from the same directory as the source code Another optional argument is udmget for local model libraries containing Fortran code
285. l spectrum will be interpolated from a pre calculated table The former is slower but more accurate For the mkcflow model the parameters are parl low temperature keV par2 high temperature keV par3 abundance relative to Solar par4 fixed redshift 213 0 calculate par5 1 interpolate 2 gt interpolate using APEC model norm Mass accretion rate solar mass yr While for the vmcflow variant the parameters are parl low temperature keV par2 high temperature keV par3 Abundances for He C N O Ne Na Mg Al Si S Ar Ca Fe Ni parl6 wrt Solar given by the Anders amp Grevesse mixture par17 Redshift 0 calculate par18 1 interpolate 2 interpolate using APEC model norm Mass accretion rate solar mass yr 6 2 52 nei vnei collisional plasma non equilibrium constant temperature Non equilibrium ionization collisional plasma model This assumes a constant temperature and single ionization parameter It provides a characterization of the spectrum but is not a physical model The references for this model can be found under the description of the equil model The references for this model can be found under the description of the equil model Several versions are available To switch between them use the xset neivers command xset neivers 1 0 gives the version from xspec v11 1 xset neivers 1 1 uses updated calculations of ionization fractions using dielectronic recombination rates from Mazzotta et al 1
286. le The default geometry is that of a lamppost with free parameters of the model being the height of the X ray source above the disk Ax the dimensionless accretion rate through the disk m the luminosity of the X ray source Lx the inner and outer disk radii and the spectral index This defines the gravity parameter the ratio of X ray to thermal fluxes etc for each radius which allows the use of a look up table to approximate the reflected spectrum This procedure is repeated for about 30 different radii The total disk spectrum is then obtained by integrating over the disk surface including relativistic smearing of the spectrum for a non rotating black hole e g Fabian 1989 In addition the geometry of a central sphere with power law optically thin emissivity inside it plus an outer cold disk and the geometry of magnetic flares are available par13 2 and 3 respectively One can also turn off relativistic smearing to see what the local disk spectrum looks like par12 2 in this case otherwise leave it at 4 In addition par11 1 produces reflected plus direct spectrum direct par11 2 produces incident reflected incident note that normalization of incident and direct are different because of solid angles covered by the disk 2 should be used for magnetic flare model and par11 3 produces reflected incident Abundance is controlled by par9 and varies between 1 and 4 at the present A much more complete description of the mo
287. le between the direction to the observer and the magnetic axis The effective temperatures span the range log T 5 5 6 8 for hydrogen and log Terr 5 8 6 9 for mid Z elements note for the latter change temperature range in nsmax_Imodel dat The models with single B Te cover the energy range 0 05 10 keV while the models with B T distributions cover the range 0 09 5 keV parl logTeff surface unredshifted effective temperature par2 1 2Zg gravitational redshift par3 switch indicating model to use see nsmax dat or model list A Rem d normalization where Rem is the size in km of the emission region and d is the distance kpc to the object Note A is added automatically by XSPEC Please send your comments questions to Wynn Ho wynnho slac stanford edu If you publish results obtained using NSMAX please reference Ho W C G Potekhin A Y amp Chabrier G 2008 ApJS 178 102 and also Mori K amp Ho W C G 2007 MNRAS 377 905 if using the mid Z models 220 6 2 58 nteea non thermal pair plasma A nonthermal pair plasma model based on that of Lightman amp Zdziarski 1987 ApJ 319 643 from Magdziarz and Zdziarski It includes angle dependent reflection from Magdziarz amp Zdziarski 1995 MNRAS 273 837 In versions 1 1 and above the Compton reflection is done through an internal call to the reflct model The Greens function integration required for the Compton reflection calculation is perform
288. lemented extend Beginning with version 12 3 0 this has been replaced by the more flexible energies command background models This has been replaced by v12 s multiple source modeling techniques Additionally we have withdrawn seldom used fitting methods anneal and genetic Future development will add new techniques A 313 Appendix Older Release Notes v12 8 0 Dec 2012 New features Parallel processing capability for specific tasks has been added by way of the new parallel command This allows the user to set a maximum number of processes to spawn when running certain XSPEC commands Currently the options for parallel processing are limited to use with the fit and error and commands though we plan to implement more in the near future This first implementation is considered to be a BETA release and we look forward to hearing your comments and suggestions XSPEC now distinguishes between the fit statistic and the test statistic The fit statistic is used to find the best fit parameter values and errors while the test statistic is used to provide a goodness of fit Consequently the goodness command now uses the test statistic Separating these two classes of statistic has allowed us to add a number of new test statistics These include Kolmogorov Smirnov and the related Anderson Darling and Cramer von Mises Also new are the runs statistic based on the number of runs of consecutive positive or negat
289. lescope effective area so no arf should be applied to input files Note that this model is very slow if any of the parameters are free 268 The model is used by reading spectra in as separate datagroups Each input file requires the XFLT0001 keyword set to a different number eg if concentric annuli are in use then number outwards The normalizations for each datagroup should be linked since the ascac model takes care of the relative normalizations based on the surface brightness model used A maximum of five different spatial regions is allowed The absolute normalization is not reliable so this model should not be used to derive fluxes parl Alpha par2 Beta par3 Core arcmin 0 beta model par4 1 2 power law 6 6 2 projct project 3 D ellipsoidal shells onto 2 D elliptical annuli This model performs a 3 D to 2 D projection of prolate ellipsoidal shells onto elliptical annuli The annuli can have varying ellipticities and position angles but must have the same center The user should extract spectra in a series of annuli Each spectrum needs three additional keywords XFLT0001 XFLT0002 XFLT0003 in the spectrum extension These keywords contain the semi major axis semi minor axis and position angle in degrees for the outer boundary of the annulus It is assumed that the inner boundary is specified by the outer boundary of the next annulus in The lengths can be in any consistent units although for numerical accuracy they should h
290. line help help and Help can be given either in summary in specific manual pages a manual section or the entire manual 16 3 6 1 Query chatter and shutting XSPEC up somewhat The fit command will run a certain number of iterations and then query the user whether he or she wants to continue While useful under most circumstances the constant questioning can be a pain if one leaves XSPEC running and expects to find it finished when one gets back or if one habitually runs scripts One way around this problem is to reset the number of iterations before the question is asked by giving a single argument For example XSPEC12 gt fit 100 will run 100 iterations before asking a question A more drastic solution is to use the query command XSPEC12 gt query yes This will suppress all questions and assume that their answer is yes while XSPEC12 gt query no will suppress all questions but assume that their answer is no The amount of output that XSPEC writes is set by the chatter command which takes two arguments applying to the terminal and to the log file 3 6 2 Scripts and the Save command XSPEC commands can be written into a file and then executed by entering XSPEC12 gt filename Alternatively from the shell prompt Q xspec filename amp for batch execution remember to end the script in file filename xcm with exit if you want the program to terminate after completion Note that the
291. line mode is used GUI false user definable setting for the dummy response Arguments required begin range end range number of bins logarithmic linear Defaults are 0 1 100 200 log respectively Setting for bin type must be linear if linear bins are to be created DUMMY 0 1 50 1000 log Chatter Level Console chatter level then log chatter level Currently 4 2001 logging has not been reimplemented CHAT 10 10 photo absorption cross section table setting possible values are vern bemc obmc XSECT Deme solar abundance table indicator Hard coded solar abundance vector Choices are feld Feldman U 1992 Physica Scripta 46 202 angr is from Anders E amp Grevesse N 1989 Geochimica and Cosmochimica Acta 53 197 aneb is from Anders E amp Ebihara 1982 Geochimica and Cosmochimica Acta 46 2363 24 ABUND angr fitting method leven anneal METHOD leven statistic to be minimized chi cstat STATISTIC chi weighting technique standard gehrels churazov model WEIGHT standard If true fitting algorithm will calculate parameter derivatives numerically If false a faster analytic expression will be used if applicable to the current fitting statistic USE_NUMERICAL DIFFE pa ENTIATION false cosmology parameters HO q0 lambdaO
292. ll cause Y axis units to be in 1 Hz This feature is turned off by setplot wave perhz off and its initial setting is determined by the WAVE PLOT _UNITS setting in the user s xspec Xspec init file Also note that when perhz is selected emodel eufspec and eemodel eeufspec will have the same Y axis units as for setplot energy hz This command makes ignore and notice operate in terms of wavelength rather than energies The units setting here also determines the units in the ignore notice range specifiers xlog on off Set the x axis to logarithmic or linear respectively for energy or wavelength plots xlog has no effect on plots in channel space recall that the default for energy plots is logarithmic xlog allows the user to override this setting xlog and ylog will not work for model related plots eg model ufspec and their variants as their axes are always set to log scale ylog on off Set the y axis to logarithmic or linear respectively for energy or wavelength plots For plot instructions that are explicitly logarithmic plot Idata plot counts the state of the ylog setting is ignored xlog and ylog will not work for model related plots eg model ufspec and their variants as their axes are always set to log scale 5 8 Setting Commands 5 8 1 abund set the Solar abundances Set the abundance table used in the plasma emission and photoelectric absorption models Syntax abund lt option gt where lt option gt Is
293. llover par3 kT_bb seed photon temperature low energy rollover par4 inp_type 0 or 1 for blackbody or disk blackbody seed photons respectively par5 redshift K normalization unity at 1 keV for a norm of 1 222 6 2 60 Optxagnf optxagn Colour temperature corrected disc and energetically coupled Comptonisation model for AGN AGN spectral energy distributions are complex but can be phenomenologically fit by a disc optically thick low temperature thermal Comptonisation to produce the soft X ray excess and an optically thin high temperature themal Comptonisation to produce the power law emission which dominates above 2 keV Here we combine these three components together assuming that they are all ultimately powered by gravitational energy released in accretion We assume that the gravitational energy released in the disc at each radius is emitted as a colour temperature corrected blackbody only down to a given radius Reorona Below this radius we further assume that the energy can no longer completely thermalise and is distributed between powering the soft excess component and the high energy tail This imposes an important energetic self consistency on the model The key aspect of this model is that the optical luminosity constrains the mass accretion rate through the outer disc Mdot provided there is an independent estimate of the black hole mass from e g the HB emission line profile The total luminosity availabl
294. ls is just the sum of their individual emissivities e Multiplicative model components do not directly produce photons but instead modify by an energy dependent multiplicative parameter the spectrum produced by one or more additive components Examples of multiplicative models are photoelectric absorption models edges absorption lines etc Convolution models components modify the spectrum as a whole acting like operators rather than simply applying bin by bin multiplication factors An example of a convolution model is a gaussian smoothing with energy dependent width Thus when using convolution models the ordering of components is in general significant see below under syntax rules 134 The pile up model is similar to the operation of the convolution models The only difference is that the flux is multiplied by the effective area on input and divided by the same factors on output Mixing model components implement two dimensional transformations of model spectra The data are divided into regions by assigning them to 2 or more datagroups and the transformation mixes the flux among the regions An example is the projct projection model which assumes that the regions are 3 dimensional ellipsoidal shells in space and projects the flux computed from the other components onto 2 dimensional elliptical annuli A list of all the currently installed models is given in response to the command model the is not a
295. ls the extra time can be considerable The error for each parameter is determined allowing the other two parameters to vary freely If the parameters are uncorrelated this is all the information we need to know However we have an indication from the covariance matrix at the data and folded model normalized counts s ke normalized counts 3 keV Energy kev Figure D The result of the command plot data resid with the ME data file from 1E1048 1 5937 bad and negative channels ignored the best fitting absorbed power law model the residuals of the fit end of the fit that the column and photon index are correlated To investigate this further we can use the command steppar to run a grid over these two parameters XSPEC12 gt steppar 1 0 0 1 5 25 2 1 5 3 0 25 Chi Squared Delta nH PhoIndex Chi Squared 1 2 162 65 118 84 0 0 0 1 35 T7159 V2 7 19 1 0 06 0 1 5 180 87 137 06 2 0 12 0 L5 190 44 146 64 3 0 18 0 15 200 29 156 49 4 0 24 0 159 316 02 272 22 4 0 24 25 3 334 68 290 88 3 0 18 25 3 354 2 310 4 2 0 12 25 3 374 62 330 82 1 0 06 25 3 395 94 352 14 0 0 25 3 and make the contour plot shown in figure E using XSPEC12 gt plot contour What else can we do with the fit One thing is to derive the flux of the model The data by themselves only give the instrument dependent count rate The model on the other hand is an estimate of the true spectrum emitted In XSPEC the model is defined in physical units C
296. m a disk around a Kerr BH nsmax NS magnetic atmosphere A 321 nthcomp thermally Comptonized continuum spexpcut super exponential cut off swind1 partially ionized absorbing material with velocity shear e zxipcf partial covering of partially ionized absorbing material cflux calculate the flux from model component s kerrconv broadening due to rotation around a Kerr BH partcov partial covering modifier for absorption models simpl Comptonization of a seed spectrum recorn Vary the correction file normalization The Irt tcl and simftest tcl scripts perform the likelihood ratio and F tests respectively The writefits tcl script writes filenames and current fit parameters and errors to a single row of a FITS file This script can be used as a template for saving other information A response of to a y n prompt will jump out of the current operation and return to the XSPEC command prompt This is particularly useful for escaping nested fits during an error command run The units have been changed for setplot wave plots model and ufspec have a y axis in photons cm 2 s Hz emodel and eufspec in Jy 10 23 erg cm 2 s Hz eemodel and eeufspec in erg cm 2 s Fakeit can now work with multiple extension response files It also works correctly when multiple models are in use this was release in patch v12 4 0r The activelinactive options can be applied to the default unnamed model
297. mand forways to completely remove the dataset from consideration Note The ARF command is currently not implemented for data formats which use multiple RMFs per spectrum such as Integral SPI data Examples It is assumed that there are currently three spectra XSPEC gt arf a b c New files for the auxiliary response are given for all three spectra XSPEC gt arf 2 none No auxiliary response will be used for the second spectrum XSPEC gt arf d fits d fits becomes the auxiliary response for the second spectrum XSPEC gt arf 2 e fits 3 4 Rows 3 and 4 of multi ARF file e fits become the auxiliary responses for the second and third spectra XSPEC gt arf 2 1 f fits fits becomes the auxiliary response for the second source of spectrum 1 5 4 2 backgrnd change the background file for a given spectrum Modify one or more of the files used in background subtraction 88 Syntax backgrnd lt filespec gt backgernd lt spectrum number gt none where lt filespec gt lt spectrum num gt lt filename gt and where lt filename gt is the name of the PHA file to be used for background subtraction The numbering scheme is as described for the data command except that the lt spectrum num gt must have previously been loaded An etror message is printed if lt spectrum num gt is greater than the current number of spectra as determined from the last use of the data command backgrnd
298. mand will start an interactive subshell 80 5 3 12 tclout create tcl variables from current state Write internal xspec data to a tcl variable This facility allows the manipulation of xspec data by tcl scripts so that one can for example extract data from xspec runs and store in output files format xspec output data as desired use independent plotting software etc Syntax tclout lt option gt lt parl gt lt par2 gt lt par3 gt gt tclout creates the tcl variable xspec_tclout which can then of course be set to any named variable The allowed values of lt option gt are Show the valid options Does not set xspec_tclout areascal n lt s b gt Writes a string of blank separated values giving the AREASCAL values for spectrum n If no second argument is given or it is s then the values are from the source file if b from the background file arf n The auxiliary response filename s for spectrum n backgrnd n Background filename for spectrum n backscal n lt s b gt Same as areascal option but for BACKSCAL value chain best last proposal stat The best option returns the parameter values corresponding to the smallest statistic value in the loaded chains The last option returns the final set of parameter values in the loaded chains The proposal option takes arguments distribution or matrix and returns the name or covariance matrix for the proposal distribution when using Metropolis Hastings The sta
299. mands 5 3 1 autosave set frequency of saving commands Set or disable autosave which saves the XSPEC environment to a file periodically Syntax autosave lt option gt where lt option gt is either of f or a non zero positive integer N If the option is of f then auto saving is disabled If the option is N the XSPEC environment is saved every N commands The saving of the environment is equivalent to the command XSPEC12 gt save all xautosav xcm i e both the file and model information is saved to the file xautosav xcm placed in the directory xspec cache Thus in case of an unexpected crash the state of XSPEC before the crash can be restored by running xautosav xcm The default value for the auto save option is 1 73 5 3 2 chatter set verboseness level Control the verbosity of XSPEC Syntax chatter lt chatter level gt lt log chatter gt where lt chatter level gt and lt log chatter gt are integer values The initial value for each argument is 10 Higher values will encourage XSPEC to tell the user more lower values tell the user less or make XSPEC quieter lt chatter level gt applies to the terminal output while lt log chatter gt controls the verbosity in the log file Currently the maximum chattiness is 25 Values below five should be avoided as they tend to make XSPEC far too obscure Some commands may temporarily modify the chattiness such as the error command A chattiness of 25 will generate a lot of de
300. mands and Chapter 4 which contains walkthroughs of XSPEC sessions They should then experiment with XSPEC and if necessary look up individual commands in Chapter 5 or descriptions of the spectral models in use in Chapter 6 The User Interface for XSPEC which employs a tel scripting shell and the XSPEC parser are described in Appendix A Users possessing X ray spectra with small numbers of counts per bin are referred to Appendix B which describes the C statistic option Users interested in adding their own models can read how to do so in Appendix C Appendix D describes the PLT plotting package which XSPEC currently uses for graphical output Some of the tools FTOOLS fortran programs scripts that can operate on XSPEC files are listed in Appendix E The XSPEC model library can be linked into other programs following the instructions in Appendix F Appendix G describes how to use your own proposal distribution for Markov Chain Monte Carlo Finally Appendix H includes some notes on the changes between XSPEC v11 and v12 1 1 Newinv12 8 1 New features e New models e cpflux a variant of cflux for photon flux e heilin Voigt absorption profiles for the Hel series e lyman Voigt absorption profiles for the HI or Hell series e zbabs EUV ISM attenuation e Anew statistic pgstat has been added for the case of Poisson distributed data with a Gaussian distributed background The whittle statistic can now be used when fitting averaged powe
301. mf 4 5 Using XSPEC to Simulate Data an Example for Chandra In several cases analyzing simulated data is a powerful tool to demonstrate feasibility For example To support an observing proposal That is to demonstrate what constraints a proposed observation would yield To support a hardware proposal If a response matrix is generated it can be used to demonstrate what kind of science could be done with a new instrument To support a theoretical paper A theorist could write a paper describing a model and then show how these model spectra would appear when observed This of course is very like the first case Here we will illustrate the first example The first step is to define a model on which to base the simulation The way XSPEC creates simulated data is to take the current model convolve it with the current response matrix while adding noise appropriate to the integration time specified Once created the simulated data can be analyzed in the same way as real data to derive confidence limits Let us suppose that we want to measure the intrinsic absorption of a faint high redshift source using Chandra Our model is thus a power law absorbed both by the local Galactic column and an intrinsic column First we set up the model From the literature we have the Galactic absorption column and redshift so XSPEC12 gt mo pha zpha zpo Input parameter value delta min bot top and max values
302. mmand These commands are appended to the list that XSPEC creates to generate the plot and so setplot command will override these values this can either be a bug or a feature depending on what you have done See also setplot delete and setplot list Example XSPEC12 gt setp co LA OT Crab Add the label Crab to future plots delete Delete a PLT command from the command list setplot delete all lt command gt lt command gt lt command gt where lt command gt is the number of a PLT command that had been entered previously using setplot command This command is used to delete commands from the list passed to PLT when you use the XSPEC plot or iplot commands Example XSPEC12 gt setp co LA OT Testing PLT label command XSPEC12 gt setp co LWidth 5 PLT line width command 148 XSPEC12 gt setplot lis List the PLT command stack 1 LAbel OT Testing 2 LWidth 5 XSPEC12 gt setplot del 1 Delete the first command in the stack XSPEC12 gt setplot lis 1 LWidth 5 device Set current plot device XSPEC12 gt setplot device lt plot device gt XSPEC12 gt setplot device lt filename gt XSPEC12 gt setplot device lt filename gt ps cps vps vcps XSPEC12 gt setplot device none If the second argument does not start with a character which indicates that the string represents a PGPLOT device it is taken to be a filename for Postscript output and the d
303. model is fixed to zero for the second data group i e the background spectrum and the parameters of the background model are linked between the data groups If there is no appropriate model for the background it is still possible to proceed Suppose that each bin in the background spectrum is given its own parameter so that the background model is b f A standard XSPEC fit for all these parameters would be impractical however there is an analytical solution for the best fit f in terms of the other variables which can be derived by using the fact that the derivative of L will be zero at the best fit Solving for the f and substituting gives the profile likelihood W Sim t t f S In t m t f B In t f S 1 In S B 1 1n B where S B t t m Fd 2 t t 5 Oe and d We t m S B 4 t t Bam The sign of d in f is chosen so that f gt 0 If any bin has S and or B zero then its contribution to W Wj is calculated as a special case So if is zero then W t m B log t t t If B is zero then there are two special cases If m lt S ts then W t m S log t t otherwise W t m S log S log t m 1 This W statistic is used for statistic cstat if a background spectrum with Poisson statistics has been read in In practice it works well for many cases but for weak sources can A 284 generate an obviously wrong best fit It is not cl
304. model with zero torque inner PIQUA Y css cls ated td tec eceante auteatadddibecdlwelhatdoiwiiluletenteriansesenteudsaetintontes 200 gadem vgadem plasma emission multi temperature with gaussian distribution Of EMISSION measure sssssssesesennnunnnnnnnnnnnnnnnnnnnnn nnmn 201 gauss Zgauss gaussian line profile eeeeeeeeeeeeeeteeeeeeeeeeeeneees 202 gnei vgnei collisional plasma non equilibrium temperature EYOU O ccsiccescnccceccecccccccwccscecssccceccacectcecsccececcctscsesccctecsscatsctecesseessesstessee 203 grad accretion disk Schwarzschild black hole cccceeessees 204 grbm gamma ray burst CONTINUUM cceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeenennee 205 kerrbb multi temperature blackbody model for thin accretion disk around a Kerr black hole sssssssnsnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn 205 kerrd optically thick accretion disk around a Kerr black hole 206 kerrdisk accretion disk line emission with BH spin as free parametet ee 207 laor accretion disk black hole emission line ceeeeeeeeeee 207 laor2 accretion disk with broken power law emissivity profile black hol emission line sii si eases skeen ananasteanacecscasehcaactuaanewersdvasnavanndennsetucedencaten 208 logpar log parabolic blazar MOdel seeeeeeeeeeeeeeeeeeeeeeeeeeeeenees 208 lorentz lorentz line profile ccccceessssssneeeeeeeeeesenseseeeeeeeeeeenseeseees 209
305. modified version of the Rumph et al 1994 model using the ismatten program by Pat Jelinsky and allows the user to set the model redshift parl nH H column density 107 atoms cm par2 nHel Hel column density 10 atoms cm par3 nHell Hell column density 10 atoms cm par4 z Redshift 6 3 36 zdust extinction by dust grains Extinction by dust grains from Pei 1992 ApJ 395 130 suitable for IR optical and UV energy bands including the full energy ranges of the Swift UVOT and XMM Newton OM detectors Three models are included which characterize the extinction curves of 1 the Milky Way 2 the LMC and 3 the SMC The models can be modified by redshift and can therefore be applied to extragalactic sources The transmission is set to unity shortward of 912 Angstroms in the rest frame of the dust This is incorrect physically but does allow the model to be used in combination with an X ray photoelectric absorption model such as phabs Parameter 1 method describes which extinction curve MW LMC or SMC will be constructed and should never be allowed to float during a fit The extinction at V A V E B V x Rv Rv should typically remain frozen for a fit Standard values for Rv are MW 3 08 LMC 3 16 and SMC 2 93 from table 2 of Pei 1992 although these may not be applicable to more distant dusty sources parl method 1 Milky Way 2 LMC 3 SMC par2 E B V color excess par3 Rv ratio of total to selective extinctio
306. modify the plot there is one more thing we can try at the XSPEC level The current bin sizes are much smaller than the resolution so we may as well combine bins in the plot but not in the fitting to make it clearer XSPEC12 gt setplot rebin 100 4 Combines four spectral bins into one The setplot rebin command combines bins till either a S N of the first argument is reached or the number of bins in the second argument have been combined We do an iplot again then do the following modifications PLT gt viewport 0 2 0 2 0 8 0 7 The first thing we ll do is change the aspect ratio of the box that contains the plot viewport in QDP terminology The viewport is defined as the coordinates of the lower left and upper right corners of the page The units are such that the full width and height of the page are unity The labels fall outside the viewport so if the full viewport were specified only the plot would appear The default box has a viewport with corners at 0 1 0 1 and 0 9 0 9 For our purposes we want a viewport with corners at 0 2 0 2 and 0 8 0 7 with this size and shape the hardcopy will fit nicely on the page and not have to be reduced for photocopying Figure I The data and folded model for the simulated Chandra ACIS S spectrum tu ty U LT gt T gt data and folded model 56 0 02 0 03 normalized counts s keV 0 01 0 2 0 5 1 2 5 Energy keV Next we want to change some of the labels l
307. n par4 z redshift 6 3 37 zigm UV Optical attenuation by the intergalactic medium This multiplicative model computes the mean attenuation of the optical UV spectrum of an object at redshift z at a random position on the sky due to intergalactic medium IGM clouds following either Madau 1995 ApJ 441 18 or Meiksin 2006 MNRAS 365 807 The model calculates the mean expected attenuation due to resonant scattering by Lyman transitions and photoelectric absorption shortward of the Lyman limit Attenuation by Helium and metals are not included in the Meiksin model but are expected to be small The total attenuation is set to zero for wavelengths less than 900 257 Angstroms The user chooses whether to include attenuation due to photoelectric absorption parl z redshift par2 model use Madau 0 or Meiksin 1 par3 include photoelectric absorption 1 or not 0 6 3 38 zredden redshifted version of redden IR optical UV extinction from Cardelli et al 1989 ApJ 345 245 The transmission is set to unity shortward of 900 Angstroms This is incorrect physically but does allow the model to be used in combination with an X ray photoelectric absorption model such as phabs parl E B V par2 redshift 6 3 39 zsmdust extinction by dust grains in starburst galaxies Extinction by dust grains suited to starburst galaxies and the hosts of gamma ray bursts The model can be applied over the IR optical and UV energy bands including t
308. n to 01 keV with 100 new linear bins XSPEC12 gt energies reset All models will go back to using the original energy arrays from responses 5 6 7 eqwidth determine equivalent width Determine the equivalent width of a model component Syntax eqwidth RANGE lt frac range gt lt model name Jmodel component number gt err lt number gt lt level gt noerr The command calculates the integrated photon flux produced by an additive model component combined with its multiplicative and or convolution pre factors FLUX the location of the peak of the photon spectrum E and the flux photons per keV at that energy of the continuum CONTIN The equivalent width is then defined as EW FLUX CONTIN in units of keV New for version 12 the continuum is defined to be the contribution from all other components of the model There are certain models with a lot of structure where were they the continuum it might be inappropriate to estimate the continuum flux at a single energy The continuum model is integrated from E 1 lt frac range gt to E 1 lt frac range gt The initial value of lt frac range gt is 0 05 and it can changed using the RANGE keyword The err noerr switch sets whether errors will be estimated on the equivalent width The error algorithm is to draw parameter values from the distribution and calculate an equivalent width lt number gt of sets of p
309. nation dependence is taken from Matt 2002 MNRAS 337 147 such that EW shoulder EWfe Ka 0 1 0 1 cos 1 The model parameters are parl y power law photon index Ng a E par2 E cutoff energy in keV if E 0 there is no cutoff par3 scale the scaling factor for reflection lt 0 no direct component gt isotropic source above the disk par4 z redshift pars A abundance of elements heavier than He relative to Solar par6 As iron abundance relative to Solar par7 cosi cosine of the inclination angle K normalization is the photon flux at 1 keV photons keV cm s of the cutoff power law only without reflection and in the Earth frame 6 2 63 pexrav reflected powerlaw neutral medium Exponentially cut off power law spectrum reflected from neutral material Magdziarz amp Zdziarski 1995 MNRAS 273 837 The output spectrum is the sum of the cut off power law and the reflection component The reflection component alone can be obtained for rel lt 9 Then the actual reflection normalization is Ir el a Note that you need to change then the limits of el en excluding zero as then the direct component appears If E 0 there is no cutoff in the power law The metal and iron abundance are variable with respect to those defined by the command abund The opacities are those set by the command xsect As expected in AGNs H and He are assumed to be fully ionized The core of this model is a Greens func
310. nce criterion XSPEC12 gt setplot rebin sqrt Uses VN to calculate error bars redshift Apply a redshift to the X axis energy and wavelength values setplot redshift lt z gt This will multiply X axis energies by a factor of 1 z to allow for viewing in the source frame Y axis values will be equally affected in plots which are normalized by energy or wavelength Note that this is not connected in any way to redshift parameters in the model or the setplot id redshift parameter and should only be used for illustrative purposes splashpage onloff When set to off the usual XSPEC version and build date information will not be printed to the screen when the first plot window is initially opened This is intended primarily for the HERA installation of XSPEC ungroup Remove previous grouping set up by setplot group resetting all spectra to be in a distinct plot group 152 wave Change the x axis on plots to wavelength and optionally change the units setplot wave lt units gt setplot wave perhz off where lt units gt is an optional string for modifying X axis wavelength units Valid choices currently are angstom cm micron and nm which are case insensitive and can be abbreviated Wavelength units initially default to angstrom Where applicable Y axis units will be modified to match the X axis selection However this behavior can be changed by the command setplot wave perhz which wi
311. nd examples in e g Mineshige et al 1994 ApJ 426 308 Hirano et al 1995 ApJ 446 350 Watarai et al 2000 PASJ 52 133 Kubota and Makishima 2004 ApJ 601 428 Kubota et al 2005 ApJ 631 1062 parl Tin temperature at inner disk radius keV par2 p exponent of the radial dependence of the disk temperature R km i cos 8 where Rin is an apparent inner disk D 10kpc m ji norm radius D the distance to the source and 0 the angle of the disk 0 0 is face on On the correction factor between the apparent inner disk radius and the realistic radius see e g Kubota et al 1998 PASJ 50 667 6 2 31 diskpn accretion disk black hole black body Blackbody spectrum of an accretion disk This is an extension of the diskbb model including corrections for temperature distribution near the black hole The temperature distribution was calculated in Paczynski Wiita pseudo Newtonian potential An accretion rate can be computed from the maximum temperature found For details see Gierlinski et al 1999 MNRAS 309 496 Please note that the inner disk radius par2 can be a free parameter only close to par2 6 otherwise par2 is strongly correlated with K parl maximum temperature in the disk keV 197 par2 inner disk radius in R GM c units 6 lt par2 lt 1000 M cosi D p distance to the source kpc i inclination of the disk and B color effective temperature ratio normalization where
312. nder described by the height to radius ratio H R sphere or hemisphere By default the lower boundary of the cloud not for spherical geometry is fully absorbive e g cold disk However by varying covering factor parameter cov_fac it may be made transparent for radiation In that case photons from the upper cloud can also be upscattered in the lower cloud below the disk This geometry is that for an accretion disk with cold cloudlets in the central plane Zdziarski Poutanen et al 1998 MNRAS 301 435 For cylinder and hemisphere geometries an approximate solution is obtained by averaging specific intensities over horizontal layers see PS96 For slab and sphere geometries no approximation is made The seed photons can be injected to the electron cloud either isotropically and homogeneously through out the cloud or at the bottom of the slab cylinder hemisphere or center of the sphere or from the central plane of the slab if cov_frac ne 1 For the sphere there exist a possibility IGEOM 5 for photon injection according to the eigenfunction of the diffusion equation sin pi tau tau pi tau tau where tau is the optical depth measured from the center see Sunyaev amp Titarchuk 1980 Seed photons can be black body bbodyrad for Tbb gt 0 or multicolor disk diskbb for Tbb lt 0 The normalization of the model also follows those models 1 Tbb gt 0 K RKM 2 D10 2 where D10 is the distance in units of 10 kpc and
313. ne can be obtained for Ir elenl lt 9 Then the actual reflection normalization is rel en Note that you need to change then the limits of lr el n excluding zero as then the direct component appears If E 0 there is no cutoff in the power law The metal and iron abundance are variable with respect to those set by the command abund When using this model it is essential to extend the energy range over which the model is calculated both on the high and low end The high end extension is required because photons at higher energies are Compton down scattered into the target energy range The low energy extension may be required to calculate ionization fractions correctly The energy range can be extended using the extend command The upper limit on the energies should be set above that for which the input spectrum has significant flux To speed up the model calculation of the output spectrum can be limited to energies below a given value by using xset to define IREFLECT_ MAX E in units of keV For instance suppose that the original data extends up to 100 keV To accurately determine the reflection it may be necessary to extend the energy range up to 500 keV Now to avoid calculating the output spectrum between 100 and 500 keV use the command xset IREFLECT_MAX E 100 0 The core of this model is a Greens function integration with one numerical integral performed for each model energy The numerical integration is done using an adaptive m
314. nformation XSPEC is distributed and maintained under the aegis of the GSFC High Energy Astrophysics Science Archival Research Center HEASARC It can be downloaded as part of HEAsoft http heasarc gsfc nasa gov docs software lheasoft download html XSPEC is available either as binaries or source We recommend downloading the source and compiling locally to avoid potential system library conflicts and allow installation of any patches we release If you have any problems compiling or running XSPEC please e mail us at xspecl2 athena gsfc nasa gov The XSPEC Web page comprises links to the anonymous ftp site a Web version of the manual and several useful documents including a list of known bugs The Web address is http xspec gsfc nasa gov with the list of issues and available patches at http heasarc gsfc nasa gov docs xanadu xspec bugs html and additional models which can be added at http heasarc gsfc nasa gov docs xanadu xspec newmodels html Further useful information can be found on the XSPEC Wiki at https astrophysics gsfc nasa gov XSPECwiki XSPECPage and the xspector blog at http xspector blogspot com 1 3 History The first version of XSPEC was written in 1983 at the Institute of Astronomy Cambridge under VAX VMS by Rick Shafer It was written to perform spectral analysis of data from the ESA EXOSAT X ray observatory which was launched that year XSPEC is a descendant of a series of spectral fitting programs wr
315. ng the familiar syntax With a few exceptions here and there the new program syntax is fully backward compatible with that of v11 most of the exceptions support new features that are enhancements and can be ignored if not relevant to the user s problems Some features of v11 previously declared to be deprecated have been removed At the same time the core of the XSPEC calculation scheme has been retained in particular the models library written almost exclusively in fortran77 Model implementation has been rewritten to support allow models written not only in single precision fortran but double precision fortran C and C Further XSPEC can now be used as a development environment for local models by allowing recompilation from the command prompt In v12 spectra can be fit with more than one distinct model simultaneously provided separate model components can be assigned distinct response functions This is particularly useful for spectra from coded aperture masks A new internal dynamic expression implementation allows more complex multiply nested models and also allows parameter links to be polynomial functions of one or more parameters Great care has been taken to optimize the program for memory usage and execution speed A revision of the numerical derivative algorithm has reduced the number of convolution operations required during fitting On the other hand v12 performs its calculations in double precision apart from
316. nged by setting REFLECT PRECISION eg xset REFLECT_PRECISION 0 05 The default precision is 0 01 ie 1 parl reflection scaling factor 1 for isotropic source above disk par2 z redshift par3 abundance of elements heavier than He relative to the solar abundances par4 iron abundance relative to the above pars cos i the inclination angle 6 4 12 simpl comptonization of a seed spectrum The SIMple Power Law model An empirical model of Comptonization in which a fraction of the photons in an input seed spectrum is scattered into a power law component Steiner et al 2009 PASP 121 1279 It is designed for use with soft thermal spectra that are not Compton thick and that have a photon index Gamma gt 1 Simpl offers the advantage of operating in a self consistent manner linking the seed spectrum to the generated power law Compared to powerlaw simpl gives equally good fits while also employing just two parameters and simpl has the virtue of eliminating the divergence of powerlaw at low energies Because simpl redistributes input photons to higher and lower energies for detectors with limited response matrices at high or low energies or with poor resolution the sampled energies should be extended to adequately cover the relevant energy range for details and an example see the appendix in Steiner et al 2009 parl Gamma the photon power law index par2 The scattered fraction between 0 and 1 par3 A flag to switch between up scattering
317. nized material This model uses a grid of XSTAR photionized absorption models calculated assuming a microturbulent velocity of 200km s for the absorption then assumes that this only covers some fraction f of the source while the remaining 1 f of the spectrum is seen directly This is the model used by Reeves et al 2008 On why the iron K shell absorption in AGN is not the signature of the local warm hot intergalactic medium and may also be more generally applicable to the spectral complexity seen in Narrow Line Seyfert 1 AGN Miller et al 2007 A amp A 463 13 parl column density 10 cm par2 log xi where xi L nr par3 covering fraction par4 redshift 6 4 Convolution Model Components Convolution components apply a convolution operator to an input model flux calculated from a source additive model as modified by other components multiplicative factors or other convolution operators They differ from multiplicative components which only apply a bin wise multiplicative factor by allowing transformations of the flux across energy bins 259 6 4 1 cflux calculate flux A convolution model to calculate the flux of other model components For example cflux phabs pow gauss with the normalization of the power law model fixed to a non zero value gives the flux and error on the entire model phabs cflux pow gauss again with the normalization of the power law fixed to a non zero value gives the unab
318. nput array of energy bins gives the boundaries of the energy bins and hence has one more entry than the output flux arrays The energy bins are assumed to be contiguous and will be determined by the response matrix in use The subroutine should thus make no assumptions about the energy range and bin sizes The output flux array for an additive model should be in terms of photons cm s not photons cm s keV i e it is the model spectrum integrated over the energy bin The output array for a multiplicative model is the multiplicative factor for that bin Convolution models are operators on the output from additive or multiplicative models Model subroutines can be written in fortran either in single or double precision in C using either C style arguments or C style arguments and in C The model dat entry In addition to the subroutine XSPEC requires a text file describing the model and its parameters The standard models are specified in the model dat file so we usually refer to this text file by that name A sample model dat entry has the following form modelentry 5r 0 s 1 e20 modelfunc add 0 0 lowT keV 0 1 0 0808 0 0808 79 9 959 0 001 highT kev 4 0 0808 0 0808 79 9 1922 9 0 001 Abundanc 1 0 0 5 5 0 01 redshift 0 0 Sswitch 1 The first line for each model gives the model name the number of parameters the low and high energies for which the model is valid the name of the subroutine to be called and the ty
319. nse to the same dataset There are several reasons why this may be useful for instance We are using data from a coded aperture mask If there are multiple sources in the field they will all contribute to the spectrum from each detector However each source may have a different response due to its position We are observing an extended source using a telescope whose PSF is large enough that the signal from different regions are mixed together In this case we will want to analyze spectra from all regions of the source simultaneously with each spectrum having a contribution from the model in other regions We wish to model the background spectrum that includes a particle component The particle background will have a different response from the X ray background because the particles come from all directions not just down the telescope We will demonstrate the third example here Suppose we have a model for the background spectrum that requires a different response to that for the source spectrum Read in the source and background spectra as separate files XSPEC12 gt data 1 1 source pha 2 2 back pha The source and background files have their own response matrices XSPEC12 gt response 1 source rsp 2 back rsp Set up the model for the source Here we will take the simple case of an absorbed power law XSPEC12 gt model phabs pow Input parameter value delta min bot top and max values for 1 0 001 0 01 0 0 100000
320. ntax and lt A gt is the cosmological constant If the cosmological constant is non zerothen at present cosmo lt H gt lt q gt lt A gt where lt H gt is the Hubble constant in km s Mpe lt do gt is the deceleration parameter XSPEC requires that the universe is flat In this case the value of lt q gt will be ignored and XSPEC will assume that Q matter lt A gt 0 73 XSP XSP EC Examples 2 gt cosmo 100 EC _ 1 1 a lt H gt 100kms Mpc 2 gt cosmo 0 jpeg am 21 A The default values are lt H gt 70 lt q gt 0 0 and 155 XSPEC12 gt cosmo 0 7 lt A gt 0 7 Set a flat universe with 0 0 5 8 3 method change the fitting method Set the minimization method Syntax method lt algorithm gt lt of trials evaluations gt lt critical delta gt method specific options where lt algorithm gt is the method in use and the other arguments are control values for the minimization Their meanings are explained under the individual methods The migrad and simplex methods are taken from the CERN Minuit2 package with documentation located at http seal web cern ch seal MathLibs Minuit2 html index html If either of these are used then the error command will use the Minuit2 minos method to find the confidence regions leven method leven lt of eval gt lt crit delta gt lt crit beta gt delay nodelay The default X
321. ntegration with one numerical integral performed for each model energy The numerical integration is done using an adaptive method which continues until a given estimated fractional precision is reached The precision can be changed by setting BEXRIV_PRECISION eg xset BEXRIV_PRECISION 0 05 The default precision is 0 01 ie 1 parl I first power law photon index par2 Evreak break energy keV par3 I second power law photon index par4 E the e folding energy in keV if E 0 there is no cutoff pars relict reflection scaling factor 1 for isotropic source above disk par6 redshift z par7 abundance of elements heavier than He relative to the solar abundances par8 par9 parl0 parl1 norm 6 2 8 bknpower A broken power law 178 iron abundance relative to the above cosine of inclination angle disk temperature K ion where Fion is the 5eV 20 keV irradiating flux n is the density of the reflector see Done et al 1992 ApJ 395 275 disk ionization parameter amp photon flux at 1 keV of the cutoff broken power law only no reflection in the observed frame broken power law KE E lt Ebreak A KE e ep E gt Ebvreak where parl T power law photon index for E lt Epreak par2 E break break point for the energy in keV par3 T gt power law photon index for E gt Epreak norm K photons keV cm s at 1 keV If POW_EMIN and POW_EMAX have been defined by the xset command
322. nto account The model eff spectra are provided as seen by a distant observer with allowance for the GR effects The user is advised to keep Mns and Rys fixed and fit the temperature and the normalization MagField must be fixed at one of 0 10 or 10 The values of the effective temperature and radius as measured by a distant observer values at infinity are 217 R Re 12 M 1 2 e 290 is the gravitational redshift parameter where Please send your comments questions to Slava Zavlin VYACHESLAV ZAVLIN nmsfc nasa gov and or George Pavlov pavlov astro psu edu If you publish results obtained using these models please reference Zavlin V E Pavlov G G amp Shibanov Yu A 1996 A amp A 315 141 for nonmagnetic models and Pavlov G G Shibanov Yu A Zavlin V E amp Meyer R D 1995 in The Lives of the Neutron Stars ed M A Alpar U Kiziloglu amp J van Paradijs NATO ASI Ser C 450 Dordrecht Kluwer p 71 for magnetic models parl log7 unredshifted effective temperature par2 Mans neutron star gravitational mass in units of solar mass par3 Ras neutron star radius in km par4 neutron star magnetic field strength 0 1e12 or 1e13 G K 1 D where D is the distance of the object in pc 6 2 55 nsagrav NS H atmosphere model for different g This model provides the spectra emitted from a nonmagnetic hydrogen atmosphere of a neutron star with surface gravitational accelerat
323. nues without any questions being asked use the command XSPEC12 gt query yes 5 3 8 save save the current session commands Save aspects of the current state to a command file Syntax save lt option gt lt filename gt Ifno lt filename gt is given then the file savexspec xcm is created If you don t give the extension to the file name the default is xcm The values of lt option gt allowed are model files and all The model option writes out commands to recreate the current model and parameter values the files option writes out commands to read in the current spectra and the all option does both of the above The default option is model To recover the saved context use the command XSPEC12 gt filename Examples XSPEC12 gt save model fname Write out model commands to the file fname xcm XSPEC12 gt save Same as above but save into file savexspec xcm XSPEC12 gt save files fname Write out data file commands 77 5 3 9 script write commands to a script file Open a script file Syntax script lt script file gt where lt script file gt is the name of the file to be opened default extension is xcm If no arguments are on the line then the default file name is xspec xcm If lt script file gt matches the string none then the current script file is closed The script file saves all commands that are input This command is useful for users who use the same set of commands repeatedly Once a script f
324. ny PLT command Numerically integrate the model over specified range Add or remove labels from the plot Control whether a line is used to connect data points Control whether data is plotted using a logio scale Change the default style of the line connecting the data points Change the default line width Control whether the data points are plotted with markers Define a PLT model Change a parameter value associated with the model Immediately re plot the data Change the PLT gt prompt Reset the minimum and maximum plot range Change the color representation of the specified color index Display the values of PLT internal variables Control how PLT divides data into vectors Compute various statistical properties of the data Allow a parameter value to vary during a fit Control whether the time stamp is plotted Uncertainty VErsion Viewport WData WEnviron WHead WModel Xaxis Yaxis filename A 300 Compute the uncertainty in a parameter value Display date of the most recent modification to PLT Control the size of the viewport plotting area Write a QDP data file to disk Write both QDP data and header files to disk Write a QDP header file to disk Write a model file to disk Define the method used to calculate the x variable Define the y axis scale for a contour plot Execute operating system commands Read commands from a PLT command PCO file A 301 Appendix E Associated programs Introduction The HEAsoft pack
325. o electric cross section normally 2 67 par4 W smearing width keV 6 3 25 spexpcut super exponential cutoff absorption A high energy super exponential roll off wera A useful for fitting gamma ray spectra of pulsars see eg Nel amp de Jager 1995 where parl E e folding energy for the absorption par2 a exponent index Caveat the absorption for an energy bin is calculated as the arithmetic mean of the function value at the start and end energies of the bin If the energy bins are large this can be inaccurate and the energies command should be used to define a finer energy grid on which to calculate the model 6 3 26 spline spline modification A cubic spline modification parl start x value 250 par2 start y value par3 end y value par4 start dy dx par5 end dy dx par6 end x value 6 3 27 SSS ice Einstein SSS ice absorption The Einstein Observatory SSS ice absorption par1 ice thickness parameter 6 3 28 swind1 absorption by partially ionized material with large velocity shear A model to fit the soft excess in AGN by partially ionized absorbing material with large velocity shear It approximates this by using XSTAR kn5 photoionization absorption model grids calculated assuming a microturbulent velocity of 100km s and then convolving this with Gaussian smearing This is the model used by Gierlinski amp Done 2006 Sobolewska amp Done 2006 and Done et al 2006 It is an update uses a newer version of XST
326. o which gain parameters belong Steppar can now also handle gain parameters Gain parameters can be displayed either with show parameter or the new show rparameter option The gain command syntax has changed when using multiple sources To better conform with the rest of XSPEC it now requires lt source number gt lt spectrum number gt rather than the reverse Gain parameter limit values can be stored in response files using the keywords GSLOP_MIN GSLOP_MAX GOFFS MIN and GOFFS MAX All input and output data filenames can now include CFITSIO FTOOLSextended syntax for specifying particular HDUs Asa result XSPEC can now handle files which contain spectra ARFs and RMFs in multiple extensions Partial derivative calculations during fitting can now be performed numerically rather than with an approximated analytical expression This option is chosen in the Xspec init initialization file If a new minimum is found during a steppar run steppar now prompts the user for acceptance of the new values Also the delta statistic column of a steppar run is now obtainable with the tclout steppar delstat option The output warning message has been improved in the case where Levenberg Marquardt fitting runs into a zero diagonal element in the second derivative matrix Similarly the more frequent pegged parameter messages due to running into hard limits is now output at higher chatter levels only All calls to the xanlib dynamic memory allo
327. oduce the following output in the file xspec log Logging to file xspec log XSPEC12 gt set i 1 set product 1 I XSPEC12 gt while i lt 5 set product expr product i incr i expr Sproduct Si set product expr Sproduct i incr i expr Sproduct Si set product expr Sproduct i incr i expr Sproduct Si set product expr Sproduct Si incr i expr Sproduct Si set product expr Sproduct i incr i expr Sproduct Si set product expr Sproduct i incr i XSPEC12 gt set product 120 XSPEC12 gt A 6 Command Completion tcl attempts to match the name of any entered command as an abbreviation of a valid command either a tcl or XSPEC command If the entered command matches more than one valid command tcl then lists the possible choices but does not execute the command For XSPEC commands aliases have been constructed matching the command to its minimum abbreviation as listed when typing at the XSPEC prompt see under Aliases For example the minimum abbreviation for the plot command is pl Thus typing pl will execute the plot command even though this would otherwise be ambiguous with the tk command place Command completion is also implemented using the tcl unknown procedure part of which is a script file loaded by tcl at run time and may be different or not exist on your system See the section in this help file on the
328. on for details of how to modify the file The individual spectral data files are created outside of XSPEC by detector specific software They are organized as XSPEC data files but often referred to as PHA files Whatever its format the PHA file contains such information as integration time detector effective area and a scaling factor BACKSCAL in the OGIP standard that estimates the expected size of the internal background The data file also contains the names of the default files to be used for background subtraction and for the detector sensitivity versus incident photon energy the response and arf files A data file has the total observed counts for a number of channels and a factor for the size of any systematic error Each channel is converted to a count rate per unit area assumed cm The default background file is used for background subtraction An error term is calculated using Poisson statistics and any systematic error indicated in the file spectrum numbering Multiple ilespec clauses can be input on a single data command or also on multiple data command Within XSPEC each set of data is referred to by its associated spectrum number lt spectrum gt as determined by the following rules For convenience we denote the number of spectra that have been previously read in by data command as N Spectra in XSPEC are numbered sequentially from 1 If no spectrum number is specified by the user the spectrum in the first
329. on normalization is relren Note that you need to change then the limits of Ir e a excluding zero as then the direct component appears If E 0 there is no cutoff in the power law The metal and iron abundance are variable with respect to those set by the command abund The opacities are those set by the command xsect As expected in AGNs H and He are assumed to be fully ionized When using this model it is essential to extend the energy range over which the model is calculated because photons at higher energies are Compton down scattered into the target energy range The energy range can be extended using the extend command The upper limit on the energies should be set above that for which the input spectrum has significant flux To speed up the model calculation of the output spectrum can be limited to energies below a given value by using xset to define REFLECT MAX FE in units of keV For instance suppose that the original data extends up to 100 keV To accurately determine the reflection it may be necessary to extend the energy range up to 500 keV Now to avoid calculating the output spectrum between 100 and 500 keV use the command xset REFLECT MAX E 100 0 The core of this model is a Greens function integration with one numerical integral performed for each model energy The numerical integration is done using an adaptive method 265 which continues until a given estimated fractional precision is reached The precision can be cha
330. onfidence contours Chi Squared min 4 380202e 01 Levels 4 610202e 01 4 841202e 01 5 301202 01 36 25 ge a D D E oO a 2 1 5 0 0 2 0 4 0 6 0 8 1 1 2 1 4 Parameter nH 107 Figure E The result of the command plot contour The contours shown are for one two and three sigma The cross marks the best fit position independent of the instrument The command flux integrates the current model over the range specified by the user XSPEC12 gt flux 2 10 Model Flux 0 003539 photons 2 232le 11 ergs cm 2 s range 2 0000 10 000 keV Here we have chosen the standard X ray range of 2 10 keV and find that the energy flux is 2 2x10 erg cm s Note that flux will integrate only within the energy range of the current response matrix If the model flux outside this range is desired in effect an extrapolation beyond the data then the command energies should be used This command defines a set of energies on which the model will be calculated The resulting model is then remapped onto the response energies for convolution with the response matrix For example if we want to know the flux of our model in the ROSAT PSPC band of 0 2 2 keV we enter XSPEC12 gt energies extend low 0 2 100 Models will use respons nergies extended to Low 0 2 in 100 log bins Fit statistic Chi Squared 43 80 using 45 PHA bins Test statistic Chi Squared 43 80 using 45 PHA bins Reduced ch
331. oportional to the probability that an incoming photon of energy E will be detected in channel I Ideally then we would like to determine the actual spectrum of a source AE by inverting this equation thus deriving J for a given set of C I Regrettably this is not possible in general as such inversions tend to be non unique and unstable to small changes in C I For examples of attempts to circumvent these problems see Blissett amp Cruise 1979 Kahn amp Blissett 1980 Loredo amp Epstein 1989 The usual alternative is to choose a model spectrum AE that can be described in terms of a few parameters i e f E p1 p2 and match or fit it to the data obtained by the spectrometer For each AE a predicted count spectrum C I is calculated and compared to the observed data C 1 Then a fit statistic is computed from the comparison and used to judge whether the model spectrum fits the data obtained by the spectrometer The model parameters then are varied to find the parameter values that give the most desirable fit statistic These values are referred to as the best fit parameters The model spectrum f E made up of the best fit parameters is considered to be the best fit model The most common fit statistic in use for determining the best fit model is X defined as follows X C C DY Kay where a l is the generally unknown error for channel I e g if C I are counts then o I is usually
332. or the second and third spectrum respectively 5 4 4 cornorm change the normalization of the correction file Reset the normalization used in correcting the background Syntax cornorm lt spectrum range gt lt cornorm gt where lt spectrum range gt lt first spectrum no gt lt last spectrum no gt sa range of spectra to which the correction is to be applied and lt cornorm gt is the value to be used for the normalization A decimal point is used to distinguish a correction norm from a single spectrum lt spectrum range gt If no correction norm is given then the last value input is used the initial value is one 1 If no range is given then the last single range input is modified See the corfile command Examples Assume that there are four spectra all with associated correction files already defined either by default in their PHA file or explicitly by using the corfile command XSPEC12 gt cornorm 1 4 1 The correction norm for all four is set to 1 0 XSPEC12 gt cornorm 0 1 2 0 3 The correction norm for the last input range which was 1 4 is set to 0 then files 1 and 2 are reset to 0 3 XSPEC12 gt cornorm 4 file 4 has the correction also set to 0 3 XSPEC12 gt cornorm 1 4 3 files 1 and 4 are set to 3 XSPEC12 gt cornorm 7 file 4 as the last input single range is set to 0 7 90 5 4 5 data read data backgroun
333. ormalization the fifth parameter from 1 0 to 1 1x107 1 00x107 1 1x10 to give the required flux The simulation is initiated with the command fakeit If the argument none is given we will be prompted for the name of the response matrix If no argument is given the current response will be used We also need to reset the energies command before the fakeit to ensure that the model is calculated on the entire energy range of the response XSPEC12 gt energies reset XSPEC12 gt fakeit none For fake data file 1 needs response file aciss_aimpt_cyl5 rmf and ancillary response file aciss_aimpt_cyl5 arf There then follows a series of prompts asking the user to specify whether he or she wants counting statistics yes the name of the fake data file test fak in our example and the 53 integration time 40 000 seconds the correction norm and background exposure time can be left at their default values Use counting statistics in creating fake data y Input optional fake file prefix Fake data file name aciss aimpt_cyl5 fak test fak Exposure time correction norm bkg exposure time 1 00000 1 00000 1 00000 40000 0 No background will be applied to fake spectrum 1 1 spectrum in use Fit statistic Chi Squared 350 95 using 1024 PHA bins x Warning Chi square may not be valid due to bins with zero variance in spectrum number s 1 Test statistic Chi Squared 35
334. ormula is K L EQ 2z E A L u eel A and parameter settings are 203 parl E line energy in keV par2 0 line width in keV par3 z redshift norm K total photons cm s in the line 6 2 39 gnei vgnei collisional plasma non equilibrium temperature evolution Non equilibrium ionization collisional plasma model This is a generalization of the nei model where the temperature is allowed to have been different in the past i e the ionization timescale averaged temperature is not necessarily equal to the current temperature For example in a standard Sedov model with equal electron and ion temperatures the ionization timescale averaged temperature is always higher than the current temperature for each fluid element The references for this model can be found under the description of the equil model Several versions are available To switch between them use the xset neivers command xset neivers 1 0 gives the version from xspec v11 1 xset neivers 1 1 uses updated calculations of ionization fractions using dielectronic recombination rates from Mazzotta et al 1988 and xset neivers 2 0 uses the same ionization fractions as 1 1 but uses APED to calculate the resulting spectrum Note that versions 1 x have no emission from Ar The default is version 1 1 The vgnei variant allows the user to set the abundances of the model For the gnei model the parameters are parl plasma temperature keV par2 Metal abundanc
335. orted limits Problem occurred in apec model when zero width lines were in the final energy bin Fix to a potential normalization problem occurring in lorentz model with low energy large width lines When running initpackage Imod from PyXspec on certain Linux builds local models calling functions in XSPEC s xslib library producing unresolved symbol link errors v12 7 1 March 2012 New features New models gadem vgadem eplogpar logpar optxagn optxagnf and pexmon The convolution models rdblur rdblur2 kdblur and kerrconv have been sped up They are now O N instead of O N 2 where N is the number of energy bins in the response A 315 Continued rationalization of Compton reflection routines eqpair eqtherm compth compps ntee now all use the same routines as reflect and ireflct For models with ionized reflector there may be changes in results because the new code uses the actual input spectrum to calculate the ionization fractions while the old code assumed a power law The parameter simulation arrays used for the calculation of eqwidth and flux error are now accessible through tclout Initpackage now works on Cygwin The static_initpackage work around is no longer needed and has been removed New Fortran interface wrapper function RFLABD for reading new abundance tables into external programs using the XSPEC models library Added an xsetbl function for use in external programs This provides access to XSPEC s
336. ortran wrapper to the Appendix F table For rmodel command the none option now also resets responses to their initial state Initpackage and Imod are now supported on Cygwin The static_initpackage workaround has been removed New tclout options nullhyp and rerror Tclout eqwidth flux and lumin now also have an errsims option for returning error values array New additive models eplogpar gadem vgadem logpar optxagn optxagnf pexmon Correction to parameter description in kerrconv model Minor rewording in cflux model description to improve clarity For apec and bapec models replaced ATOMDB 2 0 with version 2 0 1 Correction to description of par3 in gabs model 1 XSPEC XSPEC is a command driven interactive X ray spectral fitting program designed to be completely detector independent so that it can be used for any spectrometer XSPEC has been used to analyze data from HEAO 1 A2 Einstein Observatory EXOSAT Ginga ROSAT BBXRT ASCA CGRO IUE RXTE Chandra XMM Newton Integral SPI Swift and Suzaku There now over 1000 papers listed on ADS which cite the Arnaud 1996 XSPEC reference This manual describes XSPEC v12 which is available on Linux gcc 3 2 2 and later MacOSX Darwin gcc 3 3 and later Solaris 2 6 9 WS6 0 and later New users are advised to read Chapter 2 which introduces spectral fitting and the XSPEC approach Chapter 3 which gives an overview of the program com
337. ot valid for simultaneously low temperatures and low optical depth or for high temperatures and high optical depth The user is strongly urged to read the following references esp HT95 Fig 7 before and after using this model in order to fully understand and appreciate the physical assumptions made Titarchuk L 1994 ApJ 434 313 Hua X M Titarchuk L 1995 ApJ 449 188 Titarchuk L Lyubarskij Y 1995 ApJ 450 876 parl Redshift par2 Input soft photon Wien temperature keV par3 Plasma temperature keV par4 Plasma optical depth par5 Geometry switch sign denotes approximation technique magnitude determines geometry lt 1 disk gt sphere par5 20 use analytic approx for B vs t lt 0 B vs t from interpolation norm normalization 6 2 22 cplinear a non physical piecewise linear model for low count background spectra This is a simple non physical model for low count background spectra used by fitting scripts in the ACIS Extract AE package Using this model outside the context of the AE package should be done with extreme caution since it requires a choice on vertex energies and number of segments AE places the first and last vertices at the lowest and highest energy of the background counts 192 Intermediate vertices are placed at energies where a background count exists such that each segment covers a similar number of background counts Any results using this model should cite Broos et al 2010
338. otes to S in the limit of large number of counts This is what is used for the statistic cstat option For Poisson data with Poisson background cstat This case is more difficult than that of Gaussian data because the difference between two Poisson variables is not another Poisson variable so the background data cannot be subtracted from the source and used within the C statistic The combined likelihood for the source and background observations can be written as L rs m b Di zol m b z tb J exp 1 b B i l A 283 where t and t are the exposure times for the source and background spectra respectively B are the background data and b the predicted rates from a model for the expected background If there is a physically motivated model for the background then this likelihood can be used to derive a statistic which can be minimized while varying the parameters for both the source and background models As a simple illustration suppose the source spectrum is source pha and the background spectrum back pha The source model is an absorbed apec and the background model is a power law Further suppose that the background model requires a different response matrix to the source backmod rsp say The fit is set up by XSPEC12 gt data 1 1 source pha 2 2 background pha XSPEC12 gt resp 2 1 backmod rsp 2 2 backmod rsp XSPEC12 gt model phabs apec XSPEC12 gt model 2 backmodel pow where the normalization of the apec
339. panes can be put on a single page by combining multiple lt plot type gt options For example plot data resid ratio model 143 will produce a 4 pane plot However contour plots may not be combined with other plots in this manner When a certain plot type takes additional arguments eg chain model simply list them in order prior to specifying the next plot type plot chain 3 4 data ufspec In multi pane plots XSPEC will determine if two consecutive plot types may share a common X axis e g plot data delchi or plot counts ratio Ifso the first pane will be stacked directly on top of the second Note that the small subset of multi pane plots that were allowed in earlier versions of XSPEC all belonged in this category For changing plot units see setplot energy and setplot wave Also see iplot for performing interactive plots background Plot only the background spectra with folded model if defined To plot both the data and background spectra use plot data with the setplot background option chain Plot a Monte Carlo Markov chain plot chain thin lt n gt lt parl gt lt par2 gt Chains must be currently loaded see chain command and lt par1 gt and lt par2 gt are parameter identifiers of the form lt model name gt n where n is an integer specifying the parameter columns in the chain file to serve as the X and Y axes respectively To select the fit statistic column enter 0 for the lt par gt value
340. par command is used to generate a fit statistic grid Two dimensional grids may be expressed as contour plots using plot contour The model normalization can be set using the renorm command The normalization of the correction file background can be set with cornorm ftest and the Tcl script simftest can be used to calculate F test probabilities Markov Chain Monte Carlo runs can be performed using the chain command with a useful Tcl script rescalecov to rescale the proposal distribution covariance if the Metropolis Hastings algorithm is selected The results can be analyzed using the margin command 20 3 9 1 What to do when you have Poisson data The X statistic assumes that all the spectral channels are Gaussian distributed and that the estimate for the variance is uncorrelated with the observed counts If the data are Poisson then these are bad assumptions especially if there are small numbers of counts in a channel An alternative fit statistic the C statistic should be used in this case ae i 2 The C statistic can also provide confidence intervals in exactly the same way as X To use give the command XSPEC12 gt statistic cstat and then use the fit and error commands as usual An alternative and deprecated approach is to continue using the statistic but change the weighting to provide a better estimate of the variance in the small number limit This can be done using the weight gehrels or weight churazov commands
341. par6 valpha velocity law exponent v goes as r Pha_ par7 gamma adiabatic index It affects the inner hotter parts of the flow therefore we Set is to 4 3 by default pars mdot mass ejection rate in Eddington critical units par9 irrad number of iterations for irradiation norm 6 2 74 smaug optically thin spherically symmetric thermal plasma This model performs an analytical deprojection of an extended optically thin and spherically symmetric source A thorough description of the model is given in Pizzolato et al ApJ 592 62 2003 In this model the 3D distributions of hydrogen metals and temperature throughout the source are given specific functional forms dependent on a number of parameters whose values are determined by the fitting procedure The user has to extract the spectra in annular sectors concentric about the emission peak The inner boundary in arcmin the outer by the fitting procedure The user has to extract the spectra in annular sectors concentric about the emission peak The inner boundary in arcmin the outer boundary also in arcmin and the width in degrees of each annular sector are specified respectively by the three additional keywords XFLT0001 XFLT0002 and XFLT0003 to be added to the spectrum extension in each input file e g with the ftool FKEYPAR Some parameters of smaug define the redshift and other options see below The other relevant ones define the 3D distributions of hydrogen d
342. pbb Accretion disk with power law T r diskpn Accretion disk around a black hole dust Dust scattering out of the beam edge zedge Absorption edge eplogpar Log parabolic blazar model with vFv normalization eqpair eqtherm Paolo Coppi s hybrid hot plasma emission models Mode 166 Description compth equil vequil etable expabs expdec expfac ezdiskbb gabs gadem vgadem gauss zgauss gnei vgnei grad grbm gsmooth heilin highecut zhighect hrefl ireflect kdblur kdblur2 kerrbb kerrconv kerrd Equilibrium ionization collisional plasma model from Borkowski Table model for exponential of 1 times the input Low energy exponential rolloff Exponential decay Exponential factor Multiple blackbody disk model with zero torque inner boundary Gaussian absorption line Plasma emission multi temperature with gaussian distribution of emission measure Simple gaussian line profile Generalized single ionization NEI plasma model GR accretion disk around a black hole Gamma ray burst model Gaussian smoothing with an energy dependent sigma Voigt absorption profiles for He I series High energy cutoff Simple reflection model good up to 15 keV Reflection from ionized material Convolve with the Laor model shape Convolve with the Laor2 model shape Multi temperature blackbody model for thin accretion disk around a Kerr black hole Accretion disk line shape with BH spin as fre
343. pe of model add mul mix or con or acn The final argument two arguments are flags the first should be set to 1 if model variances are calculated by modelfunc and the second should be set to 1 if model should be forced to perform a calculation for each spectrum This final flag is A 292 necessary because if multiple spectra have the same energy bins the default behavior is to perform the model calculation for just one spectrum and copy the results for each of the others However if a model depends on information about the spectrum in addition to its energy ranges it must be forced to perform a calculation for each spectrum The remaining lines in the text file specify each parameter in the model For regular model parameters the first two fields are the parameter name followed by an optional units label If there is no units label then there must be a quoted blank placeholder The remaining 6 numerical entries are the default parameter value hard min soft min soft max hard max and fit delta which are described in the newpar command section There are three special types of parameter which can be used If the name of the parameter is prefixed with a the parameter is a scale parameter and cannot be made variable or linked to an other kind of parameter other than another scale parameter Since the parameter value can never vary only the initial value need be given If the name of the parameter is prefixed with a
344. pectrum The save command now stores relative rather than absolute paths to allow easier porting to other machines The recorn model component has been converted from a mixing to a multiplicative type This allows a model to define multiple recorn components A warning message is now issued if a user attempts to load a response for a source n when there are still slots to fill for source n 1 This is intended to catch cases where a user mistakenly reverses the source and spectrum number input to the response command All bug fixes to v12 5 1 released as patches a o are included in v12 6 0 In addition the following problems have been corrected It was possible for the addition of a systematic model error to actually decrease the overall variance when it was applied to a zero variance bin that was artificially increased by XSPEC for chi square fitting Bug in plot ratio when using setplot wave with Hz units Y axis model values lt 10 20 were not displayed in plot The comptt model no longer stops and prompts the user when it fails during its incomplete gamma calculation The powerlaw model has been modified to avoid a numerical instability that could occur if the index were within 10 12 to 10 15 of 1 0 v12 5 1 Aug 2009 e Gain parameters can now be used in the error freeze newpar thaw and untie commands by prefixing the command name with the letter r for response A 319 parameter the more general category t
345. per particle ionst electrons and is constant throughout the postshock flow in plane shock models Borkowski et al 2001 ApJ 548 820 par2 should always be less than pari If par2 exceeds par1 then their interpretations are switched ie the larger of pari and par2 is always the mean temperature Additional references can be found under the help for the equil model Several versions are available To switch between them use the xset neivers command xset neivers 1 0 gives the version from xspec v11 1 xset neivers 1 1 uses updated calculations of ionization fractions using dielectronic recombination rates from Mazzotta et al 1988 and xset neivers 2 0 uses the same ionization fractions as 1 1 but uses APED to calculate the resulting spectrum Note that versions 1 x have no emission from Ar The default is version 1 1 The npshock version uses relative abundances from the Anders amp Grevesse 1993 mix while the vpnshock version allows the user to set the abundances Parameters for npshock are parl Mean shock temperature keV par2 electron temperature immediately behind the shock front keV par3 Metal abundances He fixed at cosmic The elements included are C N O Ne Mg Si S Ar Ca Fe Ni Abundances are given by the Anders amp Grevesse mixture par4 Lower limit on ionization timescale in units of s cm pars Upper limit on ionization timescale in units of s cm par6 redshift z norm 107 4n D 1 a frena wh
346. perations me MODEL Compile build and initialize a package initpackage of local models PLOT As plot command but interactive using iplot PLT Imod MODEL Load a package of local models log CONTROL Open the log file to save output Irt SCRIPT Likelihood ratio test between two models MODEL Calculate the current model s luminosity lumin over a given rest frame energy range and redshift margin FIT MCMC probability distribution MODEL Define a simple model using an mdefine l arithmetic expression method SETTING Set the minimization method MODEL Define the model to be used when fitting model rmodel the data 70 Command Category Description modid MODEL Guess line IDs in the model multifake SCRIPT Perform many iterations of fakeit and save the results in a FITS file newpar MODEL Modify the model parameters use rnewpar rmewpar for response parameters DATA Restore a range of PHA channels for notice future operations CONTROL Enable parallel processing for particular paralel tasks in XSPEC PLOT Plot various information on the current plot plot device query CONTROL Switch on off prompt to continue fitting quit CONTROL An alias for exit FIT Adjust the model norms and or control renorm automatic renorming SCRIPT Rescale the covariance matrix used in rescalecov the proposal chain command DATA Reset the files used to determine the response detector responses CONTROL Save aspects of the curren
347. perature of thermal photon source in keV par2 Energy spectral index alpha par3 Log of the A parameter Note that f in Borozdin et al 1999 and Shrader amp Titarchuk 1999 is 10 norm An defined in Borozdin et al 1999 and Shrader amp Titarchuk 1999 6 2 11 bremss vbremss zbremss thermal bremsstrahlung A thermal bremsstrahlung spectrum based on the Kellogg Baldwin amp Koch ApJ 199 299 polynomial fits to the Karzas amp Latter ApJS 6 167 numerical values A routine from Kurucz private communication is used in at low temperature end The He abundance is assumed to be 8 5 of H by number Choice of fixed redshift is allowed by using zbremss variant Choice of Hydrogen to Helium abundance ratio is allowed by using the vbremss variant The parameter settings are thus For bremss parl plasma temperature in keV 15 A n n adV where D is the distance to the source cm and ne ny 4r D a norm are the electron and ion densities cm For zbremss parl plasma temperature in keV par2 z redshift norm 3 02x10 An n ndV where D is the distance to the source cm and ne ny 1 181 are the electron and ion densities cm For vbremss parl plasma temperature in keV par2 n He n H note that the Solar ratio is 0 085 15 n ndV where D is the distance to the source cm and ne ny 1 ee are the electron and ion densities cm 6 2 12 c6meklI c6vmekl c6pmekl c6pvmkI different
348. ppended curly bracket specifying use of spectra 1 19 and the separate model commands which are indexed and named in this case simply crab for the source of interest and bkg for the background model spibkg lo These commands are described in detail elsewhere in this document as are the the spibkg_lo spibkg med and spibkg_ hi models In this case 100 logarithmically spaced energy bins spanning the nominal 20 8000 keV band of the SPI instrument were used In this example only one dither point was used to solve for the Crab spectrum and the background The simple assumption of a single background spectrum i e no detector to detector variations was assumed In general and particularly for fainter sources a much larger number of spectra will be needed for a solution and even for the Crab the quality of the fit and the accuracy of the inferred parameters can be improved Also detector to detector and or time 1 e pointing to pointing variations will need to be considered This can be accomplished using the data grouping feature of XSPEC which will be described subsequently Also notice that channels between about 70 and 80 were ignored this is because there are detector electronic effects contaminating the single event data for energies from 1250 1400 keV refer to the SPI data analysis manual for additional discussion and that there are a lot of scientifically uninteresting background model parameters Also the highest energi
349. pwlw Powerlaw with pegged normalization pexmon Neutral Compton reflection with self consistent Fe and Ni lines pexrav Exponentially cut off power law reflected from neutral matter pexriv Exponentially cut off power law reflected from ionized matter ares Photo electric absorption pileup CCD pile up model for Chandra plabs Absorption model with power law dependence on energy pleabs Cut off powerlaw observed through dense cold matter posm Positronium continuum powerlaw zpowerlw projet pshock vpshock pwab raymond vraymond rdblur recorn redden redge reflect refsch sedov vsedov sirf simpl Simple photon power law 3 D to 2 D projection mixing model Constant temperature plane parallel shock plasma model Power law distribution of neutral absorbers Raymond Smith thermal plasma Convolve with the diskline model shape Change correction norm for a spectrum replaces old recornrm command IR optical UV extinction from Cardelli et al 1989 Recombination edge reflection from neutral matter E folded power law reflected from an ionized relativistic disk Sedov model with electron and ion temperatures Multi blackbody self irradiated funnel model Comptonization of a seed spectrum 169 Model Description smaug Model for an optically thin spherically symmetric thermal plasma smedge Smoothed absorption edge spexpcut Super exponential cutoff absorption spline Spline multiplicative factor srcut
350. q XSPEC12 gt statistic cstat All 4 spectra now use cstat cstat is the new default XSPEC12 gt data 5 spec5 pha New spectrum 5 will use cstat XSPEC12 gt statistic test ks All 4 spectra now use ks as the test statistic 5 8 5 xsect set the photoionization cross sections Change the photoelectric absorption cross sections in use Syntax xsect bcmc obcm vern The three options are bcmc from Balucinska Church amp McCammon 1992 Ap J 400 699 with a new He cross section based on 1998 Ap J 496 1044 obcm as bcmc but with the old He cross section and vern from Verneret al 1996 Ap J This changes the cross sections in use for all absorption models with the exception of wabs XSPEC Models 158 5 8 6 xset set variables for XSPEC models Modify a number of XSPEC internal switches Syntax xset abund cosmo delta mdatadir method seed statistic weight xsect lt string name gt lt options gt lt string value gt The arguments abund cosmo method statistic weight and xsect Just run the appropriate XSPEC commands mdatadir changes the directory in which XSPEC searches for model data files You probably don t want to change this The seed option requires an integer argument which will then be used to immediately re seed and re initialize XSPEC s random number generator The delta option is for setting fit delta values see the newpar command whic
351. r a value P is calculated by interpolation on the grid The generalization to more parameters works in the obvious way The table is specified in the model command by the special strings atable mtable or etable with the filename following in brackets see the entries in the models section of the manual Any number of table model components can be used simultaneously Table model components can be much slower than most standard models if there are significant numbers of parameters The memory requirements increase as 2 where n is the number of parameters in the model A table model with more than 3 or 4 fitting parameters is not recommended Additionally the interpolation is linear which implies that the second derivatives used by the default Levenberg Marquadt algorithm may not be accurate If the fit does not work well it may be worth trying the migrad minuit library algorithm which makes no assumptions about the second derivative As with standard models the spectra should be in terms of flux per bin and not flux per keV Any set of energy bins can be used and XSPEC will interpolate the model spectra onto the appropriate energy bins for the detectors in use It is therefore a good idea to choose energy bins such that the spectrum is well sampled over the range of interest The file structure for these models is a FITS format described at http heasarc gsfc nasa gov docs heasarc ofweg docs general ogip_92_009 ogip_92_009 html or ftp
352. r and upper energies of the plot bin 5 7 5 setplot modify plotting parameters Set one of the various plot options setplot lt subcommand string gt where lt subcommand string gt is a keyword followed in some cases by arguments Current settings of all setplot items can be viewed with show plot add Show individual additive model components on the data plots The opposite is setplot noadd 147 area noarea After setplot area is entered plot data and plot ldata will show the data divided by the response effective area for each particular channel plot residuals will necessarily also be affected by this Usual plotting is restored by setplot noarea If data is associated with more than 1 response the response effective area is calculated by simply summing the contributions from each response background nobackground When running plot data or plot ldata also show associated background spectra if any channel Change the x axis on data and residual plots to channels command Add a PLT command to the command list setplot command lt PLT command gt where lt PLT command gt is any valid PLT command very time you use setplot command that command is added to the list that is passed toPLT when you use plot or iplot The most common use of setplot command is to add a common label to all plots produced You should be careful when using this command because XSPEC does not check to see if you have entered a valid PLT co
353. r components are of course un resolvable at INTEGRAL s spatial resolution is by far the brightest source in it immediate region of the sky and its position is precisely known we can opt not to perform SPI or IBIS imaging analysis prior to XSPEC analysis We thus run the standard INTEGRAL SPI analysis chain on detectors 0 18 up to the SPIHIST level for or BIN_I level in the terminology of the INTEGRAL documentation selecting the PHA output option We then run SPIARF providing the name of the PHA II file just created and selecting the update option in the spiarf par parameter file you should refer to the SPIARF documentation prior to this step if it is unfamiliar The celestial coordinates for the Crab are provided in decimal degrees RA Dec 83 63 22 01 interactively or by editing the parameter file This may take a few minutes depending on the speed of your computer and the length of your observation Once completed SPIARF must be run one more time setting the bkg resp option to y this creates the response matrices to be applied to the background model and updates the PHA II response database table accordingly Then SPIRMF which interpolates the template RMFs to the users desired spectral binning also writes information to the PHA response database table to be used by XSPEC Finally you should run SPIBKG_INIT which will construct a set of bbackground spectral templates to initialize the SPI background model currently installed in X
354. r density functions by appending an integer so eg whittle5 is the statistic to use when fitting a pdf constructed by averaging those from 5 observations e The old CERN Minuit library which is used for the migrad minim monte and simplex fitting methods and the improve command has been replaced by the new version The minim and monte methods are no longer supported and the new version does not include an improve command The output from the migrad and simplex fitting methods now looks the same as that from the leven method Note however that the rules for when to write intermediate fit results are not directly comparable so do not provide a measure of the relative speed of the methods Fakeit now has a nowrite option to generate fake spectra without producing output files This is also now available in the multifake tcl script command Parallel processing capability has been added to the steppar command and can be invoked using the parallel command Markov Chain Monte Carlo the chain command now uses the Goodman Weare algorithm by default Previously the default was Metropolis Hastings After a chain run the best fit parameters and statistic are now displayed with chain info and are available through the tclout chain option The default atom_db version used in apec models may now be modified with the ATOMDB VERSION keyword in the user s Xspec init file Steppar now has a delta option for performing grids centered on the best fit
355. r of photons to pile up should be fixed The grade morphing is expressed through a single parameter alpha which should be left as a free parameter This model should be considered in beta test Note that to calculate fluxes etc for the model you must remove the pileup component The pile up model is similar to the operation of the convolution models differing only in the treatment of the detector efficiency during the convolution Note that renorm will not work with pileup since increasing the normalization does not linearly increase the predicted count rate Therefore you should set renorm none prior to doing a fit with pileup parl frame time in seconds 267 par2 maximum number of photons to pile up par3 grade correction for single photon detection par4 grade morphing parameter good grade fraction is assumed proportional to par4 where p is the number of piled photons pars PSF fraction Only this fraction will be treated for pile up Note that this is not the fraction of the PSF included in the extraction region but is the fraction of counts in the region which are from the point source whose pile up is being modeled For this model to work well the extraction region should be large enough to contain essentially all the PSF par6 Number of regions The counts to be piled up will be distributed among par6 regions which will be piled up independently par7 Value of FRACEXPO keyword in ARF 6 6 Mixing Model Components Mixing
356. r reflection models is that analytic approximations are used for the Chandrasekar H functions and their integrals and ELASTIC SCATTERING is assumed see Basko 1978 ApJ 223 268 The elastic scattering approximation means that the model is ONLY VALID UP TO 15 keV in the source frame Future enhancements will include fudge factors that will allow extension up to 100 keV The fact that no integration is involved at any point makes the routine very fast and particularly suitable for generating error contours especially when fitting a large number of data channels The model is multiplicative and so can be used with ANY incident continuum Parameters are as follows parl minimum angle degrees between source photons incident on the tan R H slab and the slab normal par2 maximum angle degrees between source photons incident on the E tan R H slab and the slab normal par3 Angle degrees between the observer s line of sight and the slab normal par4 Iron abundance relative to Solar pars Iron K edge energy par6 Fraction of the direct flux seen by the observer par7 Normalization of the reflected continuum 245 pars redshift Suppose the incident photon spectrum is N E photons cm s keV and that the incident continuum is steady in time and suppose further that the reflected continuum from the slab is R E When you multiply the incident spectrum with href1 what you actually get is the following
357. r structure It also MUST be named randomize dat for this name is the only clue initpackage has to distinguish between creating a chain proposal or local models library All that needs to be entered into this file is a line of the form lt class name gt lt opt string arg1 gt lt opt string arg2 gt lt opt string argN gt for each proposal class that will go in the library lt class name gt must be a case sensitive match to the actual C class name and is the only required entry on the line The class should also be stored in code files lt class name gt h and lt class name gt cxx Any additional arguments on the line will be placed in a single C string including any separating whitespace and passed to the class constructor This is to allow the option of setting initialization parameters at the class construction stage Therefore if optional arguments are included the class must have a constructor which takes a single string argument Otherwise the constructor should contain no arguments For example a randomize dat file declaring two classes might contain MyProposall MyProposal2 1 4773 on false In the code files the constructor declarations corresponding to this would then be A 307 MyProposall h class MyProposall public RandomizerBase public AE MyProposall OP oss MyProposal2 h class MyProposal2 public RandomizerBase public ie MyProposal2 const string amp initArgs LP s
358. r to v12 The other unique aspect of the INTEGRAL analysis is that the background is modeled along with the source s in a single de convolution XSPEC analysis of INTEGRAL SPI data is very different from other instruments is the manner in which the response matrices are handled Since there are a large number of responses involved in the de convolution problem memory use becomes a concern To load the required response matrices as XSPEC normally does would require Nen XNpxNa floating point memory locations per source This could become quite large for high spectral resolution and or long observation scenarios To address this problem a methodology has been developed to reconstruct the required 2 D response matrices from a basis set consisting of a small number 3 of 2 D objects template RMFs and a larger number of 1 D objects component ARFs The full matrices can then be reconstructed on the fly at the minimization step of the calculation and discarded after each use This in principle occurs all very transparently to the user A fuller description of Integral data analysis appears in section 2 of this manual and a walkthrough example is given in 4 6 Current Exclusions The v1 1 commands and features not provided in v12 are Feature Rationale for exclusion recornorm With version 12 5 0 this has been replaced and improved upon by A 312 the recorn mixing model thleqw Rarely used command not yet imp
359. r2 Maximum number of scatterings to consider par3 Iron abundance par4 Iron K edge energy 228 pars Power law photon index par6 High energy cut off threshold energy par7 High energy cut off e folding energy par8 Critical albedo for switching to elastic scattering par9 If par9 gt 1 function uses mean energy shift not integration par10 Source redshift z norm Normalization factor 6 2 66 posm positronium continuum Positronium continuum Brown amp Leventhal 1987 ApJ 319 637 K __2__ r Ec E E E DEAE E Ene E Deen i Eer E Te DB eee Eo E 2Eo Ec E pog EE EE D yf E E 2E 2E E E Ec 2E E E A E for E lt Ec 511 keV where norm K normalization 6 2 67 powerlaw zpowerlw power law photon spectrum powerlaw is a simple photon power law The zpowerlw variant computes a redshifted spectrum A E KE parl a photon index of power law dimensionless norm K photons keV cms at 1 keV 229 For zpowerlw the formula and corresponding parameters are A E K E 1 2 z where parl a photon index of power law dimensionless par2 z Redshift norm K photons keV cms at 1 keV If POW_EMIN and POW_EMAX have been defined by the xset command then the norm becomes the flux in units of 10 ergs cm s over the energy range POW_EMIN POW_EMAX keV unless POW_EMIN POW_EMAX in which case the norm becomes the flux density in micro Jansky at POW_EMIN keV In the
360. ra on its own Thus all plots will appear to have two spectra C12 gt setplot group 1 2 3 4 The spectra are reset to each be in their own group C12 gt setplot group 2 3 4 5 Now there are thr plot groups being spectrum 1 by itself and Ct XSPI Ea XSPI 150 spectra 2 3 and 4 5 as groups XSPEC12 gt setplot group 1 All the spectra are placed in a single plot group id Switch on plotting of line IDs setplot id lt temperature gt lt emissivity limit gt lt redshift gt The IDs are taken from the APEC line list for the temperature given by the first argument The plot only shows those lines with emissivities above the limit set and the lines are redshifted by the amount specified Currently the APEC version used is 1 10 If xset apecroot has been used to reset the APEC files then setplot id uses a filename based on the value of apecroot as described in the documentation for the apec model list List all the PLT commands in the command list setplot list See setplot delete for an example of use noadd Do not show individual additive model components on the data plots setplot noadd The opposite is setplot add noid Switch off plotting of line IDs setplot noid The opposite is setplot id rebin Define characteristics used in rebinning the data for plotting purposes ONLY setplot rebin lt min significance gt lt max bins gt lt plot group g
361. random access to the help system or in the online mode will open to the XSPEC manual homepage 74 The design allows for users to add help files for local models and scripts to the help system if they are placed in the help search path Examples XSPEC12 gt help show the entire manual XSPEC12 gt help fit Go to the help text for the fit command XSPEC12 gt help model pow Go to the help text for the powerlaw model Entering just XSPEC12 gt model will produce a scrolled text list of all available model components XSPEC12 gt help appendices show the manual appendices which document the user interface the Cash statistic how to add models to XSPEC a summary of PLT commands and associated FTOOLS and other programs for manipulating data XSPEC12 gt help appendix local show the appendix describing how to add local models Help also displays the following information as scrolling text XSPEC12 gt help Show a list of all available commands XSPEC12 gt help Show a brief summary and usage syntax of all available commands XSPEC12 gt lt command gt Show brief summary and syntax of lt command gt 5 3 5 log log the session output Open a log file Syntax log STAMP lt log file gt where lt log file gt is the name of the file to be opened default extension is 10g Ifno arguments are on the line then the default file name is xspec log If lt log file gt ma
362. re already known which is often the case Those unfamiliar with INTEGRAL data analysis should refer to the OSA documentation Thus the INTEGRAL SPI analysis chain must be run up to the event binning level if the field of view FoV source content is known e g from published catalogs or from IBIS image analysis or the image reconstruction level SPIHIST should be run selecting the PHA output option and selecting detectors 0 18 This will produce an OGIP standard type II PHA spectral file which contains multiple detector count spectra In addition the SPIARF procedure should be run once for each source to be analyzed plus one additional time to produce a special response for analysis of the instrumental background If this is done correctly and in the proper sequence SPIARF will create a table in the PHA II spectral file which will associate each spectrum with the appropriate set of response matrices The response matrices are then automatically loaded into XSPEC upon execution of the data command in a manner very transparent to the user You will also need to run SPIRMF unless you have opted to use the default energy bins of the template SPI RMFs Finally you will need to run the FTOOL SPIBKG INIT Each of these utilities SPIHIST SPIARF SPIRMF and SPIBKG_INIT are documented elsewhere either in the INTEGRAL or for SPIBKG_ INIT the HEAsoft software documentation There are several complications regarding the spectral de convolut
363. re is a fair amount of information here so we will unpack it a bit at a time One line is written out after each fit iteration The columns labeled Chi Squared and Parameters are obvious The other two provide additional information on fit convergence At each step in the fit a numerical derivative of the statistic with respect to the parameters is calculated We call the vector of these derivatives beta At the best fit the norm of beta should be zero so we write out beta divided by the number of parameters as a check The actual default convergence criterion is when the fit statistic does not change significantly between iterations so it is possible for the fit to end while betaj is still significantly different from zero The beta N column helps us spot this case The Lvl column also 33 indicates how the fit is converging and should generally decrease Note that on the first iteration only the powerlaw norm is varied While not necessary this simple model for more complicated models only varying the norms on the first iteration helps the fit proper get started in a reasonable region of parameter space At the end of the fit XSPEC writes out the Variances and Principal Axes and Covariance Matrix sections These are both based on the second derivatives of the statistic with respect to the parameters Generally the larger these second derivatives the better determined the parameter think of the case of a parabola in 1 D The Covariance Matrix i
364. re the electron and hydrogen densities respectively where D is the angular diameter distance Parameters for vpshock are parl plasma temperature keV par2 H density in cm par3 parl4 Abundances for He C N O Ne Mg Si S Ar Ca Fe Ni wrt the solar as defined by the abund command parl5 Lower limit on ionization timescale in units of s cm parl6 Upper limit on ionization timescale in units of s cm parl7 redshift z norm 107 f a n n Ag D 1 z H where Dy is the angular diameter distance to the source cm and ne ny cm are the electron and hydrogen densities respectively 6 2 69 raymond vraymond emission hot diffuse gas Raymond Smith An emission spectrum from hot diffuse gas based on the model calculations of Raymond and Smith ApJS 35 419 and additions including line emissions from several elements This model interpolates on a grid of spectra for different temperatures The grid is logarithmically spaced with 80 temperatures ranging from 0 008 to 80 keV 231 The vraymond variant allows independent parameters to set the abundances Abundances are the number of nuclei per Hydrogen nucleus relative to the Solar abundances as set by the abund command For raymond the parameters are parl plasma temperature keV par2 Metal abundances He fixed at cosmic The elements included are C N O Ne Mg Si S Ar Ca Fe Ni Abundances are given by the Anders amp Grevesse mixture
365. reate a number of spectrum files where the current model is multiplied by the response curves and then added to a realization of any background Statistical fluctuations can be included The integration time and correction norm are requested for each file The file names input as command line arguments are used as background The number of faked spectra produced is the maximum of the number of spectra currently loaded and the number of file specifications in the command line arguments The special case fakeit none makes one fake spectrum for each spectrum 95 loaded or one fake spectrum if there are none loaded See the examples below for a clearer description If fakeit is immediately followed by the nowrite specifier no actual output files will be generated In this case the fake spectra will exist just for the duration of the Xspec session or until they are unloaded If a faked spectrum is based on a currently loaded spectrum then by default the background response correction file and numerical information are taken from the currently defined data unless a background file is specified on the command line in which case it becomes the background The fakeit none case prompts for the rmf and arf filenames and sets the default numerical data to 1 0 except the correction norm which is set to zero If the output file is type II then the exposure time and correction scale factor will be the same for all spectra in the file For each outpu
366. red 3 161 0 FOr 42 degrees of freedom Null hypothesis probability 2 387580e 11 Current data and model not fit yet Model phabs lt 1 gt powerlaw lt 2 gt bbody lt 3 gt Source No 1 Active On Model Model Component Parameter Unit Value par comp 1 1 phabs nH 10 22 4 00000 frozen 2 2 powerlaw PhoIndex 3 59784 6 76670E 02 3 2 powerlaw norm 0 116579 9 43208E 03 4 3 bbody kT keV 2 00000 frozen 5 3 bbody norm 1 00000E 05 0 0 Notice that in specifying the initial values of the black body we have frozen kT at 2 keV the canonical temperature for nuclear burning on the surface of a neutron star in a low mass X ray binary and started the normalization at zero Without these measures the fit might lose its way Now if we fit we get not showing all the iterations this time Model phabs lt 1 gt powerlaw lt 2 gt bbody lt 3 gt Source No 1 Active On Model Model Component Parameter Unit Value par comp 1 1 phabs nH 10 22 4 00000 frozen 2 2 powerlaw PhoIndex 4 89584 0 158997 2 2 powerlaw norm 0 365230 5 25376E 02 Current Theoretical Model 44 10 Photons cm s keV 10 4 10 5 0 5 Energy keV Figure H The result of the command plot model in the case of the ME data file from 1E1048 1 5937 Here the model is the best fitting combination of power law black body and fixed Galactic absorption The three lines show the two continuum components absorbed to the same degre
367. revesse mixture parl7 fixed redshift 0 gt calculate parl8 1 gt interpolate 2 interpolate using APEC model 212 norm 107 4x D 1 z the source cm and ne ny cm are the electron and hydrogen densities respectively NMA where D4 is the angular diameter distance to The references for the MEKAL model are as follows Mewe R Gronenschild E H B M and van den Oord G H J 1985 A amp AS 62 197 Mewe R Lemen J R and van den Oord G H J 1986 A amp AS 65 511 Kaastra J S 1992 An X Ray Spectral Code for Optically Thin Plasmas Internal SRON Leiden Report updated version 2 0 Liedahl D A Osterheld A L and Goldstein W H 1995 ApJL 438 115 Similar acknowledgement may also be given for the adopted ionization balance Arnaud M and Rothenflug M 1985 A amp AS 60 425 Arnaud M and Raymond J 1992 ApJ 398 394 6 2 51 mkcflow vmcflow cooling flow mekal A cooling flow model after Mushotzky amp Szymkowiak Cooling Flows in Clusters and Galaxies ed A C Fabian 1988 This one uses the mekal or vmekal model for the individual temperature components and differs from cflow in setting the emissivity function to be the inverse of the bolometric luminosity The model assumes Ho 50 and qo 0 Abundance ratios are set by the abund command The switch parameter determines whether the mekal code will be run to calculate the model spectrum for each temperature or whether the mode
368. rgy for the absorption 6 3 10 expfac exponential modification An exponential modification of a spectrum 1 Aexp JE E gt E M E 1 E lt E where parl A amplitude of effect par2 f exponential factor par3 Ee start energy of modification 243 6 3 11 gabs gaussian absorption line 2 M E exp Pr pars exp 5 E parl par2 where parl line energy in keV par2 line width sigma in keV par3 line depth The optical depth at line center is par3 par2 V 2z 6 3 12 heilin Voigt absorption profiles for He I series This model calculate the Voigt absorption profiles for the He I series par1 nHel He I column density 10 atoms cm par2 b b value km s par3 z Redshift 6 3 13 highecut zhighect high energy cutoff A high energy cutoff exp E E E E gt E M E l f 1 0 E lt E where parl E cutoff energy in keV par2 e folding energy in keV The redshifted version zhighect has M E exp 1 2 E gt E 244 1 0 E lt E where parl cutoff energy in keV par2 e folding energy in keV par3 z redshift 6 3 14 hrefl reflection model A simple multiplicative reflection model due to Tahir Yaqoob This model gives the reflected X ray spectrum from a cold optically thick circular slab with inner and outer radii Ri amp Ro respectively illuminated by a point source a height H above the center of the slab The main difference between this model and othe
369. rix for ideal response Syntax diagrsp This command diagonalizes the current response matrix The response matrix is set so that the channel values are mapped directly into the corresponding energy ranges based on the channel energies and energy response range of the current response matrix This command is very similar to running dummyrsp in mode 1 with two important differences Unlike dummyrsp usage of this command requires that an actual response is currently loaded It takes its energy range and channel binning information from this currently loaded response rather than user input parameters Secondly this does not change the effeciency ie effective area as a function of energy stored for the current detector Invoking this command will simulate a detector with perfect spectral resolution If you wish to simulate a detector with perfect resolution AND perfect efficiency use the dummyrsp command The previous response matrices can be retmplemented with the response command with no arguments Any use of the data and notice commands will replace the dummy diagonal response with the correct set of matrices 5 4 7 fakeit simulate observations of theoretical models Produce spectra with simulated data Syntax fakeit nowrite lt file spec gt where lt file spec gt lt file number gt lt file name gt ranges is similar to the syntax used in the backgrnd corfile and response command The fakeit command is used to c
370. ross section Thus the normalizations correspond to the emission measure in each ellipsoidal shell If multiple observations are to be analyzed data sets from different observations corresponding to the same annulus should be part of the same data group For example given the following 4 data files Data sets for obs 1 obsl_anl obs1_an2 Data sets for obs 2 obs2_anl obs2_an2 The proper data loading command is XSPEC12 gt data 1 1 obsl_anl 1 2 obs2_anl 2 3 obsl_an2 2 4 obs2 an2 The projct model has 3 fixed parameters which can be used to define the inner ellipse of the region being analyzed For instance in the example above we could have only read in spectra for the outer two regions but then set the projct parameters to 1 0 0 5 0 0 This would have allowed us to determine the temperatures and emission measures of the outer two annuli without having to worry about fitting a model to the central region parl semi major axis of inner boundary ellipse par2 semi minor axis of inner boundary ellipse par3 position angle of inner boundary ellipse 6 6 3 suzpsf suzaku surface brightness model Mixing model for Suzaku data Mixes the spectra between datagroups based on the PSF overlap between selected regions A surface brightness model is required to calculate the mixing and this can be supplied in several ways If SUZPSF IMAGE has been set to some image file using xset then this image will be used for the surface brightness distrib
371. rpreter is built on the Tcl language some possible XSPEC command abbreviations might coincide with both XSPEC and Tcl commands In this case the interpreter will print the multiple possibilities and stop Command abbreviations may be specified in a start up script SHOME xspec xspec rc see Appendix A for details Inside a script command abbreviations are not recognized This behavior can be overridden but we do not recommended it however specific abbreviations can be defined in the custom startup script Operating system commands can be given from within XSPEC simply by typing the command as at the shell prompt however if wild cards are needed e g Is pha the operating system command must be preceded by syscall Note that an XSPEC abbreviation which corresponds to a system command will run the latter 3 6 Control Commands Control commands include those for controlling parallel operations parallel writing program information log save session to an ASCII file script record a set of commands save save commands needed to restore the current program state autosave automatically run the save command at specified intervals controlling program output chatter control the amount of program output query give an automatic response to prompts tclout and tcloutr create Tcl variables for manipulation in scripts displaying status information show time and version ending the session exit or quit displaying on
372. rrent plotting device Syntax cpd lt plot device gt cpd lt filename gt cpd lt filename gt ps cps vps vcps cpd none Set current plot device The same can be achieved with the setplot device command which takes the same options In XSPEC12 as in previous versions the plot device options are those allowed by the PGPLOT library When plotting to the screen the most commonly used devices are xs xserve and xw xwindow If you select xs the plot window is persistent it remains visible and in the selected 141 position even after the XSPEC session is finished With xw the plot window closes at the end of the XSPEC session Also note that on some platforms when using xs in multiple desktops you might not see the window appear in a second desktop if it is still open in the first If the second argument does not start with a character which indicates that the string represents a PGPLOT device it is taken to be a filename for Postscript output and the default postscript driver will be used The default postscript driver produces a monochrome plot in landscape orientation The filename argument can be followed by a that specifies a particular postscript driver variant Allowable variants are cps color postscript vps monochrome portrait orientation and veps color portrait orientation as well as the default ps PGPLOT devices A number of plot device types are supported in XSPEC PGPLOT devices a
373. s 178 6 2 9 bkn2pow broken power law 2 break energies 2 0 s0seeeee 178 6 2 10 bmc Comptonization by relativistic matter cccssseeeeesseeeeeeees 179 6 2 11 bremss vbremss zbremss thermal bremsstrahlung 180 6 2 12 c6mekl c6 vmekl c6pmekl c6pvmkI differential emission measure using Chebyshev representations with multi temperature mekal 181 6 2 13 cemekl cevmkl plasma emission multi temperature using mekal 182 6 2 14 Clow COOLING TOW iitascuctiiencnicantiniieiinietisantieen anu 183 6 2 15 compbb Comptonization black body ccssseeeeteseeeneeeeeseeeeeees 184 6 2 16 compLS Comptonization Lamb amp Sanford cccsseseeeeeseeeeeeeees 184 6 2 17 compmag Thermal and bulk Comptonization for cylindrical accretion onto the polar cap of a magnetized neutron star 185 6 2 18 compPS Comptonization Poutanen amp SVENSON eeeeseeeeeeeees 185 6 2 19 compST Comptonization Sunyaev amp TitarChuk ccsssseeeeees 188 6 2 20 comptb Thermal and bulk Comptonization of a seed blackbody like Spectrum seceseeeteeeteeeteeenteenseenseenseenseenseenseennneneeensnenenenssenanenseensnensnensns 190 6 2 21 compTT Comptonization Titarchuk ccccccseseeeeeeseeeeeeeseeeeeeeees 190 6 2 22 6 2 23 6 2 24 6 2 25 6 2 26 6 2 27 6 2 28 6 2 29 6 2 30 6 2 31 6 2 32 6 2 33 6 2 34 6 2 35 6 2 36 6 2 37 6 2 38 6 2 39 6 2 4
374. s for 18 elements abund photoionization cross sections xsect The xset command can be used as an interface for abund cosmo method statistic and xsect Additionally xset may set string expressions that are used by models for example the path to and version number of APEC atomic line calculations 22 or the coordinate system for surface brightness calculations used in the xmmpsf mixing model 3 12 Breaking With Ctrl C Ctrl C can be used to break out of the data chain error fit and steppar commands Ifa Ctrl C is entered elsewhere it will have no effect When a break is entered during the fitting commands error fit and steppar the fit will proceed until the end of the current fit iteration ie current lambda value when using Levenberg Marquardt before breaking This is to ensure the program remains in a stable well defined state Therefore on slower machines a user may notice a slight delay before the program actually breaks Ctrl C breaking is currently only implemented for the Levenberg Marquardt fitting method Breaking is implemented for the data command primarily for users who load a large number of Type II spectra with one data command So if you enter XSPEC12 gt data my data 1 1000 and decide it is taking too long to load you can break out at any time However if you do choose to break all spectra loaded from that particular data set will be lost For example if the command below is entered and a Ctr
375. s for the simulations Each line comprises the statistic value for the model without lt model_comp gt that for the model with lt model_comp gt and the difference Before running this script the model should be set up including the additional component to be tested The script will create temporary files model_with_comp xcm and model without _comp xcm 5 9 5 writefits write information about the current fit and errors to a FITS file Tcl script to dump a lot of useful information to a FITS file 163 Syntax writefits lt FITS filename gt This script writes filenames free parameter values and errors to one row of a FITS file The error command should have been run on all the free parameters before running this script If the FITS file already exists then a new row is appended 164 6 XSPEC V12 Models 6 1 Alphabetical Summary of Models Model Description absori Ionized absorber acisabs Extra absorption due to contamination on the ACIS filters ascac ASCA PSF mixing model apec vapec vvapec atable bapec bvapec bvvapec bbody zbbody bbodyrad bexrav bexriv bknpower bkn2pow bmc bremss vbremss zbremss c6mekl c6pmkl c6vmkl c vpmkl cabs cemekl cevmkl cflow cflux compbb APEC thermal plasma model Additive table model Velocity broadened APEC thermal plasma model Blackbody spectrum with redshift variant Blackbody spectrum with norm proportional to surface area E folded broken po
376. s in the additive group from right to left in the order they appear in the model formula 136 N B Beginning with v12 5 0 convolutions no longer have to precede the source Parentheses may also be used to specify convolution precedence so the following two examples are not equivalent C M1 A A2 and C M1 A1 A gt Mixing models are a special case The mixing transformation is applied to the entire model once the combination into a single Sum Component has been executed Note that since XSPEC12 can have multiple models applied to a given spectrum the mixing transformation can nevertheless be applied to only one of the models being fit This will be relevant for example for the case where the background is fitted by a separate model Examples Note that po powerlaw and ga gauss are additive models and that wabs and phabs different photoelectric absorption screens are multiplicative models XSPEC12 gt model po The single component po powerlaw is the model XSPEC12 gt model potga XSPEC12 gt model potga wabs XSPEC12 gt model phabs pot ga XSPEC12 gt model wa phabs po ga XSPEC12 gt model wa po phabs ga error old syntax XSPEC12 gt model wa phabs po XSPEC12 gt model potpo phabs Note that though the first and second components are the same form their parameters are varied separately XSPEC12 gt model phabs wa po A complex and almost certainly unphysical example is the
377. s the inverse of the matrix of second derivatives The Variances and Principal Axes section is based on an eigenvector decomposition of the matrix of second derivatives and indicates which parameters are correlated We can see in this case that the first eigenvector depends almost entirely on the powerlaw norm while the other two are combinations of the nH and powerlaw PhoIndex This tells us that the norm is independent but the other two parameters are correlated The next section shows the best fit parameters and error estimates The latter are just the square roots of the diagonal elements of the covariance matrix so implicitly assume that the parameter space is multidimensional Gaussian with all parameters independent We already know in this case that the parameters are not independent so these error estimates should only be considered guidelines to help us determine the true errors later The final section shows the statistic values at the end of the fit XSPEC defines a fit statistic used to determine the best fit parameters and errors and test statistic used to decide whether this model and parameters provide a good fit to the data By default both statistics are y When the test statistic is y we can also calculate the reduced y and the null hypothesis probability This latter is the probability of getting a value of y as large or larger than observed if the model is correct If this probability is small then the model is not a
378. s to vary Allow indicated parameters to vary See also freeze Syntax thaw lt param range gt where lt param range gt modelName lt param gt lt param gt lt param gt For response parameters see gain command rthaw lt param range gt 114 where lt param range gt sourceNum lt param gt lt param gt lt param gt The indicated parameter or range of parameters will be marked as variable by the fitting commands and treated as a fitting parameter in subsequent fits By default the range will be the last range input by either a freeze or thaw command See the freeze examples for an example of the use of the thaw command 5 5 12 weight change weighting used in computing statistic Change the weighting function used in the calculation of chi squared Syntax weight standard gehrels churazov model Standard weighting uses VN or the statistical error given in the input spectrum Gehrels weighting uses 1 N 0 75 a better approximation when N is small Gehrels N 1986 ApJ 303 336 Churazov weighting uses the suggestion of Churazov et al 1996 ApJ 471 673 to estimate the weight for a given channel by averaging the counts in surrounding channels Model weighting uses the value of the model not the data to estimate the weight 5 6 Model Commands Overview of XSPEC12 Changes In XSPEC12 several models can exist simultaneously unlike XSPEC11 Different models
379. scattering A modification of a spectrum due to scattering off dust on the line of sight The model assumes that the scattered flux goes into a uniform disk whose size has a 1 E dependence and whose total flux has a 1 E dependence parl scattering fraction at 1 keV par2 size of halo at 1 keV in units of the detector beamsize 6 3 7 edge zedge absorption edge The edge model is absorption edge given by 1 E lt E M E exp D E E ie E gt E where parl E threshold energy par2 D absorption depth at the threshold The zedge model given by l E lt E M E exp D E 1 z E E gt Ek allows a redshift z where parl E threshold energy 242 par2 D absorption depth at threshold par3 z redshift 6 3 8 etable exponential tabular model An exponential table model The filename to be used should be given immediately after etable in the model command For example XSPEC12 gt model etable mymod mod uses mymod mod as the input for the model XSPEC will multiply the contents of the model by 1 then take the exponential i e this model is for calculating absorption functions For specifications of the table model file see the OGIP memo 92 009 on the FITS file format for table model files available on the WWW or by anonymous ftp from ftp legacy gsfc nasa gov caldb docs memos 6 3 9 expabs exponential roll off at low E A low energy exponential rolloff M E exp E E where parl E e folding ene
380. se cases it is important that POW_EMIN and POW_EMAX lt lie within the energy range on which the model is being evaluated 6 2 68 pshock vpshock plane parallel shocked plasma constant temperature Constant temperature plane parallel shock plasma model The references for this model can be found under the description of the equil model Several versions are available To switch between them use the xset neivers command xset neivers 1 0 gives the version from xspec v11 1 xset neivers 1 1 uses updated calculations of ionization fractions using dielectronic recombination rates from Mazzotta et al 1988 and xset neivers 2 0 uses the same ionization fractions as 1 1 but uses APED to calculate the resulting spectrum Note that versions 1 x have no emission from Ar The default is version 1 1 The pshock version has abundances given by the Anders amp Grevesse 1993 mixture while the vpshock variant allows the user to set the abundance vector Parameters for the pshock version are parl plasma temperature keV par2 Metal abundances He fixed at cosmic The elements included are C N O Ne Mg Si S Ar Ca Fe Ni in ratios set by the abund command par3 par4 pars norm 230 eee ANDE A lt 3 Lower limit on ionization timescale in units of s cm nce ae 2 7 3 Upper limit on ionization timescale in units of s cm redshift z 10 gt dV 4x D 1 z J coe to the source cm and 7e ny cm a
381. second type II fake background file Now assume no data is currently loaded XSPEC12 gt fakeit 2 backb 1 2 fake spectra in one type II output file are produced as is a corresponding fake background file with 2 rows The fact that the user has entered a type II background file on the command line tells fakeit to produce type II output The first fake spectrum will have no associated background so row in the fake background file will be all zeros Row 2 will consist of the fake background generated from backb 1 5 4 8 ignore ignore detector channels Ignore data channels See also notice Syntax ignore lt rangel gt lt range2 gt lt rangeN gt ignore bad where lt rangelI gt lt spectrum range gt lt channel range gt lt channel range gt 99 Ifno lt spectrum range gt is given then the previous range is used the initial default range is file one 1 only The form of lt spectrum range gt is lt spectrum range gt lt init spectrum gt lt last spectrum gt lt spectrum gt where lt init spectrum gt lt last spectrum gt and lt spectrum gt are spectrum numbers in the order that they were input with the data command The form of channel range is lt channel range gt lt initial channel gt lt last channel gt lt channel gt If integers are given for the channel ranges then channels will be used while if reals are given then energies or wavelengths if setplot
382. seeeeeeeesseeeeeeeseeeeeeeees 239 6 3 3 cabs Optically thin Compton scattering ccseecesssseeeeeeeseeeeeeeees 240 6 3 4 constant energy independent factor c ceeeeeeeeeeeeseeeeeeeeeeenneees 240 6 3 5 cyclabs absorption line Cyclotron 2 ss eeseeeseeeeeeeseeeeeeeeeeeees 240 6 3 6 dust dust scattering aiccscii cones navesnenttweveszercsueensiwenssweseheavaaseeneseestsarsiexes 241 6 3 7 edge zedge absorption edge sssssssuuunnnnnnnnnnnunnnnnennnnnnnnnnnnnnnnn nna 241 6 3 8 etable exponential tabular model 0 2 s eeseeeseeeseeeeeeeeeeeees 242 6 3 9 expabs exponential roll off at low E s snnnsnsnnnnnnnnnennnnnnnnnnnnnnnnnnnn 242 6 3 10 expfac exponential modification sssussssesennnnnnnnennnnnnnnnnnnnnnnnnnnnn 242 6 3 11 gabs gaussian absorption line nsnnnennnunnnennnnnnnnnnnnnnnnnnnnnnnnnnnnne 243 6 3 12 heilin Voigt absorption profiles for He SerieS c seeeeeeeeeeeees 243 6 3 13 highecut zhighect high energy cutoff eeceeseeeeeeeeeeeeeeeeeeenees 243 6 3 14 hrefl reflection model 0 jc tein 244 6 3 15 Iyman Voigt absorption profiles for H or He Il Lyman series 245 6 3 16 mtable multiplicative tabular model sseeesseeeseeeeeeeseeeees 245 6 3 17 notch absorption lime NOTCH 2 ces sseeeeneeeeeeeeeeeeeeeeeeeeeeeeenennes 246 6 3 18 pcfabs zpcfabs partial covering fraction
383. shock vnpshock pshock vpshock sedov vsedov c6mekl c6vmekl c6pmekl c6pvmekl cemkl cevmkl mekal vmekal mkcflow vmclow 159 Thermally broaden emission lines in APEC input files APECVELOCITY apec vapec bapec bvapec equil vequil npshock vnpshock pshock vpshock sedov vsedov c6mekl c6vmekl c6pmekl c6pvmekl cemkl cevmkl mekal vmekal mkcflow vmclow Velocity broaden emission lines in APEC input files NEIAPECROOT gnei nei vgnei nvei equil vequil npshock vnpshock pshock vpshock sedov vsedov Switch from default NEIAPEC input files POW_EMIN POW_EMAX powerlaw bknpower bkn2pow cutoffpl Switch to normalize to a flux calculated over an energy range NEIVERS gnei nei vgnei vnei equil vequil npshock vnpshock pshock vpshock sedov vsedov Switch NEIAPEC version number CFLOW_VERSION mkcflow vmclow Switch CFLOW version number CFLOW_NTEMPS mkcflow vmclow Switch number of temperature bins used in CFLOW model SUZPSF IMAGE suzpsf Set image file to be used for surface brightness SUZPSF RA suzpsf Set RA for center surface XSPEC Models 160 brightness map which is taken from the WMAP SUZPSF DEC suzpsf Set Dec for center surface brightness map which is taken from the WMAP SUZPSF MIXFACT IFILE suzpsf Set filename to read mixing factors SUZSF MIXFAC
384. sorbed flux and error Finally phabs pow cflux gauss with the normalizaton of the gaussian fixed to a non zero value gives the flux and error on the gaussian component Note that when the cflux model is used the normalization of one of the additive models must be fixed to a non zero value It is also important to ensure that the energy range over which the model is calculated which is determined by the response matrix in use covers the energy range for which the flux is calculated If the model to which the cflux is applied integrates to zero then a divide by zero error will occur resulting in NaN values for the fit statistic Parameters are parl Emin Minimum energy over which flux is calculated par2 Emax Maximum energy over which flux is calculated par3 lg10Flux log base 10 flux in erg cm s 260 6 4 2 cpflux calculate photon flux A convolution model to calculate the photon flux of other model components For example cpflux phabs pow gauss with the normalization of the power law model fixed to a non zero value gives the photon flux and error on the entire model phabs cpflux pow gauss again with the normalization of the power law fixed to a non zero value gives the unabsorbed photon flux and error Finally phabs pow cpflux gauss with the normalizaton of the gaussian fixed to a non zero value gives the photon flux and error on the gaussian component Note that when the cpflux model is used the norm
385. spectra from time series data In this case the x axis is frequency in Hz and not keV so plots have to be modified appropriately The correct fit statistic is that due to Whittle as discussed in Vaughan 2010 and Barret amp Vaughan 2012 N E S 2y 2 tom A 286 B 3 Parameter confidence regions Fisher Matrix XSPEC provides several different methods to estimate the precision with which parameters are determined The simplest and least reliable is based on the inverse of the second derivative of the statistic with respect to the parameter at the best fit The first derivative must be zero by construction and the second derivative provides a measure of how rapidly the statistic increases away from the best fit The faster the statistic increases i e the larger the second derivative the more precisely the parameter is determined The matrix of second derivatives is often referred to as the Fisher information Its inverse is the covariance matrix written out at the end of an XSPEC fit The numbers provided for each parameter in the standard fit output are estimates of the one sigma uncertainty calculated as the square root of the diagonal elements of the covariance matrix As such these ignore any correlations between parameters Whether correlations are important can be seen by comparing with the off diagonal elements of the covariance matrix In general these estimates should be considered lower limits to the true uncertainty
386. ss G 2 Writing a Chain Proposal Class All user proposal classes must inherit from XSPEC s abstract class RandomizerBase whose interface is defined in the file headas lt version gt Xspec sre XSFit Randomizer RandomizerBase h The proposal class must declare a constructor as described in the previous section and which explicitly calls the RandomizerBase constructor passing it a lower case name string This name will become the proposal identifier when making a selection using the chain proposal option during an XSPEC session For example MyProposall cxx MyProposall MyProposall RandomizerBase myprop1 In XSPEC XSPEC12 gt chain proposal mypropl lt optional initializing args gt The RandomizerBase class contains 5 private virtual functions doRandomize doInitializeLoad doInitializeRun doAcceptedRejected and getCovariance doRandomize is the only pure virtual function and therefore is the only one which must be overridden in the inheriting class Its signature is virtual void doRandomize RealArray amp parameterValues const Fit fit where RealArray is a typedef for std valarray lt double gt and is defined in src main xsTypes h This function is called by XSPEC for each chain iteration and XSPEC passes in the current variable A 308 model parameter values The overridden doRandomize function performs the necessary parameter modifications and sends them back in the same array The f
387. stematic term to the variance 140 5 6 19 untie unlink previously linked parameters ccsseseeeeeeeeeeeeeeeeees 140 5 7 Plot COMMANGS vensecwssccsertencccece scat sacssuatsecngustsansussscnesusssutnsunssunasustees 140 5 7 1 cpd set current plotting device sceeeeeeeseeeeeeeeeeeeneeeeeeeeeeees 140 5 7 2 hardcopy print PlON sissies ectevedes motstacsceteizanatineaceeedeiternsiackasdeneetaaahies 142 5 7 3 iplot make a plot and leave XSPEC in interactive plotting mode 142 5 7 4 PIOTS MAKE a DION vas cise ses se ccewestasaaseontnecndsac ccd cunasecndsnawasearattaasancencsadhaaiee 142 5 7 5 setplot modify plotting parameters eeeeeeeeeeeeeeeeeeeeeeeeeneees 146 5 8 Setting COMMANG S vvviciicciisscccsessiecreceisssscseccrcaeenesanssereeenedcererien 152 5 8 1 abund set the Solar abundances ccceeeeeeeeeeeeeeeeeeeeeeeeeeeneneeeeeess 152 5 8 2 COSMO Set the COSMOLOOY seseeeeeeeeeeseeeeeeneeeeeeeeeeeeeeeseeneeeeeeeeennenes 154 5 8 3 method change the fitting method cseeeeeeeeeeeeeeeeeeeeeeeeeeeenneees 155 5 8 4 statistic change the objective function statistic for the fit 156 5 8 5 xsect set the photoionization cross sections 2 0eseeeees 157 5 8 6 xset set variables for XSPEC models cccseeeeeeeeeseeeeeeseeeeneeeees 158 5 9 TO SCMipts sisisessescscscsecctacseesedescceuedsasanestisdsanedewccessdaandaundeuddewsteredaenieas 161 5 9 1
388. step spec gt lt log nolog gt lt modelName gt lt param index gt delta lt step size gt lt steps gt In the first case the parameter is stepped from lt low value gt to lt high value gt in lt steps gt plus one trials In the second case the parameter is stepped from lt best fit value gt lt step size gt lt steps gt to lt best fit value gt lt step size gt lt steps gt ie a total of 2 lt steps gt 1 trials The stepping is either linear or log Initially the stepping is linear but it can be changed by the optional string log before the parameter index nolog will force the stepping to be returned to the linear form If more than one parameter is entered then lt steps gt must be entered for each one except 113 the last Note that every variable parameter whose lt param index gt is NOT entered in the command will still be allowed to vary freely during each steppar iteration To perform a steppar run on gain or response parameters the optional lt modelName gt specifier is replaced by an optional lt sourceNumber gt specifier and the letter r needs to be attached as a prefix to the lt parameter index gt For example steppar 2 r3 1 5 2 10 will step the third response parameter belonging to source number 2 The number of steps is set initially to 10 At each value the parameter is frozen a fit performed and the resulting value of chi squared given If best is given as an argument
389. t lt error type gt 151 In plotting the data from a spectrum or group of spectra see setplot group adjacent bins are combined until they have a significant detection at least as large as lt min significance gt in o However no more than lt max bins gt may be so combined Initial values are 0 and 1 respectively This argument effects only the presentation of the data in plots It does not change the fitting in particular the number of degrees of freedom The values given are applied to all the plotted data in the plot group specified as the final argument To change the rebinning simultaneously for all the plot groups give anegative value of the plot group The lt error type gt argument specifies how to calculate the error barson the new bins The default is quad which sums in quadrature the errors on the original bins sqrt uses yN where N is the number of counts in the new bin poiss 1 uses 1 N 0 75 poiss 2 uses yN 0 25 and poiss 3 is the arithmetic mean of poiss 1 and poiss 2 If background is present its error is calculated by the same method then added in quadrature to the source error Examples XSPEC12 gt setplot rebin 3 5 1 Bins in plot group 1 are plotted that have at least 30 or are grouped in sets of 5 bins XSPEC12 gt setplot rebin 5 5 The significance is increased to 50 XSPEC12 gt setplot rebin 10 1 All plotted bins can be grouped into up to 10 bins in reaching the 50 significa
390. t chain stat 3 Prints statistical information on the 3 parameter of the chain XSPEC12 gt chain proposal gaussian myfile txt New chain proposals will be a normal distribution using covariance values stored in myfile txt rather than fit correlation matrix XSPEC12 gt chain prop gauss diag 1 001 0001 New chain proposals will be a normal distribution using a 3x3 diagonal covariance matrix with the values from the command line XSPEC12 gt chain temperature 8 Sets the Metropolis Hastings temperature value to 8 for future chain runs replacing the default 1 0 XSPEC12 gt chain clear Removes the 2 loaded chains from xspec s chain list error uncertain determine confidence intervals of a fit Determine the confidence region for a model parameter Syntax error stopat lt ntrial gt lt toler gt maximum lt redchi gt lt delta fit statistic gt lt model param range gt where lt model param range gt lt modelName gt lt first param gt lt last param gt determines the ranges of parameters to be examined and lt delta fit statistic gt distinguished from the model parameter indices by the inclusion of a decimal point is the change in fit statistic used For response parameters see gain command use rerror with identical syntax except lt response param range gt lt sourceNum gt lt first param gt lt last param gt The
391. t command gt will display the manual section corresponding to lt command gt Help for individual model components can be displayed by XSPEC12 gt help model lt modelName gt if all else fails you can e mail your questions to the XSPEC team at xspecl2 athena gsfc nasa gov 3 4 Commands XSPEC commands can be divided into 6 categories Control Data Model Fitting Plotting and Setting as follows Control commands include items such as controlling logging obtaining help executing scripts and other miscellaneous items to do with the program control rather than manipulating data or theoretical models Data commands load spectral data and calibration data such as backgrounds and responses and specify channel ranges to be fit 15 Model commands define and manipulate theoretical models and their parameters and compute additional information such as fluxes or line identifications Fit commands initiate the fitting routines control the parameter set perform statistical tests and compute confidence levels Plot commands generate about 50 different kinds of 2 dimensional plots Setting commands change a variety of XSPEC internals which control details of models statistics and fitting methods These command types are summarized below For full details see Chapter 5 3 5 Issuing Commands In an interactive session the command interpreter accepts the shortest unambiguous abbreviation for any command Since the inte
392. t device data DATA Input one or more PHA data files delcomp MODEL Delete a component from the model DATA Diagonalize the current response for an diagrsp ideal response MODEL Create a dummy response covering a dummyrsp given energy range editnod MODEL Add delete or replace one component in the model airas MODEL o new energy binning for model Uxes MODEL Calculate a model component s eqwidth equivalent width FIT Determine a single parameter confidence error rerror region rerror is for response parameters i CONTROL Execute a shell command from within XSPEC bdi CONTROL Wind up any hardcopy plots and exit from XSPEC MODEL This is now obsolete See energies extend command DATA Produce simulated data files for fakeit ea l sensitivity studies fit FIT Find the best fit model parameters flux MODEL Calculate the current model s flux over an energy range FIT Do not allow a model parameter to vary freeze rfreeze during the fit rfreeze is for response parameters 69 Command Category Description FIT Calculate the F statistic between two ftest model fits ain MODEL Perform a simple modification of the 8 response gain FIT Monte Carlo calculation of goodness of goodness fit hardcopy PLOT Spool the current plot to the printer help CONTROL Obtain help on XSPEC commands identity MODEL List possible lines in the specified energy range PN DATA Ignore a range of PHA channels in 8 future fit o
393. t file the user will be prompted for an output file name Ifa background file is in use then fakeit will also simulate a new background for each spectrum Background files are given the same names as output spectrum files but with _bkg appended to the end of the stem The simulated spectra automatically become the current data files The ignore status is completely reset Statistical Issues The statistical fluctuations used to create the simulated spectra will depend on whether the current spectra have Poisson or Gaussian errors If a spectrum file has a STAT_ERR column and the POISSERR keyword is set to false then xspec assumes Gaussian errors with sigma from the values in the column Otherwise errors are assumed to be Poisson based on the number of counts Note that it is possible for the spectrum and background files to have different error types For fakeit cases when there is no current file to use Poisson errors are assumed Type I vs Type I Output Fakeit determines whether to place its fake spectra and background data into type I or type II files based on the following rules If fake spectra are based on currently loaded spectra then the output files will have the same format as those loaded For example Assume 3 spectra are currently loaded spectrum 1 from file typeTdata pha and spectra 2 and 3 from file typeIIdata pha Then XSPEC12 gt fakeit will produce 3 fake spectra in 2 output files with names prompted from the user
394. t into a Tcl list regsub all Spar4 cpar4 set lpar4 split S cpar4 Print out the result to the file Parameter value is the Oth element of the list lpar4 puts Sfileid i lindex Slpar4 0 He A 281 Close the file close Sfileid The user is encouraged to read the voluminous on line documentation and literature available about tcl in order to benefit fully its flexible command processing graphical interfacing and scripting capabilities See http www tcl tk for much more information and extensive bibliography Appendix B Statistics in XSPEC B 1 Introduction There are two operations performed in XSPEC that require statistics The first is parameter estimation which comprises finding the parameters for a given model that provide the best fit to the data and then estimating uncertainties on these parameters The second operation is testing whether the model and its best fit parameters actually match the data This is usually referred to as determining the goodness of fit Which statistics should be used for these two operations depends on the probability distributions underlying the data Almost all astronomical data are drawn from one of two distributions Gaussian or normal and Poisson The Poisson distribution is the familiar case of counting statistics and is valid whenever the only source of experimental noise is due to the number of events arriving at the detector This is a good approximation for mod
395. t option returns the output of the last chain stat command chatter Current xspec chatter level compinfo lt mod gt n Name 1 parameter number and number of parameters lt groupn gt of model component n belonging to model w optional name lt mod gt and optional datagroup lt groupn gt cosmo Writes a blank separated string containing the Hubble constant H0 the deceleration parameter q0 and the cosmological constant Lambda0 Note that if Lambda0 is non zero the Universe is assumed to be flat and the value of q0 should be ignored covariance m n datagrp n datasets dof energies n eqwidth n errsims error lt mod gt n for gain parameters use rerror lt sourceNum gt Jn 81 Element m n from the covariance matrix of the most recent fit If no indices are specified then entire covariance matrix is retrieved Data group number for spectrum n If no n is given outputs the total number of data groups Number of datasets Degrees of freedom in fit and the number of channels Writes a string of blank separated values giving the energies for spectrum n on which the model is calculated Ifn is not specified or is 0 it will output the energies of the default dummy response matrix Last equivalent width calculated for spectrum n If errsims keyword is supplied this will instead return the complete sorted array of values generated for the most recent eqwidth error simulation
396. t options return the statistic or delta statistic column respectively from the most recent steppar run Otherwise the parameter column indicated by lt parNum gt is returned Note that for multi dimensional steppars the returned parameter column will contain duplicate values in the same order as they originally appeared on the screen during the steppar run Number of variable fit parameters The XSPEC version string 85 weight Name of the current weighting function xflt n XFLT keywords for spectrum n The first number written is the number of keywords and the rest are the keyword values Examples XSPEC12 gt data filel XSPEC12 gt model pha po XSPEC12 gt fit XSPEC12 gt tclout stat XSPEC12 gt scan xspec_tclout f chistat XSPEC12 gt tclout param 1 XSPEC12 gt scan xspec_tclout f par2 XSPEC12 gt tclout param 2 XSPEC12 gt scan xspec_tclout f par3 XSPEC12 gt tclout param 3 In this example scan is a tcl command that does a formatted read of the variable xspec_tclout It reads the first floating point number into the variable given by the last argument on the line This sequence creates a simple model fits it and then writes the X statistic and the three parameters to tcl variables chistat parl par2 and Spar3 These can now be manipulated in any way permitted by tcl Examples of using tclout and tcloutr can be found in the Xspec src scr
397. t state to a save command file CONTROL Open the script file to save all script commands input Seti t PLOT Modify the plot device and other values P used by the plot routines CONTROL Display current file and model show information SCRIPT Generate simulated datasets to estimate simftest the F test probability for adding a model component 71 Command Category Description source CONTROL Execute a script file statistic SETTING Change the fit statistic in use FIT Step through a range of parameter steppar values perform a fit at each step syscall CONTROL Runa shell command systematic MODEL Set the model systematic error tclout CONTROL write xspec data to a tcl variable tcloutr CONTROL _ tclout with return value thaw thaw FIT Allow a model parameter to vary during the fit rthaw is for response parameters MODEL Calculates expected fluorescent line thleqw equivalent width time CONTROL Display elapsed time and other statistical information uncertain FIT Alias for error MODEL Untie linked parameters runtie is for untie runtie response parameters version CONTROL Print XSPEC version and build date time FIT Change the weighting function used for weight chi squared fits writefits SCRIPT Write information about the current fit and errors to a FITS file ee SETTING Change the photoelectric absorption cross sections in use iset SETTING Modify a number of XSPEC internal switches 72 5 2 Descr
398. t to the value of parameter 3 parameter 5 plus 6 7 C12 gt newpar 6 3 1 9 5 e r ESj XSPI J XSPI The value of parameter 6 is set to 0 1 times the value of parameter 3 minus 9 5 C12 gt newpar 5 2 5 The value of parameter 5 is set to the value of parameter 2 plus 5 XSPEC12 gt newpar 8 1 4 6 parameter 8 is set to parameter 1 divided by 4 6 XSPEC12 gt untie 6 Makes parameter 6 independent of parameter 3 and a free parameter TA XSPI 140 5 6 18 systematic add a model dependent systematic term to the variance Syntax systematic lt model systematic error gt Set a systematic error term on the model to be added in quadrature to that on the data when evaluating chi squared The default value is zero 5 6 19 untie unlink previously linked parameters Untie the specified parameter from any links to other parameters Syntax untie lt param range gt where lt param range gt is of the form lt param range gt modelName lt param gt For response parameters see gain command runtie lt param range gt where lt param range gt is of the form lt param range gt sourceNum lt param gt Parameters previously linked together with commands such as XSPEC12 gt newpar lt param spec gt are unlinked The parameter will retain its current value for the next fit 5 7 Plot Commands 5 7 1 cpd set cu
399. tA3 tA tM As are used for the continuum The range has been reset to the original value XSPEC12 gt eqwidth 1 Illegal as M is not an additive component 5 6 8 flux calculate fluxes Calculate the flux of the current model between certain limits Syntax flux lt lowEnergy gt lt hiEnergy gt err lt number gt lt level gt noerr where lt lowEnergy gt and lt hiEnergy gt are the values over which the flux is calculated Initial default values are 2 to 10 keV The flux is given in units of photons cm s and ergs cm s The energy range must be contained by the range covered by the current spectra which determine the range over which the model is evaluated Values outside this range will be reset automatically to the extremes Note that the energy values are two separate arguments and are NOT connected by a dash see parameter ranges in the freeze command The flux will be calculated for all loaded spectra If no spectra are loaded or none of the loaded spectra have a response the model is evaluated over the energy range determined by its dummy response In XSPEC12 models are automatically assigned default dummy responses when there is no data so the dummyrsp command need not be given If more than 1 model has been loaded whichever model the user has specified to be the active one for a given source is the one used for the flux calculation
400. ta pha which used ROWS 3 AND 4 of the 3 arf files for their own responses However the responses used above to generate the 2 fake spectra will use ROWS 1 AND 2 of the 3 arf files This is necessary since the fake spectra will be placed in rows and 2 of their fakeit output file Examples Type I files For each of these examples assume 3 spectra are currently loaded each in its own type I file and that the second spectrum has a background file XSPEC12 gt fakeit This will produce 3 fake spectra each in its own type I output file and the user will be prompted for the file names The response file information will come from each of the original spectra If any response information is invalid the user will then be prompted A fake background file will be produced for the second spectrum XSPEC12 gt fakeit 4 Produces 4 fake spectra the first 3 created as in the previous example The fourth will be created with no background spectrum and this user is prompted for response information XSPEC12 gt fakeit backa none 4 Produces 4 fake spectra For the first spectrum a fake background file will be generated from the file backa The second uses its own background file as before The third fake spectra will no longer use the response information from loaded spectrum 3 the user will be prompted instead and its default numerical data will be reset to 1 The fourth spectrum will be created as in the previous example If no data is currentl
401. tartup Xspec init file Output from the fit command also depends on the fitting method currently in use Using the Levenberg Marquardt algorithm the parameters accepted are the maximum lt number of iterations gt before the user is prompted the lt critical delta gt which is the absolute not fractional change in the statistic between iterations less than which the fit is deemed to have converged and lt critical beta gt The lt critical beta gt provides an optional second stopping criterion and it refers to the beta N value reported during a Levenberg Marquardt fit This is the norm of the vector derivatives of the statistic with respect to the parameters divided by the number of parameters At the best fit this should be zero and so provides another measure of how well the fit is converging lt critical beta gt is set to a negative value by default which renders it inactive Including the string delay as an argument to fit turns on delayed gratification It is turned off by nodelay Delayed gratification modifies the way the damping parameter is set and has been shown in many cases to speed up convergence The default is nodelay If lt number of iterations gt lt critical delta gt lt critical beta gt delay or node lay is entered through the fit command it also becomes the future default value for the currently loaded fit method ie Levenberg Marquardt Examples XSPEC12 gt fit Fit with the default number o
402. tatistic is simply the largest difference between the observed and model EDFs D supremum Y M The XSPEC statistic test ks option returns log D The significance of the ks value can be determined using the goodness command Cramer von Mises cvm The Cramer von Mises statistic is the sum of the squared differences of the EDFs F r N 2 WET Dae M The XSPEC statistic test cvm option returns log w and its significance should be determined using the goodness command Anderson Darling ad Anderson Darling is a modification of Cramer von Mises which places more weight on the tails of distribution w Za M 1 Runs runs The Runs or Wald Wolfowitz test checks that residuals are randomly distributed above and below zero and do not cluster Suppose N is the number of channels with ve residuals N the number of channels with negative residuals and R the number of runs then the Runs statistic is A 289 Runs R p u 1 u 2 N 1 where 2N_N N N N and w 1 N As for the EDF tests XSPEC returns log Runs B 5 References Barret D amp Vaughan S 2012 Maximum likelihood fitting of X ray power density spectra application to high frequency quasi periodic oscillation from the neutron star X ray binary 4U 1608 522 ApJ 746 131 Cash W 1979 Parameter estimation in astronomy through application of the likelihood ratio ApJ 228 939 Loredo T 1992 In St
403. tatus for channels is not affected by the command See the ignore and notice commands Examples It is assumed that there are currently three spectra Single source usage XSPEC12 gt response a b c New files for the response are given for all three files XSPEC12 gt response 2 none No response will be used for the second file XSPEC12 gt response d 2 The second response in d becomes the response for the second file 102 Multiple source usage XSPEC12 gt response 2 1 e A second source with response e pha is now added to the first spectrum A second model can be assigned to this source XSPEC12 gt response 2 2 f 3 2 g A second and third source is assigned to spectrum 2 XSPEC12 gt response 2 2 none The second source is now removed from spectrum 2 5 5 Fit Commands 5 5 1 bayes set up for Bayesian inference Syntax bayes lt option gt lt mod par gt lt prior type gt lt hyperparameters gt where lt option gt off on cons Ifa parameter number is given as the first argument then this command sets up the prior for the specified model parameter but does not turn Bayesian inference on If the first argument to the bayes command is not a parameter number then one of the options off on or cons is used The first two turn Bayesian inference off or on while cons turns Bayesian inference on and gives all parameters a constant prior Th
404. tches the string none then the current log file is closed If the string STAMP is given as an argument then the log filename will include a data and time stamp If lt log file gt has no suffix then the stamp is appended to the name and a 10g suffix added To change the chattiness level for the log file ie the amount ofinformation written to the log file use the chatter command The default chatter level for the log file is 10 Examples XSPEC12 gt log Turn on the log file default xspec log XSPEC12 gt log none Close the log file XSPEC12 gt log mylog Open the log file mylog log XSPEC12 gt chatter 12 Set the log file chattiness to 12 75 5 3 6 parallel enable parallel processing for particular tasks in XSPEC Syntax parallel lt task gt lt max num of processes gt where lt task gt is currently limited to leven error or steppar For best results it is recommended that you set lt max num of processes gt to the number of CPU cores on your machine Set lt max num processes gt back to 1 to turn parallel processing off for the particular task To display current settings type parallel with no arguments The leven option will spawn up to lt max num gt processes during the Levenberg Marquardt fitting specifically to perform the N independent calculations of the parameter first order partial derivatives N being the number of variable fit parameters This will not apply if the
405. tcov partial covering A convolution model to convert some absorption model into a partial covering absorption If the absorption model is M E then this is converted to 1 CvrFract Cvrfact M E Note that when specifying the model it is important to put parentheses in the right place Let this model be P E which we want to apply to an absorption model M E then use the result to multiply an additive model A E The combined model should be specified as P M A not P M A or P M A 264 The parameters are parl CvrFract Covering fraction 0 lt parl lt 1 6 4 10 rdblur convolve with the diskline model shape A convolution model to smooth a spectrum by relativistic effects from an accretion disk around a non rotating black hole Modified from diskline model Fabian et al MNRAS 238 729 by Andy Fabian and Roderick Johnstone parl Index power law dependence of emissivity scales as R If this parameter is 10 or greater then the accretion disk emissivity law ore is used par2 inner radius units of GM c par3 outer radius units of GM c par4 inclination degrees 6 4 11 reflect reflection from neutral material Convolution model for reflection from neutral material according to the method of Magdziarz amp Zdziarski 1995 MNRAS 273 837 This is a generalization of the pexrav and lt 0 Then the actual bexrav models The reflection component alone can be obtained for n el en reflecti
406. ter Unit Value par comp 1 1 phabs nH 10522 1 00000 0 0 2 2 bbody kT keV 3 00000 0 0 3 2 bbody norm 1 00000 f 0 0 Fit statistic Chi Squared 3 377094e 09 using 45 PHA bins Test statistic Chi Squared 3 377094e 09 using 45 PHA bins Reduced chi squared 8 040700e 07 for 42 degrees of freedom Null hypothesis probability 0 000000e 00 Current data and model not fit yet XSPEC12 gt fit Parameters Chi Squared beta N Lvl 1 nH 22 kT 3 norm 1602 34 3 49871le 11 3 1 00000 3 00000 0 000767254 1535 61 63 3168 0 0 334306 3 01647 0 000673086 1523 48 112166 0 0 157481 2 96616 0 000613283 1491 74 170832 0 0 0668722 2 87681 0 000570110 1444 73 204639 0 0 0228475 2 76753 0 000535213 1387 84 226852 0 0 00205203 2 64901 0 000504579 1325 6 243760 0 0 000843912 2 52648 0 000476503 1256 04 258202 0 0 000287666 2 40140 0 000450137 1179 2 271528 0 3 10806e 05 2 27482 0 000425541 1083 47 283137 0 7 99181e 06 2 13278 0 000401083 Number of trials exceeded continue fitting Y P23 8 773 25 397 8 1 87147e 08 0 890295 0 000278599 Number of trials exceeded continue fitting xxxWarning Zero alpha matrix diagonal element for parameter 1 Parameter 1 is pegged at 1 87147e 08 due to zero or negative pivot element likely caused by the fit being insensitive to the parameter 123 743 1 92501 3 1 87147e 08 0 890205 0 000278596 Variances and Principal Axes 2 3 39 2 8677E 04 1 0000 0 0000 2 2370E 11 0 0000 1 0000
407. th gt specified in keV the lower bound of the first channel starting at an energy of lt channel offset gt Then the data can be fit to models etc under conditions that assume a perfect detector response For mode 2 usage channel width 0 0 one can use this command to examine the current model outside the range of the energy response of the detector When examining several aspects of the current model such as plotting it or determining flux XSPEC uses the current evaluation array This in turn is defined by the current response files being used which depend on the various detectors For example low energy datasets such as those from the EXOSAT LEs may have responses covering 0 05 to 2 keV while non imaging proportional counters can span the range from 1 to 30 keV If the user wishes to examine the behavior of the model outside of the current 119 range then he or she temporarily must create a dummy response file that will cause the model to be evaluated from lt low energy gt to lt high energy gt using lt of ranges gt as the number of steps into which the range is logarithmically or linearly divided If one wishes only to set the energy response range than the lt channel width gt argument may be omitted In this case or in the case where no data file has been read in all entries of the dummy response matrix are set to zero Under these circumstances the dummyrsp has no physically correct way of mapping the model in
408. th zero model value in spectrum number s 1 Current data and model not fit yet As we can see from the warning message we need to ignore some channels where there is no effective response Looking at a plot of the data and model indicates we should ignore below 0 15 keV and above 10 keV so XSPEC12 gt ignore 0 15 10 0 11 channels 1 11 ignored in spectrum i 340 channels 685 1024 ignored in spectrum 1 Fit statistic C Statistic 510 55 using 673 PHA bins and 669 degrees of freedom Test statistic Pearson Chi Squared 635 19 using 673 PHA bins Reduced chi squared 0 94947 for 669 degrees of freedom Null hypothesis probability 8 217205e 01 Current data and model not fit yet We assume that the Galactic column is known so freeze the first parameter We then perform a fit followed by the error command XSPEC12 gt freeze 1 XSPEC12 gt fit XSPEC12 gt parallel error 3 XSPEC12 gt err 2 4 6 Parameter Confidence Range 2 706 2 1 16302 5 64805 2 00255 2 48247 4 1 73345 195011 0 106137 0 111521 6 0 00126229 0 00221906 0 000397759 0 000559019 Note that our input parameters do not lie within the 90 confidence errors however since this will happen one times in ten by definition this should not worry us unduly For a real observing proposal we would likely repeat this experiment with different input values of the intrinsic absorption to learn how well we could constrain it given a range o
409. than the option without thermal broadening so you should only use this when necessary Velocity broadening of lines can be included by using xset APECVELOCITY lt velocity gt where lt velocity gt is sigma in km s This is added in Gaussian quadrature with any thermal broadening in use 171 The apec model uses abundances set by the abund command The vapec and vvapec variants allow the user to set the abundance using additional parameters For apec and vapec the abundances of the trace elements ie Li Be B F Na P Cl K Sc Ti V Cr Mn Co Cu Zn can be set using xset APEC_TRACE ABUND These trace element abundances can be set either to the abundance of one of the main elements or to a numerical value relative to Solar For instance XSPEC12 gt xset APEC TRACE ABUND Fe sets trace element abundances to that of iron while XSPEC12 gt xset APEC TRACE ABUND 1 0 sets them to Solar The default value for APEC_TRACE ABUND is 1 0 Note that this means that the apec and vapec models will show emission lines even if the abundance parameters are set to Zero For the apec model the parameters are parl par2 par3 norm plasma temperature keV Metal abundances He fixed at cosmic The elements included are C N O Ne Mg Al Si S Ar Ca Fe Ni Relative abundances are set by the abund command The trace element abundances are from xset APEC TRACE ABUND the default is 1 0 Re
410. that the character must be used to separate the options from the expression If type is not given default is add emin emax user may also specify the minimum and maximum energy values for the model the default values are 1 e 20 and 1 e 20 respectively Note that MDEFINE can also be used to display and delete previously defined models 1 To display the name type and expression of all previously defined models XSPEC12 gt mdefine 2 To display the name type and expression of a previously defined model by the name MNAME XSPEC12 gt mdefine MNAME 3 To delete a previously defined model by the name MNAME XSPEC12 gt mdefine MNAME Operators The following operators are recognized in an expression plus operator minus operator multiplying operator dividing operator exponentiation operator exponentiation operator Functions The following internal functions are supported Unary Functions EXP expr exp ofa vector expression SIN expr sine of vector expression in rad SIND expr sine ofa vector expression in degree COS expr cosine of a vector expression in rad COSD expr cosine of a vector expression in degree TAN expr tangent ofa vector expression in rad TAND expr tangent of a vector expression in degree LOG expr base 10 log of a vector expression LN expr natural log of a vector expression SQRT expr sqrt of a vector expr
411. the best fit exceeds lt redchi gt The default value for lt redchi gt is 2 0 Since there are very many scenarios which may cause an error calculation to fail it is highly recommended that you check the results by viewing the 9 letter error string which is part of the output from the tclout error command see tclout for a description of the error string If everything went well the error string should be FFFFFFFFF Examples Assume that the current model has four model parameters XSPEC12 gt error 1 4 Estimate the 90 confidence ranges for each parameter XSPEC12 gt error 9 0 Estimate the confidence range for parameters 1 4 with delta fit statistic 9 0 equivalent to the 3 sigma range XSPEC12 gt error 2 706 1 3 1 2 Estimate the 90 ranges for parameters 1 and 3 and the 1 sigma range for parameter 2 XSPEC12 gt error 4 Estimate the 1 sigma range for parameter 4 XSPEC12 gt error stop 20 3 Estimate the 1 sigma range for parameter 3 after resetting the number of trials to 20 Note that the tolerance field had to be included or at least skipped over 109 5 5 4 fit fit data Find the best fit model parameters for the current data by minimizing the current statistic Syntax fit lt fit method parameters gt The arguments to fit depend on the fitting method currently in use See the method command for details and for the usage of the USE NUMERICAL DIFFERENTIATION option in the user s s
412. the emissivity scales as Rpar2 2 pee inner radius units of GM Ssi 2 pord outer radius units of CM c par5 inclination degrees norm photon cm 2 s 1 in the spectrum 6 2 28 diskm accretion disk with gas pressure viscosity A disk model with gas pressure viscosity The spectrum from an accretion disk where the viscosity scales as the gas pressure From Stella and Rosner 1984 ApJ 277 312 parl accretion rate in Eddington Luminosities par2 central mass in solar mass units par3 inner disk radius in gravitational 3 Schwarzschild radii par4 viscosity norm 2cosi d where i is the inclination of the disk and d is the distance in units of 10 kpc 6 2 29 disko accretion disk inner radiation pressure viscosity A modified blackbody disk model The spectrum from the inner region of an accretion disk where the viscosity is dominated by radiation pressure parl accretion rate in Eddington Luminosities 196 par2 central mass in solar mass units par3 inner disk radius in gravitational 3 Schwarzschild radii par4 viscosity norm 2cosi d where iis the inclination of the disk and d is the distance in units of 10 kpc 6 2 30 diskpbb accretion disk power law dependence for T r A multiple blackbody disk model where local disk temperature T r is proportional to r where p is a free parameter The standard disk model diskbb is recovered if p 0 75 If radial advection is important then p lt 0 75 See the discussion a
413. the models library and this with the more complex model expression evaluations reduces execution speed Taken together v12 should outperform v11 when the number of channels is large and the model to be fitted is relatively simple and should be comparable in other circumstances The default fitting algorithm Levenberg Marquadt has been retained intact New fitting algorithms and objective functions statistics may be added to the program at runtime The CERN Minuit migrad algorithm has been better integrated into the code and its documentation is now directly accessible during XSPEC sessions Type II multi spectrum OGIP files are now fully supported Multiple ranges can be selected in the data command and support is present for Type II background and arf files Observation simulations the fakeit command now operate on Type II inputs The online documentation scheme is now implemented using pdf or html files replacing the older VMS style help system The help scheme can be configured to use external applications such as Adobe Acrobat or the xpdf readers as well as web browsers Users can document their own local models and tcl scripted procedures in pdf and html files and add them to the help system A 311 Plotting within v12 is backward compatible with a few small extensions Although it is currently implemented using PLT explicit dependence on the plot library has been removed This will allow alternative plotting libraries to be used
414. the same sort of steps as the original investigators Seward Charles amp Smale 1986 The ME spectrum and corresponding response matrix were obtained from the HEASARC On line service Once installed XSPEC is invoked by typing xspec as in this example xspec XSPEC version 12 8 0 Build Date Time Thu Nov 29 12 40 42 2012 XSPEC12 gt data s54405 pha 1 spectrum in use Spectral Data File s54405 pha Spectrum 1 Net count rate cts s for Spectrum 1 3 783e 00 1 367e 01 Assigned to Data Group 1 and Plot Group 1 Noticed Channels 1 125 Telescope EXOSAT Instrument ME Channel Type PHA Exposure Time 2 358e 04 sec Using fit statistic chi Using test statistic chi 27 Using Response RMF File s54405 rsp for Source 1 The data command tells the program to read the data as well as the response file that is named in the header of the data file In general XSPEC commands can be truncated provided they remain unambiguous Since the default extension of a data file is pha and the abbreviation of data to the first two letters is unambiguous the above command can be abbreviated to da s54405 if desired To obtain help on the data command or on any other command type help command followed by the name of the command One of the first things most users will want to do at this stage even before fitting models is to look at their data The plotting device should be set first with the command cpd change plo
415. this and issue a warning More Examples XSPEC12 gt data a The file a pha is read in as the first and only spectrum XSPEC12 gt data b b pha becomes the second spectrum the first spectrum is unmodified i e it is still a pha XSPEC12 gt data c 3 d e f c pha replaces a pha as the first spectrum d pha e pha and f pha provide the third fourth and fifth spectra XSPEC12 gt data g g pha replaces c pha as the first spectrum the slash indicates that the 2nd through the 5th spectra remain as before XSPEC12 gt data 2 none the string none indicates that the 2nd spectrum b pha is to be totally removed The current total number of datasets thus becomes one less 4 The current spectra are g pha d pha e pha and f pha XSPEC12 gt data h The current total number of spectra becomes 2 the current data sets are from h pha and d pha XSPEC12 gt data There is no change in the data status XSPEC12 gt data 1 The number of spectra is set explicitly to one that being from pha XSPEC12 gt data 1 1 a 2 2 b 3 3 c 94 Read a PHA into data group 1 b pha into data group 2 and c pha into data group 3 XSPEC12 gt data 1 1 a 1 2 b 2 3 c Read a pha and b pha into data group 1 and c pha into data group 2 XSPEC12 gt data a 3 Read the third spectrum in the file a pha 5 4 6 diagrsp set a perfect response for a spectrum Diagonalize the current response mat
416. tion 6 2 13 cemeklI cevmkI plasma emission multi temperature using mekal A multi temperature plasma emission model built from the mekal code Emission measures follow a power law in temperature dEM 7 T Oe d7 Tnax The switch parameter determines whether the mekal code will be run to calculate the model spectrum for each temperature or whether the model spectrum will be interpolated from a pre calculated table The former is slower but more accurate For the cemekl version the abundance ratios are set by the abund command The cevmkl variant allows the user to define the abundances The parameters for cemek are parl oa par2 T max par3 par4 par5 index for power law emissivity function maximum temperature 3 ny cm abundance relative to solar redshift z par6 norm 183 0 calculate 1 interpolate 2 interpolate using APEC model Normalization For the cevmkl variant the parameters are parl index for power law emissivity function par2 maximum temperature par3 ny cm par4 17 abundance relative to solar Abundances for He C N O Ne Na Mg Al Si S Ar Ca Fe Ni wrt Solar defined by the abund command parl8 redshift z 0 gt calculate parl9 1 interpolate 2 interpolate using APEC model norm Normalization 6 2 14 cflow cooling flow A cooling flow model after Mushotzky amp Szymkowiak Cooling Flows in Clusters and Galaxies ed Fabian 1988 An index of zero for the power l
417. tion integration with one numerical integral performed for each model energy The numerical integration is done using an adaptive method which continues until a given estimated fractional precision is reached The precision can be changed by setting PEXRAV_ PRECISION eg xset PEXRAV_ PRECISION 0 05 The default precision is 0 01 ie 1 parl I first power law photon index Np E 226 par2 Es cutoff energy keV if E 0 there is no cutoff par3 relsen reflection scaling factor 0 no reflected component lt releni lt 1 for isotropic source above disk par4 redshift z pars abundance of elements heavier than He relative to the solar abundances par6 iron abundance relative to that defined by abund par7 cosine of inclination angle norm photon flux at 1 keV photons keV cm s of the cutoff broken power law only no reflection in the observed frame 6 2 64 pexriv reflected powerlaw ionized medium Exponentially cut off power law spectrum reflected from ionized material Magdziarz amp Zdziarski MNRAS 273 837 1995 Ionization and opacities of the reflecting medium is computed as in the absori model The output spectrum is the sum of the cutoff power law and the reflection component The reflection component alone can be obtained for rel en lt 9 Then the actual reflection normalization is Ir el a Note that you need to change then the limits of el en excluding zero as then the direct component appears
418. to the data PHA channels so the user should not try to fit or plot the data while the dummyrsp is active in this mode Also data need not even be loaded when calling this command in mode 2 The previous response matrices can be reimplemented with the response command with no arguments Any use of the data and notice commands will replace the dummy response with a correct set of matrices or with no response matrix if none was originally present Examples XSPEC12 gt dummyrsp Create the dummy response for all spectra and sources with the default limits initially 01 100 and 200 bins XSPEC12 gt dummyrsp 001 1 Create a dummy response with 200 bins that cover the range from 0 001 to 1 kev XSPEC12 gt dummyrsp 500 The same range but now with 500 bins XSPEC12 gt dummyrsp lin The same range but now with linearly spaced bins XSPEC12 gt dummyrsp 0 1 The same range but now create a diagonal response matrix with channel widths of 0 1 keV XSPEC12 gt response Restore any previous correct responses Example dummy response matrix Assume a spectrum with 4 channels then XSPEC12 gt dummyrsp 0 30 0 3 lin 5 0 8 0 will produce the following response Detector channel energies 5 0 13 0 13 0 21 0 21 0 29 0 29 0 37 0 _ 0 0 10 0 0 5 0 0 0 2 ON 5 10 0 20 0 0 3 0 7 0 0 g jaa 20 0 30 0 0 0 1 0 8 0 1 120
419. tra computed for different geometries using exact numerical solution of the radiative transfer equation The computational iterative scattering method is similar to the standard Lambda iteration and is described in Poutanen J Svensson R 1996 ApJ 470 249 186 PS96 The Compton scattering kernel is the exact one as derived by Jones F C 1968 Phys Rev 167 1159 see PS96 for references Comptonization spectra depend on the geometry slab sphere hemisphere cylinder Thomson optical depth tau parameters of the electron distribution spectral distribution of soft seed photons the way seed soft photons are injected to the electron cloud and the inclination angle of the observer The resulting spectrum is reflected from the cool medium according to the computational method of Magdziarz amp Zdziarski 1995 see reflect pexrav pexriv models rel_refl is the solid angle of the cold material visible from the Comptonizing source in units 2 pi other parameters determine the abundances and ionization state of reflecting material Fe_ab_re Me_ab xi Tdisk The reflected spectrum is smeared out by rotation of the disk due to special and general relativistic effects using diskline type kernel with parameters Betor10 Rin Rout Electron distribution function can be Maxwellian power law cutoff Maxwellian or hybrid with low temperature Maxwellian plus a power law tail Possible geometries include plane parallel slab cyli
420. trix could be entered as 0 98 0 15 0 96 fit Covariance is taken from the correlation information produced by the current fit matrix lt values gt The lower half and diagonal of a symmetrical square covariance matrix are entered directly on the command line separated by commas and or spaces Coed C2 22 S Blt C3 2 6 33 Conn Typing chain proposal with no other arguments will show a list of all available proposal options For an alternative to XSPEC s lt distr gt lt source gt proposal options the user may instead want to provide their own custom randomization algorithm This can be done by writing their own C class es derived from an XSPEC randomizer base class The custom class is added at runtime using the same initpackage Imod command sequence as for local models and is specified by proposal lt name gt where lt name gt is the unique name attribute the user provides for their class Please see Appendix G for more information on writing a custom randomizing class and initpackage for building and loading it rand on off recalc run stat gt lt filename gt lt modName gt lt parIdx gt linel line2 line3 line4 lines Specifies whether the chain start point will be randomized or taken from the current parameters A deprecated option that performs the equivalent of proposal gaussian chain Runs a new chain written to the specified file or append to an already
421. trum area normalized A blackbody spectrum with normalization proportional to the surface area Kx1 0344 x10 E dE A E E exp er 1 parl temperature kT keV R D where R is the source radius in km and Dio is the norm K distance to the source in units of 10 kpe 6 2 6 bexrav reflected e folded broken power law neutral medium A broken power law spectrum multiplied by exponential high energy cutoff exp E E and reflected from neutral material See Magdziarz amp Zdziarski 1995 MNRAS 273 837 for details The output spectrum is the sum of an e folded broken power law and the reflection component The reflection component alone can be obtained for lr eleal lt 9 Then the actual reflection normalization is rel en Note that you need to change then the limits of n el en excluding zero as then the direct component appears If Ee 0 there is no cutoff in the power law The metal and iron abundance are variable with respect to those set by the command abund The opacities are those set by the command xsect As expected in AGNs H and He are assumed to be fully ionized The core of this model is a Greens function integration with one numerical integral performed for each model energy The numerical integration is done using an adaptive method which continues until a given estimated fractional precision is reached The precision can be changed by setting BEXRAV_ PRECISION eg xset BEXRAV_ PRE
422. tting device Here we use the pgplot X Window server xs XSPEC12 gt cpd xs There are more than 50 different things that can be plotted all related in some way to the data the model the fit and the instrument To see them type XSPEC12 gt plot plot data models fits etc Syntax plot commands background chain chisq contour counts data delchi dem emodel eemodel efficiency eufspec eeufspec foldmodel goodness icounts insensitivity lcounts ldata margin model ratio residuals sensitivity sum ufspec Multi panel plots are created by entering multiple commands e g plot data chisq The most fundamental is the data plotted against instrument channel data next most fundamental and more informative is the data plotted against channel energy To do this plot use the XSPEC command setplot energy Figure A shows the result of the commands XSPEC12 gt setplot energy XSPEC12 gt plot data Note the label on the y axis The word normalized indicates that this plot has been divided by the value of the EFFAREA keyword in the response file Usually this is unity so can be ignored The label also has no cm so the plot is not corrected for the effective area of the detector We are now ready to fit the data with a model Models in XSPEC are specified using the model command followed by an algebraic expression of a combination of model components There are two basic kinds of model components additive wh
423. unction s second argument is a const pointer to XSPEC s global Fit class object For those willing to further explore XSPEC s internals this pointer provides access to various fit and chain information such as covariance matrices which may be necessary for the user s proposal scheme doInitializeLoad and dolInitializeRun may be optionally overridden to perform initialization tasks at different stages during runtime The default versions of these functions in RandomizerBase do nothing doInitializeLoad is called by XSPEC immediately after the proposal is selected with the chain proposal command Therefore one may find it useful to have this function process any additional arguments which may be entered on the command line chain proposal myprop lt optional initializing args gt XSPEC automatically bundles lt optional initializing args gt into a single string and places it in the m_initString data member of RandomizerBase to which the inheriting class has access doInitializeRun is called once at the start of a chain run and is useful for any tasks which must be performed one time immediately after the chain run command is entered doAcceptedRejected is called after each iteration in the chain Its first argument is an array filled with the most recently attempted model parameter values and its second argument is a boolean true or false indicating whether the attempt was accepted or rejected The base class function does noth
424. utines for reading and writing the extensions in FITS format spectral and response files More information on their use can be obtained from the xspec website at http heasarc gsfc nasa gov docs xanadu xspec fits fitsfiles html RDPHA2 WTPHA3 RDRMFS5 WTRMFS5 RDEBD4 WTEBD4 RDARF1 WTARFI1 Read a spectrum extension Write a spectrum extension Read the matrix extension Write the matrix extension Read the channel boundaries extension Write the channel boundaries extension Read the effective area extension Write the effective area extension A 303 Appendix F Using The XSPEC Models Library In Other Programs For those who wish to incorporate the standard XSPEC model functions library into their own programs XSPEC provides a set of functions and wrappers that can be called from external C C or Fortran programs F 1 Calling Model Functions From C And Fortran An increasing number of XSPEC model functions are written in C and have the C style function interface described in Appendix C XSPEC provides function wrappers for each of these to make them callable from Fortran or C programs The wrappers are stored in the files funcWrappers h and funcWrappers cxx in the XSFunctions directory For each C model function there are 2 wrappers one for passing single precision arrays and one for double precision with the interfaces as shown in Appendix C for single precision Fortran style and C style respectively The single pre
425. ution If SUZPSF IMAGE has not been set then either a beta or two power law model is used In this case the model parameters determine the shape of the surface brightness distribution If SUZPSF RA and SUZPSF DEC are set they are used as the center of the distribution They should be specified either in decimal degrees or as hh mmiss s and dd mm ss s If SUZPSF RA and SUZPSF DEC are not set then the centroid of the wmap will be used as the center of the surface brightness distribution The PSF used is an empirical model of a sum of two exponentials and a Gaussian with coefficients determined from an observation of MCG 6 30 15 performed early in the mission The model works by calculating the mixing factors It will recalculate these factors if any of the SUZPSF or any of the model parameters are changed Calculating the mixing factors is very slow so should be avoided as much as possible To speed things up it is possible to save the mixing factor array to a FITS file and re use it during 270 a later calculation To save a mixing factor calculation prior to loading the mixing model using the model command use xset to set the variable SUZPSF MIXFACT OFILEn to the name of the output FITS file and where n is an integer corresponding to the observation number XSPEC12 gt xset SUZPSF MIXFACT OFILE1 fact _obsl fits Conversely a saved factor array can be read in by setting SUZPSF MIXFACT IFILEn XSPEC12 gt xset SUZPSF MIXFA
426. ux l1g10Flux cgs 10 3000 0 0 5 3 powerlaw PhoIndex 2 23646 0 126455 6 3 powerlaw norm 1 30320E 02 2 56146E 03 The Emin and Emax parameters are set to the energy range over which we want the flux to be calculated We also have to fix the norm of the powerlaw because the normalization of the model will now be determined by the lg10Flux parameter This is done using the freeze command XSPEC12 gt freeze 6 We now run fit to get the best fit value of lg10Flux as 10 2787 then XSPEC12 gt error 4 Parameter Confidence Range 2 706 4 10 4574 10 0796 0 178807 0 199057 for a 90 confidence range on the 0 2 2 keV unabsorbed flux of 3 49x10 8 33x107 ergs em s 38 The fit as we ve remarked is good and the parameters are constrained But unless the purpose of our investigation is merely to measure a photon index it s a good idea to check whether alternative models can fit the data just as well We also should derive upper limits to components such as iron emission lines and additional continua which although not evident in the data nor required for a good fit are nevertheless important to constrain First let s try an absorbed black body XSPEC12 gt mo pha bb Input parameter value delta min bot top and max values for 1 0 001 0 01 0 0 100000 1e 06 1 phabs nH gt Model phabs lt 1 gt bbody lt 2 gt Source No 1 Active On Model Model Component Parame
427. vailable on Unix machines are GIF Graphics Interchange Format file landscape orientation VGIF Graphics Interchange Format file portrait orientation NULL Null device no output PPM Portable Pixel Map file landscape orientation VPPM Portable Pixel Map file portrait orientation PS PostScript file landscape orientation VPS PostScript file portrait orientation CPS Colour PostScript file landscape orientation VCPS Colour PostScript file portrait orientation TEK4010 Tektronix 4010 terminal GE GraphOn Tek terminal emulator RETRO Retrographics VT640 Tek emulator GTERM Color gterm terminal emulator XTERM XTERM Tek terminal emulator ZSTEM ZSTEM Tek terminal emulator V603 Visual 603 terminal KRM3 Kermit 3 IBM PC terminal emulator TK4100 Tektronix 4100 terminals VT125DEC VT125 and other REGIS terminals XDISP pgdisp or figdisp server XWINDOW X window window node display screen xw XSERVE An XWINDOW window that persists for re use Closes the device For Postscript output it flushes the write buffer into the file and closes the file Note that in XSPEC12 each plot command produces a separate page in the postscript file unlike previously where each plot overwrote the previous plot Example 142 produce a set of color postscript plots in landscape orientation commands to produce a plot XSPEC12 gt cpd dataplot ps cps XSPEC12 gt plot d
428. value is 1 If this variable is set to 0 the commands from the script file will not be echoed to the terminal A 13 Summary In summary we suggest the following convention e Running an xspec script from the unix command prompt is intended to be used for background processing or overnight batch jobs Using the unix at command one can arrange to receive the log file by e mail e The usage is intended for processing previously run xspec command sequences such as are produced by the save command e The source usage as well as executing the commands in the script performs the equivalent of pre compiling the script for later invocation Its most appropriate use is in preparing new custom XSPEC command procedures Once the script is working correctly it can be placed in the user script directory and become part of the user s standard command set For examples see the scripts addline tcl and modid tcl in the directory SSPECTRAL scripts that implement the commands addline and modid These also show how to make commands self documenting A 14 Unix Shell Commands Shell commands can be executed within XSPEC using the exec command see the help entry on the exec command When running interactively if tcl cannot find a command that matches that entered on the command line it will search for a shell command that matches the entered command If it finds a match it automatically executes the shell command via exec Note that this feature
429. ver them writing the joint probability distribution of the source parameters as P p 9 I S B 1 ab 0 9 2 3 1 5 Bh 7 A 285 where 0 are the source parameter bx the background rate parameters and I any prior information Using Bayes theorem that the 0 and independent of the bx that the bk are individually independent and that the observed counts are Poisson gives p 0 i y tipit e mls e le S B k where b t tt J db p b 1 m b pire lh p To calculate J_k we need to make an assumption about the prior background probability distribution p b I We follow Loredo 1992 and assume a uniform prior between 0 and b Expanding the binomial gives Je 1 Seo S y S B j 1 b2 4 Bee Dj S i s B j TUS IN Gag A where yla B ibs xed Again follow Loredo we assume that z b gt B and using the approximation yla 8 a 1 when a gt gives 5 B 1 s t t Sk S B j j ane o br ae mM iS j t i Jat Note that for mx 0 only the j 0 term in the summation is non zero Now we define Istat by calculating 2 In P and ignoring all additive terms which are independent of the model parameters N Sk S B J k Istat a 2Inp 6 I aE ma ol Sm FNS aay az t For power spectra from time series data whittle XSPEC has been used by a number of researchers to fit models to power
430. ves of the model with respect to its parameters may be ignored This may be changed by setting the USE NUMERICAL DIFFERENTIATION flag to true in the user s startup Xspec init initialization file XSPEC will then calculate all second derivatives numerically which can be noticeably slower 156 migrad method migrad lt of eval gt The Minuit2 migrad method lt of eval gt is the number of function evaluations to perform before giving up Migrad uses an internal convergence criterion The current version of Minuit2 included is that from ROOT v5 34 Documentation on Minuit2 can be found at http seal web cern ch seal MathLibs Minuit2 html If migrad is not working well try experimenting with different hard and soft limits on parameters e simplex method simplex lt of evaluations gt The Minuit2 simplex method lt of evaluations gt is the number of function evaluations to perform before giving up Simplex uses an internal convergence criterion This method is included for historical interest and is almost always outperformed by migrad 5 8 4 statistic change the objective function statistic for the fit Change the fit or test statistic in use for one or more spectra Syntax statistic chi cstat lstat pgstat pstat whittle lt spectrum range gt statistic test ad chi cvm ks pchi runs lt spectrum range gt The fit statistic options are chi squared chi C statistic cstat Loredo
431. ving two options for the plot command generates a plot with vertically stacked windows Up to six options can be given to the plot command at a time Forty channels were rejected because they were flagged as bad but do we need to ignore any more Figure B shows the result of plotting the data and the model in the upper window and the contributions to y in the lower window We see that above about 15 keV the S N becomes small We also see comparing Figure B with Figure A which bad channels were ignored Although visual inspection is not the most rigorous method for deciding which channels to ignore more on this subject later it s good enough for now and will at least prevent us from getting grossly misleading results from the fitting To ignore energies above 15 keV XSPEC12 gt ignore 15 0 78 channels 48 125 ignored in spectrum 1 Fit statistic Chi Squared 721 57 using 45 PHA bins Test statistic Chi Squared 721 57 using 45 PHA bins Reduced chi squared 17 180 for 42 degrees of freedom Null hypothesis probability 1 250565e 124 Current data and model not fit yet If the ignore command is handed a real number it assumes energy in keV while if it is handed an integer it will assume channel number The just means the highest energy Starting a range with means the lowest energy The inverse of ignore is notice which has the same syntax 32 We are now ready to fit the data Fitting is initiate
432. wave has been specified Energy and wavelength units are determined by the setplot energy and wave settings If only the last channel is indicated then a default value of one 1 is used for the initial channel Channels remain ignored until they are explicitly noticed with the notice command or if a spectrum is replaced Examples Assume that 4 spectra have been read in the first 2 with 100 channels and the last 2 with 50 channels XSPEC12 gt ignore 1 10 The first 10 channels of all 4 spectra are ignored XSPEC12 gt ignore 80 An attempt will be made to ignore channels gt 80 in all four data sets as that was the last spectrum range specified As a result only channels 80 100 will be ignored for spectra 1 and 2 No change will occur for spectra 3 and 4 as they have no channels greater than 50 XSPEC12 gt ign 4 1 20 3 30 40 45 Channels 11 20 for spectrum 4 are ignored 1 10 were ignored already while channels 30 40 and 45 50 of spectrum 3 are ignored XSPEC12 gt ignore 1 1 5 No channels are ignored as these were ignored at the beginning XSPEC12 gt ignore 2 1 5 gnore all channels between 1 and 5 keV in the second dataset 5 4 9 notice notice data channels Notice data channels See also ignore Syntax notice lt rangel gt lt range2 gt lt rangeN gt 100 notice all where lt rangelI gt lt spectrum range gt lt channel range gt lt channel range
433. wer law fit Perhaps then the power law fit is not so good after all What we can do is fix freeze in XSPEC terminology the value of Ny at the Galactic value and refit the power law Although we won t get a good fit the shape of the residuals might give us a clue to what is missing To freeze a parameter in XSPEC use the command freeze followed by the parameter number like this XSPEC12 gt freeze 1 The inverse of freeze is thaw XSPEC12 gt thaw 1 data and folded model 42 normalized counts s keV normalized counts s keV Energy keV Figure G As for Figure D amp F but the model is the best fitting power law with the absorption fixed at the Galactic value Under the assumptions that the absorption really is the same as the 21 cm value and that the continuum really is a power law this plot provides some indication of what other components might be added to the model to improve the fit Alternatively parameters can be frozen using the newpar command which allows all the quantities associated with a parameter to be changed We can flip between frozen and thawed states by entering 0 after the new parameter value In our case we want Ny frozen at 4x10 cm so we go back to the power law best fit and do the following XSPEC12 gt newpar 1 Current value delta min bot top and max values 0 537843 0 001 0 00537843 0 0 100000 1e 06 1l phabs 1 nH 1 gt 4 0 Fit statistic Chi Squared 823 34 usin
434. wer law reflected from neutral matter E folded broken power law reflected from ionized matter Broken powerlaw Three segment broken powerlaw Comptonization by relativistically moving matter Thermal bremsstrahlung with redshift variant 6th order Chebyshev polynomial DEM using mekal and variants Compton scattering non relativistic Multi temperature mekal Cooling flow model Calculate flux of other model components Comptonized blackbody spectrum after Nishimura et al 1986 165 Model Description compLsS Comptonization spectrum after Lamb and Sanford 1979 puak Thermal and bulk Comptonization for cylindrical accretion onto the polar cap of a magnetized neutron star compPS Comptonization spectrum after Poutanen and Svenson 1986 compST Comptonization spectrum after Sunyaev and Titarchuk 1980 comptb Thermal and bulk Comptonization of a seed blackbody like spectrum compTT Comptonization spectrum after Titarchuk 1994 constant Energy independent multiplicative factor cpflux Convolution model to calculate photon flux cplinear Non physical model for low count background spectra cutoffpl Powerlaw with high energy exponential rolloff cyclabs Cyclotron absorption line disk Disk model diskbb Multiple blackbody disk model diskir Irradiated inner and outer disk diskline Line emission from relativistic accretion disk diskm Disk model with gas pressure viscosity disko Modified blackbody disk model disk
435. wn from a Gaussian distribution centered on the best fit with sigma from the covariance matrix The sim switch turns on this option nosim turns it off in which case all simulations are drawn from the best fit model The default starting setting is nosim 5 5 8 margin MCMC probability distribution Use the currently loaded MCMC chains to calculate a multi dimensional probability distribution Syntax margin lt step spec gt lt step spec gt where lt step spec gt LOG or NOLOG lt model name gt lt fit param index gt lt low value gt lt high value gt lt no steps gt The indicated fit parameter is stepped from lt low value gt to lt high value gt in lt no steps gt 1 trials The stepping is either linear or log Initially the stepping is linear but this can be changed by the optional string log before the fit parameter index nolog will force the stepping to be returned to the linear form The number of steps is set initially to ten The results of the most recently run margin command may be examined with plot margin for 1 D and 2 D distributions only This command does not require that spectral data files are loaded or that a valid fit must exist Examples Assuming chain s are loaded consisting of 4 parameters 112 XSPEC12 gt margin 1 10 0 12 0 20 log 3 1 0 10 0 5 Calculate a 2 D probability distribution of parameter 1 from 10 0 12 0 in 20 linear bins and par
436. y loaded XSPEC12 gt fakeit 2 98 Produces 2 fake spectra in separate type I files unless the first user entered response file belongs to a format that is explicitly type II ie SPI Integral Type II files Assume four spectra with no backgrounds have been loaded from one type II file XSPEC12 gt data original type2_ data pha 5 8 Then after model s have been entered and a fit XSPEC12 gt fakeit This will produce 4 fake spectra in rows 1 to 4 of one type II output file with responses and arfs taken from the columns of original _type2_data pha XSPEC12 gt fakeit backb 1 3 This produces 5 fake spectra in two type II output files and 3 fake background spectra also placed in two type II output files The first 4 fake spectra are placed in one output file since that is how the 4 spectra they were based on were originally organized The default numerical data for this file are taken from the original spectra Fake spectra 3 and 4 now have backgrounds based on backb 1 and backb 2 respectively These will generate 2 fake background spectra placed in rows 3 and 4 of the first output fake background file Rows 1 and 2 of this file will just consist of zeros since the first 2 spectra have no backgrounds The fifth fake spectrum will be placed in the second type II PHA file Response and numerical data will not be based on the existing loaded spectra A fake background will be generated from backb 3 and placed in row 1 of the
437. y matter undergoing relativistic bulk motion The typical scenario involves thermal X rays from the inner region of an accretion disk in a black hole binary illuminating in falling matter in close proximity to the black hole event horizon For a detailed description of the model refer to Titarchuk Mastichiadis amp Kylafis 1997 ApJ 487 834 Titarchuk amp Zannias 1998 ApJ 493 863 Laurent amp Titarchuk 1999 ApJ 511 289 Zannias Borozdin Revnivtsev Trudolyubov Shrader amp Titarchuk 1999 ApJ 517 367 or Shrader amp Titarchuk 1999 ApJ 521 L21 The model parameters are the characteristic black body temperature of the soft photon source a spectral energy index and an illumination parameter characterizing the fractional illumination of the bulk motion flow by the thermal photon source It must be emphasized that this model is not an additive combination of power law and thermal sources rather it represents a self consistent convolution The bulk motion up scattering and Compton recoil combine to produce the hard spectral tail which combined with the thermal source results in the canonical high soft state spectrum of black hole accretion The position of the sharp high energy cutoff due to recoil can be determined using the theta function 180 O E E The model can also be used for the general Comptonization case when the energy range is limited from above by the plasma temperature see compTT and compST parl Tem

An X-Ray Spectral Fitting Package User's Guide for version 12.8.1

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