spimodfit Explanatory Guide and Users Manual
Contents
1. Software versions 2 2 2005 22 Feb 2005 26 Feb 2005 02 Mar 2005 12 Mar 2005 13 Mar 2005 21 Mar 2005 24 Mar 2005 19 Apr 2005 20 May 2005 H Halloin First separate version from spidiffit version 26 various bug fixes improve variability handling allow zero source and or skymap H Halloin Remove NAG subroutines use LAPACK eigen vec tors lbfgs_bcm minimization tn minimization correct some minor bugs H Halloin Remove eigenvalues calculation and replace with direct hessian 6 7 times faster H Halloin Add possibilities for detector selection on entry H Halloin Output sources catalogue H Halloin Possibility to load default parameters from a previous run H Halloin Add Levenberg Marquadt algorithm H Halloin Modify the way to specify the energy modulation H Halloin Use common libraries instead of locally defined H Halloin Allow more flexibility in time variation combination of multiple definitions first documentation release Aug 2006 1 3 1 Supported platforms The following table gives some information about the platforms on which spimodfit has been compiled e System value of the SYS environment variable e Platform hardware architecture as given by uname i e Kernel version as given by uname rs e Operating system as given by uname o 2 8 5 1 linux i386_rh90 Linux 2 4 21 241 smp GNU Linux g gcc icpc icc 1 4 Known issues e spimodfit han2. and it is important to check that there is no drift in the average values since this indicates lack of convergence and the result will then be influenced by the starting parameter values 15 Chapter 4 Using spimodfit From the user point of view the data processing is done in 4 major steps which all have their own options e Definition of the input observation data on input spimodfit expects the different files constituting a SPI observation events rate poitings dead times good times energy bins and background models The energy bins can be redefined and will be processed independently It is also possible to select a subset of the detectors in the input data The background models can be collected into one single model or limited to a maximum nulber only the first ones will be loaded In addition to these files the Instrument response function files IRFs file has to be specified Many IRFs files can be given to handle a time dependent response e Definition of the fitted parameters spimodfit can fit extended emission images point sources sources and background parameters For each of these components the time and detector variability should be given as well as some other fitting or normalization parameters explained below e Fitting options as the minimization routines and its initialization MCMC options e Definition of the output files spimodfitgenerate a FITS file table containing the results of the
3. blocks will be fitted independantly Please note that it is not possible to define block with non following detector numbers Parameter image_det_rges_ Type list in integer ranges Range Description Definition of the detector blocks Each block is fitted independently Time selection The observation can be divided into time intervals that are fitted indepen dently image_var_coef allows to define an arbitrary time variability and therefore more flexibility in the time dependance of the image components The argument of image_var_coef is a string composed of comma separated fields each of one defining additionnal time nodes i e boundaries of the time intervals Each field define the variability either by periodicity or nodes values The unit of the variability is either in days or in pointings More precisely the format of a field consists of numbers separated by blank characters followed by 2 characters specifying 26 the variability unit d dyas p pointings and the variability type i increments n nodes For example the string 1000 2000 d n 3 0 d i will define 1 time node every 3 days plus 2 specific time nodes at 1000 and 2000 ISDC Julian days Between nodes the time varaibility is defined as a piecewise function of parametrized reg ularity i e derivability order Thus a zero order variability means a constant term for each time interval Order 1 ensures linear variation so that the function is con
4. by typing ac_stuff configure help In partic ular the compiler name and options can be set manually on the configure line by typing ac_stuff configure CC CFLAGS CXX CXXFLAGS where CC is the name of the C compiler and CFLAGS is the list of options to pas to the C compiler CXX and CXXFLAGS follow the same definition for the C compiler At the MPE a compilation with the Intel compiler and a optimized code for Pentium 4 an compatible CPUs would then be ac_stuff configure CC icc CFLAGS axW CXX icpc CXXFLAGS axwW The program will anyhow be compiled with the 03 and Wno deprecated options 3 Build the binary make all This should compile the program and put it in a subdirectory called SYSARCH_COMP where SYSARCH is the system architecture as defined by the SYS environment variable type echo SYS to see its value and COMP is the compiler gcc g icc icpe What to do if anything went wrong in one of the previous step Well First look carefully at the error message s to see if it is not an OSA or local system configuration problem Second if it seems to be a bug in any of the configuration script or even in the source code you may consider to one or maybe much more cup of coffee and dive into the code and scripts In desperate cases you may also contact the programmer to complain about the software eventually s he will be able to identify and maybe solve your problem 1 3
5. value 1 so that negative counts shall be filtered but this should not happen anymore 21 Parameter data_filter_counts Type integer Range f Description All data counts lower than this threshold will be filtered out DEPRE CATED One of the way to regularize the background model is to generate a model from the count rate from an off observation and use it directly as a background model for an on observation This method can nevertheless exhibit a strong variability of the model and introduces unexpected short term variation To avoid this problem the background model can be smoothed using a sliding mean over a given number of energy bins set by background_smooth If set to one no smoothing is performed background_smooth must be odd Parameter background_smooth Type integer Range gt 1 Description Number of energy bins used for background smoothing must be odd 4 2 4 Loading the IRF files spimodfit needs to load Instrument Response Functions IRFs in order to calculate the expected detector count rates from a given sky distribution The program can handle more than 1 IRF to take into account changes in the instrumental response such as the loss of detectors which is not exactly equivalent to set the corresponding livetimes to 0 If no sky nor point source emission is fitted e g for background fitting then no IRF is required The number of loaded IRF is set with n_irf and their loca
6. A VE requiring the additional parameter A o highecut 1 0 if E lt Bay and exp E Evut Efoia ortherwise requiring the additional parameters Evut E fola e wabs should be the absorbtion by a column density Np of hydrogen In spimodfit This function returns inconditionnaly 1 and is only implemented for compatibility with most of the XSPEC formulations It requires an additional not used parameter Np When using these functions the additonal parameters that is all except the energy are specified within a separate list The order of the parameters in the list should match the order of the functions in the formula and for each function the order of parameters as given in the above description of the function For example the above spectral shape exp E 511 3 0 2 E 1 2 can also be entered as gaussian powerlaw with the additional parameter list 511 3 0 1 0 1 2 1 0 the three first values being used by gaussian and the two last ones by powerlaw The formula is entered with the image_energy_model_ parameter and any additional required values with image_energy_model_pars_num_ and image_energy_model_pars_ Parameter image_energy_model_ Type string Range Description Spectrum shape of image component This should be a valid math ematical expression optionnaly involving XSPEC energy models whose parameters are given by the following parameters See above for details Para
7. an Dyk et al 2001 these can be used to incorporate the user s knowledge into the problem Results The posterior for one parameter is obtained by marginalizing over the other parameters P 6 D P O D 0 Udi 12 and its mean value is lt 6 D gt 6 P e D a8 Peper with standard deviation A6 D sart 0 lt 6 D gt P 6 D d0 sart 0 lt 0 D gt P 8 D d 0 The results are expressed in terms of the posteriors and mean and standard deviations of the parameters but also more conveniently in terms of the fitted skymaps i e the input maps multiplied by the fitted parameters together with the error estimates lt Ii gt lt 0 D gt Mij Ali A0 D M i The average total map is the sum of the average maps l So UMa i lt Ij gt J EOMP 5 lt 6 D gt Mij but the error is more complicated to compute since it involves the correlations between the 0 Al sart f 1 lt Ij gt P 8 D d 0 AI srt E 0i Mij Ss lt 0 D gt Mij P D a 0 Al sart S7 My lt 65 D gt My PO D aNo In general we want statistics for a linear function of the parameters i Swi The full posterior distribution for a given set of w must come from the MCMC method see below but the standard deviation can be more generally derived from the covariances as follows Asai if biwi lt 6 gt wi PO D AN i 13 biwi lt 6 gt wil as wilBi
8. auto h hidden q query hl hidden learn ql query learn With the a mode the effective mode is set to the value of the parameter named as mode in the parameter file If the mode parameter is not found the effective mode is set to h With the h mode no questions are asked unless the default value is invalid for a given data type whereas with the q mode you are always asked for a parameter With the additional I mode if an application changes a parameter value the new value will be written to the parameter file when the application terminates spimodfit makes use of parameter types i r and Some of the parameters require to enter multiple arguments with the same parameters This is done via a string which is then decomposed into different elements and interpreted A multiple a Bs arguments parameter can be either a vector or a list e A vector is a array of values of the same kind i e reals integers etc separated by blanks for example 1100 5 1433 0 1500 0 is a vector of 3 reals This is a extension or the IRAF format coded in the OSA PIL library e A list is a array of values or fields not necessary of the same kind separated by commas Sometimes an additional keyword can be put at the end of the list to modify its interpre tation For example 1785 1802 1802 1815 1815 1826 keV selects 3 energy ranges in keV This possibi
9. cal methods but straightforward in the Bayesian approach In view of the large amount of literature on this topic explicitly for astronomical applications and the availability of algorithms and also software it is proposed to take advantage of this in providing such an approach for spimodfit Up to a few years ago the method was regarded as impractical for many parameter problems because of the difficulty of evaluating multi dimensional integrals but now methods are readily available Markov Chain Monte Carlo which make this both tractable and relatively straightforward to implement Last but not least one of the leading Bayesian groups is at the Centre for Interdisciplinary Studies in Garching neighbouring institute to MPE Possibily both approaches should be developed 3 2 2 Model Fitting Details The objective of the model fitting analysis is now to extract information about 6 in the form of posterior probability distributions and their moments mean standard deviation etc and any other functions of interest e g the total image Fitting Constraint The likelihood function is L D 6 e dg ng k where nz are the measured data denoted collectively by D and the posterior probability P 0 D is expressed in terms of the likelihood and the prior probability Pr using Bayes theorem P 6 D L D 6 Pr 6 P D where P D is known as the evidence E Suitable analytical forms for the prior Pr are given by e g v
10. ct_background_models integer 0 1 If set to 1 all the backgournd components are collected into one and the process continues as if there is only one component in the background model 4 2 1 3 Energy rebinning of the input data The observation data can be selected and rebinnned in energy This is done by specifying the first and last bins and the number of bins per rebinnined energy These bin numbers refer to the bins sequence of the original data Parameter first_energy_bin Type integer Range gt 1 Description First selected bin as indexed in the original observation data beginning at 1 Parameter last_energy_bin Type integer Range gt 1 Description Last selected bin as indexed in the original observation data beginning at 1 Parameter m_energy_rebin Type integer Range gt 1 Description Number of original bins per rebinned energy 20 4 2 1 4 Detector selection of the input data The input data can also be filtered to select only the events from a given subset of pseudo detectors The selected detectoirs are given with the detector_selection parameter There is usually no need to reject dead detectors since they are automatically taken into account and their param eters not fitted This paremetr is more intened to select single and or multiple events in a given observation Parameter detector_selection Type list of integer ranges Range Description Comma separate
11. d list of selected detectors or detector ranges For ex ample the list 00 01 03 18 select events from dectors 00 01 and 03 to 18 4 2 2 Simulation of detector events Instead of fitting the model directly from an existing data set spimodfit can generate simulated detector events Monte Carlo sampling based on the provided emission and background models and the observation characteristics pointings dead times etc Once the data have been simulated the fitting process continues as usual At the end of the programm a count rate FITS file is created with the name given by counts_input_file which then acts as an output parameter instead of an input one and the simulated counts recorded in it Data simulation is switched on by the simulate parameter Parameter simulate Type integer Range 0 1 Description If set to 1 the data are first simulated Monte Carlo sampling and the resulting counts rate recorded in counts_input_file The fitting process is then performed as usual 4 2 3 Rejection of bad data counts and background smoothing In some early version of standard data processing some data counts could have been set to spurious negative values The detector events with counts number lower than a user defined limit this parameter are then set to 0 as well as the corresponding term in the convolution matrix This behaviour appears now deprecated and it is recommended to keep the threshold to its default
12. dependant and spimodfit will rely on the image keyword E_MIN and E M AX to select the correct models to be convolved for a given fitted energy range Usually only 1 image is defined in the indexes and in this case the same sky model is used for all energy ranges regardless of the values of E MIN and E MAX The locations of the index files are specified with the parameters image idx_ where stands for the number from 01 to n_image_parameters of the model component Parameter image idx_ Type string Range Description Location of the index for the image component The extension number doesn t need to be precised spimodfit looking for the exten sions named SPI SKY IMA IDX but their should not be more than one index table per FITS file 4 3 1 2 Sky models units and energy dependent rescaling The unit of the input maps is assumed to be in ph s71 em srt keV while the output maps for each energy will be rescaled to ph s cm7 sr that is integrated over energy The spectral shape of the sky emission can be precised through the three following parameters and its integral is used to ponderate the images for each energy bin More precisely at each energy the fitted map is multiplied by Ef f ao fs E dE where Emin and E are the boundaries of the energy bin being fitted and fs is the spectral shape jf has to be a valid arithmetic expression spimodfit uses the FastMathParser version 1 09 to par
13. dles time variability through the use of splines The spline order can be 0 to 5 0 corresponding to a piecewise constant function with one scaling parameter per interval and 3 corresponding to cubic splines In many cases when using n order splines n gt 1 the fitting algorithm fails to find the optimal parameters This is thought to be due to over parametrized time variability because of the additional parameters of the splines 1 5 Use and syntax of the parameter file The parameters of the the program are defined in a file called spimodfit par This file should be readable in one of the directory set in the PFILES environment variable Usually the user updates the parameter file in the working directory so one should set the variable accordingly setenv PFILES The syntax of the file follow the IRAF standards that is the one used by ISDC softwares In this file each parameter is described in the format parameter_name parameter_type parameter_mode default_value minimum_value maximum_value description_prompt The parameter_type can be b boolean i integer r real s string or f file ap name The f type can be followed by any combination of r read access w write access e existence of file n absence of file Thus the fw type means to test whether the file given as a value of the parameter is writable The parameter_mode can be a
14. e if image_init_from_file is set to 1 is loaded to get the defaults values low and high boundary constraints of all image parameters 29 4 3 1 5 Configuration of the output sky models The fitted sky models images are stored and recorded in the output fits file in Galactic or celestial J2000 coordinates Moreover in this coordinate system the images can be limited to a rectangular area every pixel lying outside this area will be set to zero Additionnally the size of the sky pixels as used in the convolution process and image recording has to be defined The coordinate system of the output map is set with skymap_system G for galactic C for celestial Parameter Type Range skymap_system string aC Set the coordinate system of the output sky models G for galactic C for celestial J2000 Description The boundaries of the fitted sky area is set with the chi_0 chi_1 min and max values in longitude and the psi_0 psi_1 min and max values in latitude d_chi and d_psi set the size of the sky pixel Parameter Type Range Description Parameter Type Range Description Parameter Type Range Description Parameter Type Range Description chi_O real Minimum longitude of the sky model area in degrees chil real Maximum longitude of the sky model area in degrees d_chi real Pixel size along the longitude in degrees psi_O
15. e parameter at a time or global changing all parameters at once schemes In general it has been found that the local proposal distribution is more robust and less sensitive to the stepsize than the global scheme This is presumably because it uses information per parameter so can more easily find an accepted point For highly correlated basis functions extreme case two identical maps however the local scheme needs a very small step since it can only move at an angle to the major axis and even then does not cover the full region here the global scheme is much better since it has a reasonable probability to sample along the major axis The stepsize must then be correspondingly chosen to reflect the uncertainty in a single parameter In all cases the stepsizes for all parameters should be chosen by trial to give an acceptance ratio around 0 23 NB find references on this topic and the range 0 15 0 5 is recommended Gilks et al 1996 page 55 although the algorithm theoretically converges to the correct result for any acceptance ratio the value quoted should optimize the rate of convergence In has been found that a stepsize equal to the expected uncertainty on the parameter is a good trial choice A possible way to automate this is to use the current estimate of the standard deviation to determine the step Gilks et al 1996 but still a starting step is required The results are evaluated at intervals in the sampling interval is user defined
16. e the model parameters More generally the image will still be described by a sum of components but the image components will be non linear functions of the parameters e g Gaussian exponential and each component is described by several parameters 6 Ij My i Similarly the background can be constructed from components of a background model Bik bk gt 0i Bik 10 where 9 now introduces background parameters The sums in the above expressions are over the appropriate subsets of parameters for image and background model respectively In this way we can treat image and background model in the same way in the subsequent analysis and O includes both The only formal difference between image and background model is that the image is convolved with Rj and the background is not i Ny1 i N7 NpB d Y Rix X OMyt YO OBix j i 1 i Nr 1 where there are N image components and Ng background components and N N NB In our modelling approach the measured signal is represented through model components dk gt 0i Sik where the sky part is Sik XO RirMij i 1 Nr j and the instrumental background part is Sik Bik i Nr 1 Nr Ng In the non linear case we have to convolve explicitly for each parameter set i e we cannot pre convolve to get Sig i Ny i N NpB dk S Rik 5 Mi 0i gt 0i Bik j i Nr 1 The procedure above is for a single energy and hence a implies a diagonal response in energy space Howeve
17. ed sky emission This can be done with image_parameters_fit_ If set to 0 the parameters are held fixed set to their default values as defined by image_parameters_ Parameter image_parameters_fit_ Type integer Range 0 1 Description Fitting flag for the parameters of image component If 0 the parameters are not fitted set to their defaults values as defined by image_parameters_ 27 When using the MCMC procedure for fitting and error estimation the user has to define the parameter step to be multiplied by the uniform of Cauchy distribution The step value is defined with image_parameters_step_ Parameter image_parameters_step_ Type real Range 7 gt 0 Description Parameter step to be multiplied by the uniform or Cauchy distribution used during the MCMC fitting process Relative to the image component Hit The default parameter values and boundary constraints can be set either globally for all fitted parameters of a given image component or from an initialization file Global parameters initialization In this paragraph it is assumed that no initialization file is used see below Otherwise the loaded values from the file override the ones defined in the parameters file Unless using an unconstrained least square fit the fitting processes require to start from default parameters They can be set for an image component via image_parameters_ Parameter image_parameters_ Type
18. ed spectral law for all sources from the parameter file or individually for each source from the catalogue or a recorded spectrum per source from the catalogue 31 Index of spimodfit parameters background input file 19 pointing input file 18 background_ smooth 22 precalculate_ irf 23 collect background models 20 rogroup 17 counts input file 18 skymap _ system 30 data filter counts 21 deadtime dol 19 title 17 debug 17 detector_ selection 21 ebounds_ input file 19 first_ energy_ bin 20 gti dol 19 image idx_ 24 image det rges 26 image energy model 25 image energy model_ pars 26 image energy model_ pars num 25 image init_ file 29 image init_ from file 29 image IRF gamma cor 26 image_ parameters 28 image parameters fit 27 image_ parameters max 28 image parameters min 28 image parameters step 28 image var coef 27 image var order 27 irf_ input file 22 last_ energy_ bin 20 log integration step irf 23 m energy rebin 20 n background loaded 20 n image_ parameters 23 n irf 22 output idl 17 32
19. es can not be opened with write rights If the simulate parameter is set to 1 see below counts_input_file is the name of the output simulated detector events This file will thus be created by spimodfit and should not exist prior to the run Parameter counts_input_file Type string Range Description Location of the detector events table as existing in a SPI observation The index of the binary table can be omitted e g evts_det_spec fits in which case spimodfit will look for the first binary table named SPI OBS DSP Parameter pointing_input_file Type string Range Description Location of the pointing definition file as existing in a SPI observation The index of the binary table can be omitted e g pointings fits in which case spimodfit will look for the first binary table named SPI OBS PNT 18 Parameter Type Range Description Parameter Type Range Description Parameter Type Range Description Parameter Type Range Description ebounds_input_file string Location of the energy binning definition file as existing in a SPI observation The index of the binary table can be omitted e g energy_boundaries fits in which case spimodfit will look for the first binary table named SPI EBDS SET deadtime dol string Location of the dead time definition file as existing in a SPI observa tion The index of the binary table can be omitted e g dead_time fits If not spec
20. fit By default this file contains the different skymodels original map and fitted images and an binary table containing the fitted parameters with associated configuration and estimated error bars Optionally it can also add an exposure map in this FITS file create a background model for the observation write residues of the model light curves apectra and an updated point source catalog in other files 4 1 General parameters First let us begin with some general purpose parameters These parameters do not influence the fitting process they mainly are present for documentation purpose 16 Parameter Type Range Description Parameter Type Range Description Parameter Type Range Description Parameter Type Range Description debug integer Debugging flag used during software development to dump some in ternal parameters to the screen Leave the value to 0 no debugging information for normal use title string This string will be written in the header of the output FITS data units keyword OBS_ID This record is only for information purpose and it is up to the user to give a good observation descriptor with less than 69 characters output_idl integer 0 1 If set to 1 print fitted parameters and associated errors on the screen The values are separated by commas and enclose by saure brackets val1 val2 valN This is mainly intended to be copy pasted from the screen
21. ified spimodfit will look for the first binary table named SPI OBS DTI gti dol string Location of the good time intervals definition file as existing in a SPI observation The index of the binary table can be omitted e g gti fits in which case spimodfit will look for the first binary table named SPI OBS GTI background_input_file Location of the background model index file as produced by e g spiorthomodel or spiback The index of the binary table can be omit ted e g gti fits in which case spimodfit will look for the first binary table with the group name SPI BMOD DSP IDX 4 2 1 2 Background models selection and combination The background model index file pointed by background_input_file can contain a lot of differ ent components The following paraeters allow the user to select only a subset the component the first ones and or combine the loaded components into a single one 19 Parameter Type Range Description Parameter Type Range Description n_background_loaded integer aaa This parameter sets the maximum number of loaded background com ponents rejecting the last ones in the index This is mainly intended for use in conjunction with spiorthomodel Actually by default this software records the different background components in decreasing or der of pertinence This parameter allows then to run the model fitting with different refinements of the background model colle
22. l detect point sources and diffuse extended emission with an angular accuracy of about 1 over its energy range of 40 8000 keV The purpose of the software package described here is to represent the measurement in terms of spatial models on the sky fitting parameters of these models and estimating their uncertainty This tool is oriented towards large scale surveys eg GCDE which combine a large set of individual pointings of the spacecraft It concentrates on fitting spatial as opposed to spectral models although through using the different energy channels of the measurement it will be an important method to generate spectra of diffuse emission The principal use will be fitting to maps of physically based tracers of y ray emission Exam ples are fitting the 1809 keV 7 Al line to free free or IR emission maps fitting diffuse continuum y ray s to gas HI CO maps It will also allow fitting spatial functions e g Gaussian exponen tial where there is no physical model available Fitting components is the best method to get the spectra of diffuse emission when a good spatial but a poor spectral model is available The analysis of measurements with this tool is complementary to deriving results from deconvolved images e g from spiskymax and methods specifically designed for point sources e g spiros The algorithm performs fitting of raw data binned counts for many observations to multi component models using the full instrumen
23. l correspond to the current fitted energy interval The index of the corresponding bin is then used to move to the corre sponding parameters data unit named SPI DFIT RES_ where stands for the index of the energy bin This data unit has to contain at least 4 columns with one row per parameter e PAR_TYPE This string column specifies the type of the parameters If the string contains Sky then it is considered as an image parameter Similarly Point refer to a point source and Background to a background parameter e MIN_VALUES Low boundary constraint of the parameter e MAX_VALUES High boundary constraint of the parameter e FIT_VALUES_ML As an output of spimodfit this column correspond to the fitted values through the maximum likelihood or least squares method not MCMC As an initialization file this column is used to set the defaults values of the parameters The initialization file for images is loaded if image_init_from_file is set to 1 The name of the corresponding file is given by image_init_file Parameter image_init_from_file Type integer Range 0 1 Description If set to 1 an initialization file is loaded to set the defaults values low and high boundary constraints of all image parameters The name of the initialization file is given by image_init_file Parameter image_init_file Type string Range Description Location and name of the initialization file This fil
24. lity is a local extension of the IRAF standards Unless specified in the parameter description all parameters are required to appear in the parameter file even if their value is not used by the program Blank lines and lines beginning with comments are ignored Chapter 2 Introduction spimodfit is intented to perform model fitting with SPI data By model fitting we mean the fit of a linear combination of sky emmission models point sources and background This program is based on a former model fitting program for SPI spidiffit developped by A Strong The main changes in spimodfit w r t spidiffit are e a more flexible handling of time variability for all kind of sources e time dependent instrument response function IRF e the use of NAG free constrained minimization procedures and the addition of a Levenberg marquadt algorithm e optimized matrix calculations and memory usage e more output files updated catalog of sources background model residues etc spimodfit is mainly dedicated to the study of long duration observations large scale emission focusing on the emission morphology as opposed to sopectral tools like XPEC The aim and basic algorithm of spimodfit are anyhow identical to those of spidiffit The next introductive sections are then directly taken from the spidiffit user manual 24 version 2 1 Scope The coded mask imaging y ray spectrometer SPI on the INTEGRAL space observatory wil
25. lt 0 gt I DI Oe lt 0 gt 0 lt 6 gt D tte lt Oy gt 8g lt 9q gt Ap EE uptraly lt b gt Oa lt ba gt POID A E D4 SOS wy g lt 0pbq gt 2 lt Op gt lt Og gt lt Op gt lt Oy gt P q y V wale pq gt lt Op gt lt Og gt P q which shows that to get the standard deviations on any linear function of the parameters it is enough to compute the parameter means lt 6 gt and covariances lt 6 64 gt In the case of a single parameter wp dip Af A8 lt 6 gt lt b gt In the case of uncorrelated parameters lt 0 4 gt lt Op gt lt bq gt pq Af X w lt 0 gt lt 6 gt In the general case the off diagonal elements give the correlation between different parame ters and can be either positive or negative i e can either increase or decrease the error in the linear function Spectral Aspects To get a total spectrum we average over regions of the total map for each energy range The average total map is the sum of the average maps but the errors on the total map must be computed by an appropiate sum over the total map corresponding to each sample This can be done by defining the w based on the maps Mij and using the covariance matrix The weights are defined by n DMD JCA jCA where A is a mask defining the sky region for which the spectrum is required and the denomi nator just normalizes to an average intensity over
26. mazx log Emin lstep lstsep is the logarithmic step as given by the parameter log_integration_step_irf It is recommended to keep this parameter to its default value of 0 03 A zero value causes the integration to be performed on a single interval Emin Emax Parameter log_integration_step_irf Type real Range gt gt 0 Description Logarithmic base 10 integration interval of the IRF 4 3 Definition of the fitted components spimodfit load and fit 3 types of components images i e extendend sky emissions point sources and background models For each of these components the parameters constraints variability order etc should be set in the parameter file 4 3 1 Image components The provided sky emission models has to conform to the OSA standard for images that is with one image index refering to a FITS image extension 4 3 1 1 Number and location of sky models The number of images to load is given by the n_image_parameters parameter Parameter n_image_parameters Type integer Range gt gt 0 Description Number of sky emission models 23 spimodfit requires the user to provide as many image indexes as sky emission models An image index is a FITS data unit containing the location of 1 or more regular image extensions This is the standard way of specifying sky models in ISDC softwares If more than one image are listed in the index file then the corresponding sky models are assumed to be energy
27. meter image_energy_model_pars_num_ Type integer Range gt 0 Description Number of parameters required to evaluate the XSPEC functions defined in the spectrum model for image component 25 Parameter image_energy_model_pars_ Type vector of reals Range Description Vector of parameters as required by the spectrum model for image com ponent Gamma correction for IRF The IRF interpolation within an energy bin assumes that the component spectrum follows a powerlaw F x E 7 The powerlaw exponent y can be set via image_IRF_gamma_cor_ For relatively narrow energy bins this parameter is expected to have only little influence on the output result Parameter image_IRF_gamma_cor_ Type real Range gt 0 Description Gamma correction of the IRF within an energy bin for image component Hit 4 3 1 3 Definition of detector and time intervals As for other fitted components sources and background models the user has to specified the detector and time ranges to be optionnaly fitted This is done via the image_det_rges_ image_var_coef_ and image_var_order_ parameters Detector selection The argument of image_det_rges_ is a list of individual or ranges of detectors For example 00 03 04 05 18 will define three virtual detector blocks the first one with detectors 01 to 03 the second one containing the single detector 04 and the third one with detectors 05 to 18 These 3
28. or better a log file into an IDL code rogroup string Leave blank The name of the read only i e input group This parameter is needed by the CommonPreparePARsStrings routine used to read the parameter file Nevertheless spimodfit doesn t support external input observation group and this parameter should be left blank 4 2 Observation and IRF files spimodfit fits an emission bakground model w r t an SPI observation For that purpose the user needs to give the location of the different observation files as well as the location of the IRF s Additionnal parameters allow to use a energy rebinned observation select only a subset of detectors filter the data counts or even simulate the detector events before fitting 4 2 1 Loading and configuring the observation data The observation data are loaded from 5 files 17 e events count rate e pointings e energy bins definition e dead time information e good time intervals e background index file The user must specify the path to these files and some options that give the possibility to modify the observatoin structure and vlues 4 2 1 1 Path to the observation files The path to the observation files are given by the following parameters By default these files will be opened with read and write mode In order to avoid data corruption if the programs exit abnormally it is strongly recommended to make these files read only or to gzipped them compressed fil
29. r it is simple to generalize to the case of a dataset including many energy channels and parameters for each energy so that the solution constitutes an energy deconvolution In this case S includes the off diagonal response terms From the point of view of the analysis technique there is no difference just Sj is larger by a factor equal to the square of the number of energy channels and d and 6 are correspondingly expanded 3 2 Model Fitting 3 2 1 Approaches Various approaches are possible based on well established principles An important point is that the data are Poisson so that any method must be able to handle such data correctly For COMPTEL EGRET and other y ray missions the maximum likelihood ratio method has been widely used The properties of this method and its used for the generation of error estimates are well understood It is a classical statistical method 11 In recent years much attention has been paid to Bayesian methods and their advantages are well documented e g Loredo vanDyk Bayesian approaches have been incorporated in e g Chandra standard packages Especially in GRB and cosmological statistical analyses it has become the method of choice in many publications see reference list The main advantage comes in handling multi parameter problems where the classical methods have fundamental limitations In particular the handling of so called nuisance parameters is in general not possible in classi
30. re documentation e amakeisdc in file used to configure the installation process This version of spimodfit depends on some locally installed libraries listed in table 1 2 These libraries should have been compiled on the same architecture and with the same compiler These libraries are located in subdirectories of afs ipp mpe gamma instruments integral software halloin_src subdirectory dal CorrectedDAL dal recompiled version corrected for use with a 64 bits machine dal3gen CorrectedDAL dal3gen recompiled version corrected for use with a 64 bits machine CommonCLib CommonCLib 2 1 OSA independent C libraries for gen eral use spicommonlib spicommonlib 2 2 collection of common C utilities objects and methods used for local SPI programs fftw3 0 fftw 3 0 1 The Fastest Fourier Transform In The West package Not directly used in spimodfit but necessary to some sub routines of spicommonlib Table 1 1 Required local libraries for compilation of spimodfit Assuming that all required libraries are available for the appropriate machine and compiler version the compilation procedure is the following 1 Clean any previous installation make distclean Please note that you may have to use gmake instead of make on some systems 2 Configure the current installation ac_stuff configure This configure script accepts many parameters and optional configuration flags You may have an overlook of these option
31. real Minimum longitude of the sky model area in degrees 30 Parameter psi_1 Type real Range Description Maximum longitude of the sky model area in degrees Parameter d_psi Type real Range Description Pixel size along the latitude in degrees 4 3 2 Point sources components The definition of point sources component is primarly performed through the use of a source catalog conforming to the SPI SRCL CAT SPI source catalogue or GNRL REFR CAT general reference catalogue The location of the input catalogue is given with source cat dol If its value is left empty then no point source is loaded Parameter source cat dol Type string Range Description Path and filename of the point sources catalogue conforming to the SPI SRCL CAT or GNRL REFR CAT template format No point source is loaded if the field is left empty The sources catalog contains a ineteger column named SEL_FLAG Only sources with SEL_FLAG set to a non zero value will be loaded and used for fitting in spimodfit 4 3 3 Source flux As for the images components the fitted parameters for point sources are unitless scaling factors It is therefore necessary to set a reference flux for each source in ph s71 ecm keV 1 In the same step an energy dependence of the flux can be set i e the definition of a reference spectrum There are three different ways to define the reference source spectrum the same pre defin
32. real Range Description Default fitted parameter value rescaling factor for image component This value is overridden in case of initialization by an external file or an unconstrained least squares fit Moreover the fitting process handles boundary constraints on parameters These are set globally for all parameters of a given image components by using image_parameters_min_ and image_parameters_max_ Parameter image_parameters_min_ Type real Range Description Low boundary constraint of image component parameters It is overridden in case of the use of an initialization file Parameter image_parameters_max_ Type real Range Description High boundary constraint of image component parameters It is overridden in case of the use of an initialization file 28 Initialization from an external file Optionnaly the image parameters for all components can be initialize from an output file FITS format This possinility is mainly intended to start a new fit from the results of a previous one Consequently the format of the FITS file should follow a precise format Moreover the number of image parameters defined in the file must match the number of parameters deduced from the number of sky models the detectors blocks and the time variability First spimodfit looks for a data extension defining the energy bins named and conforming to the SPI EBDS SET template One of the defined energy bin shal
33. se any expression involving the basic operators conditionnal relations lt gt lt gt and or and single or multiple arguments functions e trigonometric function sin cos tan asin acos atan e hyperbolic functions sinh cosh tanh asinh acosh atanh e logarithm functions log2 log10 log alias for log10 In e miscellaneous functions exp sqrt sign gives the sign of an expression rint nearest integer abs if e variable number of arguments functions sum the sum of the arguments avg mean value min min of the arguments max max of the arguments The two numerical constants _pi and _e are also supported When using these functions the only non fixed parameter should be the energy in keV refered as the variable E e g 1 0 sqrt 2 _pi 3 0 exp E 511 3 0 2 E 1 2 24 These functions should be sufficient to define any relevant spectral shape Nevertheless to ease the formulation and to conform to the XSPEC standard 7 functions shortcuts have been defined e powerlaw A x E 7 requiring the additional parameters y A e cutoff Ax ETY x exp E E uz requiring the additional parameters y Eeut A e bknpower AxE if E lt Ebreak and Ax E 2 7 E 7 otherwise requiring the additional parameters 71 Ebreak Y2 A e gaussian A V270 exp 0 5 E E c requiring the additional parameters Ey 0 A e constant
34. spimodfit Explanatory Guide and Users Manual H Halloin MPE Garching halloin mpe mpg de Software version 2 9 May 12 2009 Present address APC 11 place Marcelin Berthelot 75005 Paris halloin apc univ paris7 fr Contents 1 Getting started Pr compiled binaries seis aae a ain Seyi a Yee ed od oes PR ae Booed aR Compiling from sources 2 5 amp stare do 8 ie ee Gee wb Gere Ge Ee Dobie ee Se ae Software Versions os 20a Gone ae 4 dP ee dR ew hk Bah Ba eb he 1 1 1 2 1 3 1 4 1 5 1 3 1 Supported platforms 2 KnOwn BSu ee ea ee Ee a ol ee he a ee Be ee wR A Use and syntax of the parameter file 020200004 2 Introduction 2 1 Scope 3 Method and Algorithms 3 1 Imaging Data and Models 0 0 0 0 0000 pee ee 3 2 Model Fitting o e rrio dace Be Ate ae a ed a 3 2 1 3 2 2 Approaches iniaa awe Pee arene Ebene bre ie ee Mah eee Model Fitting Details asio rr acia kd ee Se ee BS i Pb ee aA 4 Using spimodfit 4 1 General parameters vu dasa ae he ce Poe ks Re ee I a a 4 2 Observation and IRF files aoaaa 4 3 4 2 1 4 2 2 4 2 3 4 2 4 Loading and configuring the observation data oa oaoa a a 4 2 1 1 Path to the observation files ooa aa 000 4 2 1 2 Background models selection and combination 4 2 1 3 Energy rebinning of the input data 4 2 1 4 Detector selection of the input data Simulation of detector even
35. t response information In addition to parameter estimation a Bayesian statistical analysis is used to include information on model characteristics and other prior information so that the uncertainties of the fitted parameters are properly assessed The prime results of the package are fitted model parameters with their uncertainty complementing these the fitted models are given also in the forms of skymaps and spectra The package will be referred to as spimodfit The package is closely related to imaging packages response convolution background treatments are common or similar Chapter 3 Method and Algorithms This chapter is entirely taken from the spidiffit user manual version 2 It describes the overall data representation and MCMC fitting method spimodfit can also fit the parameters from more classical first or second derivatives methods modified and truncated newton Levenberg Marquadt These algorithms are not yet documented though their use is explained in a latter section 3 1 Imaging Data and Models We distinguish image space and data space in the usual way and define the instrument response as the relation between them The image is J and the expected data is dy The expected background is by Let Rj be the response of data element k to image element j Then dy X Rygl br j An image modelis a parameterized algorithm for composing an image from components For OM i a linear model where 0 ar
36. the region as required for spectra in photons SD ei od G ae a Such spectra can be produced for any map regions after the MCMC run see below is complete so that the MCMC code does not need to use the maps explicitly and only needs Sik 14 MCMC methods Sampling from P 6 D is the main computational problem and it is proposed to use Markov Chain Monte Carlo MCMC methods A good reference is Gilks et al 1996 while Chen et al 2000 is more advanced and technical but has useful sections A clear and compact presentation of the basics is in Christensen et al 2001 Usually we are interested in the posterior for particular parameters with the rest integrated out marginalization The Metropolis Hastings MCMC algorithm is simple to implement and does not require any special sampling functions Data augmentation algorithms van Dyk et al 2001 should also be investigated but these are considerably more sophisticated The burn in phase is important in getting to the right region of the parameter space before starting to compute statistics Lack of incomplete burn in is manifested in a slow trend in the statistics with increasing samples instead of random fluctuations about the converged values The posterior average standard deviation and covariance matrix are easy to obtain from the sampled set of 8 Both uniform and Cauchy tan z uniform variate proposal distributions are imple mented for both local changing on
37. tinuous Order 3 corre sponds to the well known cubic spline Possible varaibility orders are form 0 to 5 odd numbers 0 are strongly recommended Note that this mechanism requires additiionnal parameters as many as the desired order for each set of contiguous intervals As a consequence fitting an order 1 or more time variability usually fails because of some over parametrized time intervals This could be considered as a bug Parameter image_var_coef_ Type list of real vectors specifiers Range gt 0 p d i n Description Specifies the nodes of the time variability for image component The format of the argument is detailed in the above text Parameter image_var_order_ Type integer Range 0 5 Description Regularity order of the time variability Recommended to be 0 or odd A variability order greater than 0 usually induces an unstable fitting process Use with care 4 3 1 4 Default parameters values and fitting flags The optimization process consists of finding a linear combination of components images point sources background models that minimizes a given function either least squares or maximum likelihood optimization In spimodfit the fitted parmeters are unitless scaling coefficients of the different components after having applied energy dependent rescaling and integration for the emission models In some cases it may be useful to define a fixed i e not fitt
38. tion by irf_input_file_ where stands for the IRF number from 01 to n_irf Parameter n_irf Type integer Range gt 0 Description Number of loaded time dependent IRFs Can be set to 0 when no emis sion model is given Parameter irf_input_file_ Type string Range Description Location of the IRF grouping file niumber The indication of the extension number is optional Two additionnal parameters are also used when loading the IRFs If only one enegy bin is fitted and all the gamma correction for the sky sources are identical see the corresponding section the instrument response can be pre calculated for a given 22 observation thus saving memory and time If the precalculate_irf parameter is set to 1 then the response is pre calculated if possible If the precalculation is not possible a warning message is issued and the algorithm continues using on the fly response calculation Parameter precalculate_irf Type integer Range 0 1 Description Pre calculate instrument response if possible The precalculation is only possible if only one energy bin is fitted and the gamma i e source spectral index corrections are identical In order to calulate the instrument response the IRF has to be integrated in the energy domain This is done with a 4 points interpolation on a logarithmic energy sampling The number of integration interval in Emin Emaz is then given by log E
39. ts 2 00 0 000 eee ee ee Rejection of bad data counts and background smoothing Loading the IRF files 0 0 020200 0002 eee Definition of the fitted components 0 000000 eee eee 4 3 1 Image components s e s s p aoa a a 0 00 eee ee 4 3 1 1 Number and location of sky models 4 3 1 2 Sky models units and energy dependent rescaling 4 3 1 3 Definition of detector and time intervals NATANDADKHWH Go 10 10 11 11 12 4 3 1 4 Default parameters values and fitting flags 27 4 3 1 5 Configuration of the output sky models 30 4 3 2 Point sources components 0 0 00 eee eee eee 31 ABB ASOULCE MU oy os te Beas deg at lee igi kd ot Ae ee ae ede A 31 Index of spimodfit parameters 1 a 32 Chapter 1 Getting started Either you are using a binary version of spimodfit or want compile it from sources the OSA environment has to be set At MPE this is done by sourcing the configuration script locating in the OSA subdirectory source lt Path_to_osa gt init_osa best lt Path_to_osa gt stands for afs ipp garching mpg de mpe gamma instruments integral isdc osa at the MPE In the above command line stands for the UNIX or LINUX prompt don t type it Then you have to set the PFILES environment variable to the directory of the parameter file Usually the parameter file is in the working directory and so yo
40. u should type setenv PFILES 1 1 Precompiled binaries At the MPE the documentation parameter file and pre compiled binaries of additional SPI software are in subdirectories of afs ipp mpe gamma instruments integral software So in spimodfit 2 9 one can find e the program binaries in subdirectories whose name reflect the machine architecture and compiler Their name is then of the form SYSARCH_COMP where SYSARCH is the system architecture as defined by the SYS environment variable type echo SYS to see its value and COMP is the compiler gcc g icc icpe e the documentation directory doc that should at least contain a user manual called spimodfit ps e an example of parameter file called spimodfit par If you are working on a machine for which a binary version exists you probably have to use it The next section compiling from the source is mostly intended for expert user in case of bug correction or compilation on a new system 1 2 Compiling from sources The source directory of additional SPI software can be found by following the afs ipp mpe gamma instruments integral software halloin_src symbolic link In the spimodfit 2 9 subdirectory the following items should be present e source cpp c and header h C and or C files e an ac_stuff subdirectory containing a slightly modified in order to support 64 bits ma chine configuration scripts from ISDC e a doc containing the softwa
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