Nonthermal Module User`s Manual
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1. The first two arguments give the name of the shared library and the name of the PDF If the PDF has any fit parameters the remaining array arguments should provide the parameter names default values default freeze thaw state and default allowed minimum and maximum values See Also 6 2 make sync table Synopsis Generate a synchrotron lookup table Usage make_sync_table String_Type file Description The make_sync_table function can be used to generate a new lookup table for the angular integration that arises in the computation of the sync model 25 26 Chapter 6 Utility Functions See 6 3 The file name may be provided as a parameter If no file name is provided the default file name is used The output file is a FITS bintable To customize details of the table computation modify the script 1ib sync_make_table sl which is installed in prefix share isis nonthermal Also 6 11 _sync_angular_integral make invc_ table Synopsis Generate an inverse Compton lookup table Usage make_invc_table String_Type file Description See 6 4 The make_invc_table function can be used to generate a new lookup table for the integral over incident photons that arises in the computation of the inve model The file name may be provided as a parameter If no file name is provided the default file name is used The output file is a FITS bintable To customize details of the table computation modify the2. also provides a few simple usage examples The physical assumptions used to create the models and various computational details are discussed in Houck amp Allen 2006 ApJS 167 26 Chapter 1 Introduction Chapter 2 Examples In the following examples we assume that the nonthermal module has been installed in the default location so that isis will find it automatically 2 1 X ray Synchrotron Emission In this section we describe how to fit X ray data using the synchrotron model For a more general discussion of how to use isis in data analysis see the ISIS documentation http space mit edu cxc isis manual html First import the nonthermal module using require nonthermal to make the spectral models and related functions available to isis Next load the spectral data background spectrum and instrument responses variable pha load data pha fits assign_arf load_arf arf fits pha assign_rmf load_rmf rmf fits pha O define_bgd pha back fits At this point it may be desirable to rebin the data to improve the count statistics in certain regions and to ignore selected spectral intervals For example to ensure that each bin contains at least 25 counts use rebin_data pha 25 and to fit only data in the range 2 8 keV use xnotice_en pha 2 8 Next define the spectral model For this example we will use a simple model consisting of a single synchrotron emission component mod
3. energies needed for the inverse Compton spectrum model The first two parameters are gamma 1 sqrt 1 beta 2 E m c72 omega where gamma is the Lorentz factor of the electron E is the energy of the incident photon and m is the electron mass The third argument is the radiation field temperature K If the fourth is non zero the integral will be evaluated by spline interpolation on a pre computed table Otherwise the value will be computed by numerical integration See Also 6 13 ee haugl Synopsis Electron electron bremsstrahlung lab frame differential cross section Usage sigma _ee_haugl T omega 6 14 ee haugl lab 31 Description The _ee_haug1 function computes the lab frame differential cross section for electron electron bremsstrahlung by applying a numerical Lorentz transformation to the center of momentum frame cross section The parameters are T incident electron kinetic energy in units of the electron rest energy omega scattered photon energy in units of the electron rest energy The cross section is in units cm 2 erg See Also 6 14 _ee_haugi_lab 6 14 ee haugl lab Synopsis Electron electron bremsstrahlung lab frame differential cross section Usage sigma _ee_haugi_lab T omega Description The _ee_haugi_lab function computes the lab frame differential cross section for electron electron bremsstrahlung The parameters are T incident electron kinetic energy in units
4. ray spectrum for a specified nonthermal particle distribution function The primary pion decay spectrum parameter is the normalization norm n_p Ap V 4 pi d72 where n_p density of target protons cm 3 A_p nonthermal proton density at 1 GeV cm 3 GeV 1 V emitting volume cm 3 d distance cm The first argument of the pizero function is an integer index identifying a particular instance of this fit function The second and third arguments specify the particle distribution function PDF and its parameters Normally the second and third arguments are provided as return values by a special fit function that acts as an interface to the desired PDF For example fit fun pizero 1 default 1 causes the neutral pion decay function calculation to use the PDF named default which has parameters 3 4 pizero 15 index curvature E_cutoff When this fit function by pizero See Also momentum power law index amount of curvature above 1 GeV cut off momentum TeV is evaluated default 1 returns second and third parameters needed 16 Chapter 3 Spectral Models Chapter 4 Built In Particle Distribution Functions 4 1 default Synopsis default PDF Usage default id Description This distribution function provides a power law in momentum with curvature above some specific particle momentum and with an exponential cut off The distribution function has the for
5. Enforce charge conservation by adjusting the proton norm Usage force_charge_conservation electrons protons method Description The force_charge_conservation function take structures defining the electron and proton particle distribution functions and adjusts the normalization of the nonthermal proton dis tribution protons n_ GeV to enforce some definition of charge conservation The supported definitions are method 0 equal density of electrons and protons at some chosen injection kinetic energy method 1 equal integrated density of nonthermal electrons and protons The default is method 0 See Also 6 6 particle_info_struct 6 11 sync angular integral Synopsis Synchrotron angular integral 30 Chapter 6 Utility Functions Usage _sync_angular_integral x interp Description The _sync_angular_integral function computes the angular integral needed for the syn chrotron spectrum model The first argument x is defined as x f fc where f_c is the synchrotron critical frequency If the second argument is non zero the integral will be evaluated by spline interpolation on a pre computed table Otherwise the value will be computed by numerical integration See Also 6 12 invc photon integral Synopsis Inverse Compton integral over incident photon energies Usage _invc_photon_integral gamma omega T interp Description The _invc_photon_integral function computes the integral over incident photon
6. Nonthermal Module User s Manual John C Houck houck space mit edu Apr 1 2010 Contents 1 Introduction 2 Examples 21 Aras Synchrotron Emission c 2 62 2 4 aaa ee Y ea 2 2 Inverse Compton Gamma ray Emission 02 2 0005 3 Spectral Models AL COYNE ar AAA A AAA A E O AAN es OE A AAA ee ee ee ae ey POOR fi ok Si ee ea ee Oe eee ee eee ee ee 4 Built In Particle Distribution Functions Aol BIE eee BO a 8 ee ee ee BA ADS DE Pees Ee Sh Ane a2 break adds amp Ho Ee See ee ae ee A LA ke CUO cc a eae aAa aoai i e eee ee ee ee ee ee es LL BB oc a a ee a we ee Oe Se r eee ea a An MOREE oo nk ka A ee ee ede eee E Eee AG MO soe bee RA A he Pe Oe ees an BOE foo 25 eee iS A PS EEE Be nee ewe Pe Oe ees Ae PDOA i oo eee eRe ee ee eee Cee ee eee Ee Oe ee BS FONE os eek 8 Eh oe SE ERE OO EES Rae Se REE RS 5 User Defined Particle Distribution Functions 6 Utility Functions Bol add PO oss ee ye ER ee anina i a OEE Ee She oe G2 make syne table 4 22 cdg saari b dea a wees Pe ee ee aes 11 11 12 13 14 17 17 18 18 19 19 19 20 20 20 23 CONTENTS 6 3 6 4 6 5 6 6 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 make inve table ooo eae bee se eed eA Se ee 26 make ntbrem table 0 00224 2252 53 4 eee eee de eee Pes 26 nib sel process weights oc eo sacs co o toa sob s doi ee ee 27 particle infe SETUEL oo coes sera odor ee e eE e e RE 27 find momentum min aaa aaa a 28 HOntheria
7. a as counts even though the spectral values are given in flux units This subterfuge allows us to simultaneously fit X ray data in counts and gamma ray data in flux units However to make this work we must remember to turn off one of the normal data input validation tests By default when isis reads counts spectra it requires that the uncertainty in the number of counts be greater than or equal to one If the input data do not satisfy this requirement isis replaces the relevant input uncertainties with acceptable values To keep isis from modifying our input uncertainties in this way we set the intrinsic variable Minimum_Stat_Err to a small positive value smaller than any of the input uncertainties Having converted the Cas A HEGRA spectrum into the above format we can load the data into isis Minimum_Stat_Err 1 e 30 variable id load data casa_hegra_data txt Once the data have been loaded we can define and fit a model exactly as before For example to fit a model which includes both inverse Compton and neutral pion decay components we can use fit fun invc 1 default 1 pizero 1 default 2 Note that two particle distribution functions appear in this spectral model The inverse Compton component uses default 1 to define the electron momentum distribution and the neutral pion decay component uses default 2 to define the proton momentum distribution 10 Chapter 2 Examples Chapter 3 Spect
8. ameters specified using header keywords Using HEGRA observations of Cas A as a concrete example we might create a file that looks like this flux in photons s cm 2 bin object Cas A bintype counts xunit TeV exposure 1 0 we E_lo E_hi flux error 4 997493e 01 7 913994e 01 2 839012e 12 1 783329e 12 7 913994e 01 1 256344e 00 3 729176e 13 2 399393e 13 1 256344e 00 1 992807e 00 1 503555e 13 7 308948e 14 1 992807e 00 3 168774e 00 7 704922e 14 3 311765e 14 3 168774e 00 4 997493e 00 4 837415e 14 1 612472e 14 4 997493e 00 7 913994e 00 1 115603e 14 1 247306e 14 7 913994e 00 1 258409e 01 1 821113e 14 1 224027e 14 1 258409e 01 2 001003e 01 1 804125e 15 3 373713e 15 Details of this format are described in the ISIS documentation Lines beginning with a symbol are ignored and may be used to insert comments The first two columns define the lower and upper edges of histogram bins The bins must be in monotonic increasing order and may not overlap The xunit keyword specifies the 2 2 Inverse Compton Gamma ray Emission 9 bin coordinate units in this case the bin coordinates give the photon energy in TeV The next two columns contain the flux in photons s cm 2 and the associated uncertainty assumed to be symmetric Lines beginning with a semicolon define various keywords recognized by isis The exposure keyword specifies a nominal exposure time of one second Note that the bintype keyword labels the dat
9. dd pdf 4 9 full1 4 9 fulll Synopsis RMB Cutoff Power Law PDF Usage ful11 id 4 9 fulll 21 Description This particle distribution function consists of a relativistic Maxwell Boltzmann thermal distri bution rboltz plus a nonthermal tail default The fit parameters are those of rboltz plus default plus an additional parameter A_GeV which gives the density of nonthermal particles with p 1 GeV c cm 3 GeV 1 See Also 6 1 add_pdf 4 8 rboltz 4 1 default 22 Chapter 4 Built In Particle Distribution Functions Chapter 5 User Defined Particle Distribution Functions A user defined particle distribution function may be implemented in a compiled language such as C or Fortran compiled as a shared library and then imported into isis at run time via dynamic linking A detailed example of how to do this is provided in the examples subdirectory of the module source code distribution 23 24 Chapter 5 User Defined Particle Distribution Functions Chapter 6 Utility Functions 6 1 add pdf Synopsis Add a particle distribution function Usage add pdf String Type libname String Type pdfname param_names param_values freeze min max Description The add pdf function can be used to load a particle distribution function PDF from a shared library An example implementation of such an object is provided in the examples directory of the source code distribution
10. deristy lt lt d SSS ea eee i 28 nontherm energy density osne ss ea ER ESS KE aa a e eee 29 force charge conservation 29 _sync_angular integral 0500 29 _ mee photon integral ss oses med como o a dad a As ye 30 BO Haigh pesos sda Aaaah RA 30 Hane TAR A ee PE ee ee eee 31 ep Nees ce og aera ee a a a ee ee e 31 Chapter 1 Introduction As part of our work on cosmic ray acceleration in supernova remnants we wanted to search for evidence of curvature in relativistic particle momentum distributions However to the best of our knowledge no publically available spectral fitting package included models for photon emission generated by relativistic particles via synchrotron inverse Compton nonthermal bremsstrahlung and neutral pion decay processes and also allowed one to easily investigate the effect of different particle distribution functions XSPEC includes the synchrotron models SRCUT and SRESC but these models are based on a fixed particle distribution function parameterization By implementing the necessary spectral models in a form accessible to the ISIS spectral analysis system we gain the ability to fit these models not just to X ray data but also to radio and gamma ray observations as well By simultaneously fitting observations from several wave bands one can try to better constrain the important fit parameters This manual describes each of the spectral models and particle distribution functions and
11. ensity of nuclei n The default weights are appropriate for a fully ionized gas with cosmic abundances so that most electrons come from hydrogen and helium In that case the number fractions of hydrogen and helium are roughly X_H X_HE 1 0 1 1 0 9091 0 1 1 1 0 0909 The electron electron bremsstrahlung contribution proportional to the ambient electron den sity has weight wt_ee X_H 2 X_HE 1 09091 and the total electron proton bremsstrahlung contribution proportional to n Z 2 has weight wt ep X_H 4 X_HE 1 27273 See Also 6 6 particle info struct Synopsis Get a template structure for specifying the PDF Usage Struct_Type particle_info_struct Description The particle_info_struct returns a template structure with the following fields 28 Chapter 6 Utility Functions __Name__ __Definition__ pdf_name name of the particle distribution function params parameter values particle type electron 0 proton 1 n_GeV density at 1 GeV cm 3 GeV 1 kT temperature of thermal particles n_th density of thermal particles See Also 6 7 find momentum min Synopsis Find the momentum at which the thermal and nonthermal PDFs intersect Usage pc_min find_momentum_min Struct_Type p Description The find_momentum_min function takes a structure defining the thermal and nonthermal com ponents of the particle distribution function and computes the momentum at which those two distributions contrib
12. his distribution function is a power law in total energy N p A E EO index where E0 1 GeV The power law index is the only fit parameter See Also 6 1 add_pdf 4 5 dermer Synopsis PDF from Dermer 1986 Usage dermer id Description This distribution function is a power law in total energy with momentum dependent curvature above the momentum specified by the intrinsic variable Min_Curvature_Pc which is 1 GeV by default The fit parameters are then index power law index curvature curvature parameter See Also 6 1 add_pdf 4 6 mori Synopsis PDF from Mori 1997 Usage mori id 20 Chapter 4 Built In Particle Distribution Functions Description This distribution function was taken from Mori 1997 and is designed to represent the Galactic cosmic ray proton distribution It has no free parameters See Also 6 1 add_pdf 4 7 boltz Synopsis Non relativistic Maxwell Boltzmann Distribution Usage boltz id Description This distribution function provides a non relativistic Maxwell Boltzmann thermal particle dis tribution The only fit parameter is the temperature kT in keV See Also 6 1 add_pdf 4 8 rboltz Synopsis Relativistic Maxwell Boltzmann Distribution Usage rboltz id Description This distribution function provides a relativistic Maxwell Boltzmann thermal particle distri bution The only fit parameter is the temperature kT in keV See Also 6 1 a
13. ified by line of sight absorption To compute the synchrotron 7 8 Chapter 2 Examples emission spectrum it is necessary to specify the underlying particle momentum distribution function For this example we will use the default momentum distribution function described in Houck amp Allen 2006 ApJS 167 26 To model the effects of line of sight absorption we will use the phabs function from XSPEC The spectral model is then fit_fun phabs 1 sync 1 default 1 Before fitting the data is usually a good idea to choose initial parameter values such that the starting model is reasonably close to the data Once we re satisfied with the initial parameter values perform the fit and then overplot the model and data histograms O fit_counts rplot_counts pha At this point it is usually a good idea to investigate the neighborhood of the fitted parameters to make sure that the best possible fit has been achieved For example we might use conf to compute single parameter confidence limits for fit parameters of interest 2 2 Inverse Compton Gamma ray Emission The process of fitting gamma ray data is essentially identical to that used to fit X ray data in the previous example The primary difference is that before the data can be loaded into isis TeV gamma ray spectra must first be cast into a suitable form One suitable form is an ASCII file with spectral data in four columns and with a small number of scalar par
14. lt which has parameters 3 3 ntbrem 13 index momentum power law index curvature amount of curvature above 1 GeV E_cutoff cut off momentum TeV When this fit function is evaluated default 1 returns second and third parameters needed by invc By default the value of the integral over incident photon energies is determined via spline interpolation in a pre computed table and the value of the T_photon parameter is not used To compute this integral via direct integration set the intrinsic variable _invc_interpolate to a non zero value See Also 6 12 _invc_photon_integral 3 3 ntbrem Synopsis Nonthermal bremsstrahlung spectrum model Usage ntbrem Int_Type i String Type pdf name Double Type pdf_params Description The ntbrem function computes the nonthermal bremsstrahlung spectrum for a specified non thermal particle distribution function assuming a stationary target The primary nonthermal bremsstrahlung spectrum parameter is the normalization norm n_t A_e V 4 Api d72 where n_t density of target nuclei cm 3 A_e nonthermal electron density at 1 GeV cm 3 GeV 1 V emitting volume cm 3 d distance cm The first argument of the ntbrem function is an integer index identifying a particular instance of this fit function The second and third arguments specify the particle distribution function PDF and its parameters Normally the second and third arguments are provided as
15. m N p A p p0 f p a exp p0 p cutoff where f p a f p a index p lt p0 index curvature log10 p p0 p gt p0 The value of pO is determined by the value of Min_Curvature_Pc 1 GeV by default The fit parameters are index power law index curvature curvature parameter cutoff cut off energy TeV See Also 6 1 add_pdf 17 18 Chapter 4 Built In Particle Distribution Functions 4 2 cbreak Synopsis cooling break PDF Usage cbreak id Description This distribution function is the same as the default distribution function except that it also has a cooling break above a particular momentum The cooling break is implemented by adding an additional multiplicative factor of the form break pc for pc gt break g p 1 for pc lt break where p is the particle momentum and break is the break energy The fit parameters are then index power law index curvature curvature parameter cutoff cut off energy TeV break cooling break energy TeV See Also 6 1 add_pdf 4 3 ke cutoff Synopsis PDF with cutoff in particle kinetic energy Usage ke_cutoff id Description This distribution function is the same as the default distribution function except that the exponential cutoff depends on kinetic energy T instead of momentum p See Also 6 1 add_pdf 4 4 etot 19 4 4 etot Synopsis Energy dependent PDF Usage etot id Description T
16. of the electron rest energy omega scattered photon energy in units of the electron rest energy The cross section is in units cm 2 erg See Also 6 15 ep heitlerl Synopsis Bethe Heitler cross section Usage sigma _ep_heitler1 T omega Description The _ep_heitler1 function computes the Bethe Heitler cross section for electron ion bremsstrahlung The parameters are 32 Chapter 6 Utility Functions omega incident electron kinetic energy in units of the electron rest energy scattered photon energy in units of the electron rest energy The cross section is in units cm 2 erg See Also
17. ral Models Note on differential vs histogram forms Differential and histogram forms of each spectral model are provided The histogram form is the one used in fitting models to data For this reason input data must be converted to histogram form The differential form is normally used for testing and for making plots See the ISIS documentation for additional details 3 1 sync Synopsis Synchrotron spectrum model Usage sync Int_Type i String Type pdf name Double Type pdf_params Description The sync function computes the synchrotron spectrum for a specified nonthermal particle distribution function The synchrotron spectrum parameters are B_tot total magnetic field strength microgauss norm normalization A_e V 4 pi d72 where A_e nonthermal electron density at 1 GeV cm 3 GeV 1 V emitting volume cm 3 d distance cm The first argument of the sync function is an integer index identifying a particular instance of this fit function The second and third arguments specify the particle distribution function PDF and its parameters Normally the second and third arguments are provided as return values by a special fit function that acts as an interface to the desired PDF For example 11 12 Chapter 3 Spectral Models fit_fun sync 1 default 1 causes the synchrotron function calculation to use the PDF named default which has pa rameters index momentum power law index curva
18. return values by a special fit function that acts as an interface to the desired PDF For example fit fun ntbrem 1 default 1 causes the nonthermal bremsstrahlung function calculation to use the PDF named default which has parameters index momentum power law index curvature amount of curvature above 1 GeV E_cutoff cut off momentum TeV 14 Chapter 3 Spectral Models See 3 4 When this fit function is evaluated default 1 returns second and third parameters needed by ntbrem By default the value of the electron electron differential cross section is determined via spline interpolation in a pre computed table To compute these cross sections without interpolation set the intrinsic variable _ntbrem_interpolate to a non zero value The relative contributions of electron electron and electron proton bremsstrahlung are con trolled by the ntb_set_process_weights function To use an alternate somewhat faster numerical integration algorithm set the integer intrinsic variable _ntbrem_integration_method to a non zero value Note that changing the numerical integration method will cause small changes in the computed model values Also 6 5 ntb set process weights 6 13 _ee_haug1 6 14 _ee_haug1_lab pizero Synopsis Neutral pion decay spectrum model Usage pizero Int_Type i String Type pdf name Double Type pdf_params Description The pizero function computes the neutral pion decay gamma
19. script lib invc make table sl which is installed in prefix share isis nonthermal A blackbody radiation field is used by default To use a different radiation field it is necessary to modify the source code replacing src bbody c and making any other necessary changes Also 6 12 _invc_photon_integral make ntbrem table Synopsis Generate an ee Bremsstrahlung lookup table Usage make_ntbrem_table String_ Type file Description The make_ntbrem_table function can be used to generate a new lookup table for the electron electron bremsstrahlung differential cross sections that arise in the computation of the ntbrem model The file name may be provided as a parameter If no file name is provided the default file name is used The output file is a FITS bintable To customize details of the table computation modify the script 1ib ntbrem_make_table sl which is installed in prefix share isis nonthermal 6 5 ntb set process weights 27 See Also 6 13 _ee_haug1 6 14 _ee_haug1_lab 6 5 ntb set process weights Synopsis Set the relative weights of ee and ep bremsstrahlung Usage ntb set process weights wt_ee wt ep Description The ntb set process weights function can be used to set the weights used for electron electron and electron proton bremsstrahlung The total contribution from both processes is S E wt_ee S_ee E wt ep S_ep E The fluxes are scaled relative to the ambient number d
20. ture amount of curvature above 1 GeV E_cutoff cut off momentum TeV When this fit function is evaluated default 1 returns second and third parameters needed by sync By default the value of the angular integral is determined via spline interpolation in a pre computed table To compute the angular integral value via direct integration set the intrinsic variable _sync_interpolate to a non zero value See Also 3 2 6 11 _sync_angular_integral inve Synopsis Inverse Compton spectrum model Usage invc Int_Type i String Type pdf name Double Type pdf_params Description The invc function computes the inverse Compton spectrum for a specified nonthermal particle distribution function The inverse Compton spectrum parameters are T_photon radiation field temperature K norm normalization A_e V 4 pi d72 where A_e nonthermal electron density at 1 GeV cm 3 GeV 1 lt I emitting volume cm 3 a ul distance cm The first argument of the inve function is an integer index identifying a particular instance of this fit function The second and third arguments specify the particle distribution function PDF and its parameters Normally the second and third arguments are provided as return values by a special fit function that acts as an interface to the desired PDF For example fit fun invc 1 default 1 causes the inverse Compton function calculation to use the PDF named defau
21. ute equally If the thermal PDF is everywhere below the nonthermal PDF the momentum at the thermal peak is returned See Also 6 6 particle_info_struct 6 8 nontherm density Synopsis Compute the density of nonthermal particles Usage n nontherm_density Struct_Type p Description The nontherm_density function takes a structure defining the thermal and nonthermal com ponents of the particle distribution function PDF and computes the integral over the non thermal PDF The lower limit of this integral is the momentum at which the thermal and nonthermal PDFs intersect If the thermal PDF is everywhere below the nonthermal PDF the momentum at the thermal peak is used See Also 6 7 find_momentum_min 6 9 nontherm energy density 29 6 9 nontherm energy density Synopsis Compute the energy density of nonthermal particles Usage n nontherm_energy_density Struct_Type p Description The nontherm_energy_density function takes a structure defining the thermal and nonther mal components of the particle distribution function PDF and computes the energy density in nonthermal particles by integrating over the nonthermal PDF The lower limit of this inte gral is the momentum at which the thermal and nonthermal PDFs intersect If the thermal PDF is everywhere below the nonthermal PDF the momentum at the thermal peak is used See Also 6 7 find_momentum_min 6 10 force charge conservation Synopsis
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