Calculation of Energy Flux from a count rate (CONVERT/RATE_TO_FLUX )

For most of the ROSAT detected sources the number of source counts is too low to support a detailed spectral modeling. If the source was only observed with the ROSAT High Resolution Imager (HRI) which as a micro-channel plate detector has practically no spectral resolution (c.f.  The ROSAT Handbook ) no spectral informations are available in the data at all. A quite frequent task is therefor to estimate the integrated energy flux of a source from the count rate by assuming a spectral model and fixing the column density to a reasonable value.

EXSAS now supports this task with the command:

CONVERT/RATE_TO_FLUX   par_file   rate/tbl   detector   [E_low]   [E_high]

The accepted command line options are:

par_file: is a parameter file in the usual EXSAS format which contains the spectral model and its parameters. Important to note is that the program assumes always that in par_file the "PARAMETER 1" is the column density and "PARAMETER 2" is the photon flux amplitude in photons/s/ . An example of a valid parameter file is:

      !                                                          
      ! TASK: FIT                                                
      !                                                          
      ! --- power law ---
      MODEL  gamm(1)*powl(2,3,4)      ! gal_abs.*power_law
      PARAMETER 1  0.08               ! x 10^21 cm^-2
      PARAMETER 2  1.0                ! photon flux ampl. at E0
      PARAMETER 3 -2.6                ! photon index 
      PARAMETER 4  1.0                ! ref_energy E0 keV

      NOTE: The line  "! TASK: fit"  is mandatory 
   

The required parameter file has to define only the spectral model and the "Task" which is "FIT". No additional directives are needed. The maximum number of 1000 steps is used to integrate over the requested energy range.

rate/tbl: is the count rate within the ROSAT energy band or a table name which has to have the columns :RATE (count rate in units of counts per second) and :Nh (column density in units of 10**21 1/  ). If the count rate is passed to the command as a number from the command line the column density (Nh, PARAMETER 1) has to be set in the parameter file. If the second argument of the command is a table name the program loops through the table using the count rates and column densities listed in the columns :RATE and :Nh.

detector: depending of what instrument was used to observe the source. The names HRI, PSPC, PSPCc and PSPCb are accepted. If no name is given the ROSAT PSPC (PSPCb) is used by default.

E_low, E_high: are the lower and upper energy boundaries (in keV) of the energy range for which the integrated energy flux is computed. Here any numbers can be given. The default is 0.1 - 2.4 keV. The maximum number of 1000 steps is used to integrate over the requested energy range.

Note: This command does not support models which are normalized to the integrated energy flux or normalized to luminosity flux, i.e. don't use models like BBEF, PLEF, BPEF, EXEF, EPEF, TBEF, GSEF, BBLM, PLLM, BPLM, EXLM, EPLM, TBLM to convert the count rate to the integrated energy flux. Also care has to be taken using user defined models (!).

The command works fine with the additive models: BBDY, DIBB, POWL, BRPL, PWLB, EXPO, PLEX, THBR, COMP, RSMF, GAUS and ASYG.

Another point to note is that always the instrument's on-axis effective area is used during the energy flux computation. This is not a restriction if you have deduced your count rate with one of the EXSAS spatial analysis programs. However, if your source is not on-axis and you have used some non-EXSAS procedure for the count rate estimate make shure that your count rate is vignetting corrected (!!).

How the command works in detail:

Lets explain it with an example. Assume that we have an HRI source which is found to have a count rate of 0.037 counts/s. The source spectrum is known from previous PSPC observations and is a power-law with photon index -2. The column density between the source and the observatory is also known from other observations and is taken to be . Not known a priori is the photon flux amplitude at E0=1 keV. This number is therefor fixed at the beginning of our task to 1.0.

The following parameter file passed to model/spectrum then computes the HRI count rate for the assumed spectrum and photon flux amplitude 1.0 photons/s/ .

  
 Midas 001> $vi powl_fx_start.par:
 CALCULATE  
 FOLD             
 CORRECTION_FILE     exsas_cal:effarea_hri  ! corr_effective_area
 RESPONSE_FILE       exsas_cal:drmhri       ! det_response_matrix

 ! --- power law ---
 MODEL  gamm(1)*powl(2,3,4)      ! gal_abs.*power_law
 PARAMETER 1  0.8                ! x 10^21 cm^-2
 PARAMETER 2  1.0                ! photon flux at E0
 PARAMETER 3 -2.0                ! photon index 
 PARAMETER 4  1.0                ! ref_energy E0 keV

 Midas 002> model/spectrum powl_fx_start.par
 Got spectral parameters from      powl_fx_start.par.
 Got corrected effective area from exsas_cal:effarea_hri.
 Got detector response matrix from exsas_cal:drmhri.
 DATA SET    1   
 MODEL   1  GAMM(1)*POWL(2,3,4)
 PARAMETER   1  0.8
 PARAMETER   2  1.0
 PARAMETER   3 -2.0
 PARAMETER   4  1.0
 Detector Response Matrix covers .71345E-01 keV to 3.01 keV
 count rate  =  6.281E+01 counts/s

Since the photon flux amplitude at E0 has been set in a first step arbitrarily to 1.0 photons/s/ the resultant count rate of 62.81 counts/s does obviously not match the observed HRI count rate and is too large by a factor 62.81/0.037 = 1697.56. This information can be used to rescale the photon flux amplitude to 1/1697.56 = 5.890E-04 photons/s/ so that the parameter file necessary to compute the flux of our fictional source looks like:

 Midas 001> $vi powl_fx_final.par :
 CALCULATE
 ENERGY 0.1 2.4            ! Energy range

 ! --- power law ---
 MODEL  gamm(1)*powl(2,3,4)      ! gal_abs.*power_law
 PARAMETER 1  0.0                ! x 10^21 cm^-2
 PARAMETER 2  5.890E-04          ! photon flux at E0
 PARAMETER 3 -2.0                ! photon index 
 PARAMETER 4  1.0                ! ref_energy E0 keV

Note that the column density here has been set to zero since the flux usually wanted is the unabsorbed energy flux. Because no stepwidth is given with the parameter ENERGY the maximum number of 1000 steps is used to integrate over the requested energy range.

The computation of the the energy flux in the energy range 0.1-2.4 keV is than done by:

 Midas 002> model/spectrum powl_fx_final.par
 Got spectral parameters from      powl_fx_final.par.  
 DATA SET    1  
 MODEL   1  POWL(1,2,3)
 PARAMETER   1 5.890E-04
 PARAMETER   2 -2.0
 PARAMETER   3 1.0

 Detector Response Matrix covers 0.1 keV to 2.40 keV
 photon flux =  5.645E-03 photons/cm^2/s
 energy flux =  1.872E-03 keV/cm^2/s
             =  2.999E-12 erg/cm^2/s
             =  2.999E-15 Watt/m^2

The example described above lists in detail the steps which have to be done to convert the count rate to an energy flux. The EXSAS comand CONVERT/RATE_TO_FLUX is a powerful tool which does the steps described above in a very comfortable way by changing the parameter file entries, normalising the photon flux amplitude and handling table input. Typical calling sequences are:

CONVERT/RATE_TO_FLUX   powl_fx   0.037   HRI   2.0   5.0

Computes the integrated energy flux within 2.0-5.0 keV for an HRI source which has a count rate of 0.037 counts/s in the ROSAT energy band. The column density is given in the parameter file powl_fx.par in units of 10^21 1/cm^2 as PARAMETER 1

CONVERT/RATE_TO_FLUX   powl_fx   solst   HRI   0.1   3.0

Computes the integrated energy flux within 0.1-3.0 keV for all source count rates given in the table solst.tbl under the column :RATE. The column density Nh (in units of 10^21 1/cm^2) is taken from the table column :Nh. The computed energy fluxes are listed on the screen and written to the table solst.tbl in a column labeled :FLUX

Author: Werner Becker (e-mail: web@mpe-garching.mpg.de ) / Page last modified: 09-SEP-97