Calculation of Energy Flux from a Count Rate

 

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 [David et al.1993], no spectral informations are available in the data at all. A quite frequent task is therefore 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.

Let's 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 textttmodel/spectrum then computes the HRI count rate for the assumed spectrum and photon flux amplitude 1.0 photons/s/cm .

 
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</PRE>

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/sm 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/cm 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</PRE>

Note:That the column density here has been set to zero since the flux usually wanted is the unabsorbed energy flux.

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, normalizing 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 cm 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 cm ) is taken from the table column :Nh. The computed energy fluxes are listed on the screen and written to a new column :FLUX_0.1-3.0 of table solst.tbl.