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Calculation of Luminosity

 

In connection with command model/spectrum in its calculate mode the command integrate/flux delivers the luminosity of a red-shifted source. Care must be taken that the model spectrum defined in the parameter file has no absorption part. An appropriate model can be chosen for a Friedmann-Lemaitre cosmology by setting the Hubble parameter (default tex2html_wrap_inline17809 = 50 km/s/Mpc) and the deceleration parameter (default tex2html_wrap_inline17811 = 0.5).

First we define a power law model in parameter file spectrum_flux.par by using the standard editor edt. Then we run model/spectrum with this parameter file and output the unabsorbed spectrum to table spectrum_flux.tbl. We use command integrate/flux with table spectrum_flux.tbl as input and calculate the photon and energy flux and the luminosity between the boundaries of 0.5keV and 4.5keV. The output appears only on the terminal.

Midas 001> $edt spectrum_flux.par
 cal                          ! calculates only photon flux
 energy     0.1  5.0          ! energy interval, unit in keV
 out_mode   spectrum          ! output mode
 out_file   spectrum_flux     ! output file
 model      powl(1,2,3)       ! power law model
 par 1      .01               ! photon flux amplitude at E0 = 2keV
 par 2      -1.5              ! photon index gamma
 par 3      2.0               ! reference energy E0 in keV
 redshift   0.1               ! red shift z
Midas 002> model/spectrum spectrum_flux
 ...
 Initialize table spectrum_flux.tbl.
Midas 003> integrate/flux spectrum_flux 0.5 4.5
 energy bounds (OBS.) Emin: 5.00000E-01 keV
                      Emax: 4.50000E+00 keV

 energy bounds (REST) Emin: 5.50000E-01 keV
                      Emax: 4.95000E+00 keV

 redshift:                  1.00000E-01
 Hubble parameter:          5.00000E+01 km/s/Mps
 deceleration parameter:    5.00000E-01
 luminosity distance:       6.13869E+02 Mpc

 flux on top of atmosphere: 5.08497E-02 photons/(cm**2 s)
                            7.62768E-02 keV/(cm**2 s)
                            1.22209E-10 erg/(cm**2 s)
 log10(flux):               -1.29371E+00 [photons/(cm**2 s)]
                            -1.11761E+00 [keV/(cm**2 s)]
                            -9.91294E+00 [erg/(cm**2 s)]

 luminosity in REST frame : 3.43990E+21" *1.E33 keV/s"
                            5.51132E+12 *1.E33 erg/s
 log10(luminosity)          5.45365E+01 [keV/s]
                            4.57413E+01 [erg/s]
To derive a luminosity directly from observed data of a red shifted   source one can use standard models with names ending on **lm. For these models the normalization or amplitude is defined as a luminosity using the luminosity distance as a parameter to convert the flux into a luminosity. This possibility has the advantage that one gets also an error.



If you have problems/suggestions please send mail to rosat_svc@mpe-garching.mpg.de