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 
= 50 km/s/Mpc)
and the deceleration parameter (default 
= 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.