9.5  Computation of IRS Synthetic Photometry

Photometry calculations are carried out in using the following definitions:

ν = c / λ

T_ν = value in the response (transmission curve) table, interpolated for ν

R_ν = T_ν         for MIPS 24

     = T_ν / ν   for all others

f_ν = interpolated flux at ν

σ_ν = interpolated uncertainty of flux at ν

unc_adjust = uncertainty adjustment factor: SL2=0.011, SL1=0.011, LL2=0.016, LL1=0.018

CC = color correction factor, 0.9679 for MIPS 24, and 1.0000 for all others.

            Computation of the MIPS 24 value is explained below.

BB(ν)  = blackbody flux density at ν for a temperature of 10,000 Kelvin

Photometric flux is calculated as follows:

FLUX  = CC * ∫  f_ν R_ν dν   /     ∫  R_ν dν

The flux uncertainty is calculated by first integrating the input uncertainties:

UNC_initial  =  ∫  σ_ν R_ν dν   /      ∫  R_ν dν

and then adding the uncertainty adjustment in quadrature:

 UNC_final  =  sqrt ( UNC_initial² + (FLUX * unc_adjust)² )

For all bands except MIPS 24, the standard reference spectrum is f_ν =1/ν so that the color correction factor is CC=1. For MIPS 24, a 10,000 Kelvin blackbody is used as a reference, necessitating a modest color correction factor at 24 microns.  Calculation of the color correction factor CC for MIPS 24 starts with computing the effective wavelength:

λ _eff   =  ∫ R_λ  dλ   /    ∫ λ^-1  R_λ  dλ     =    23.6749 micron

ν_eff    =  c  / λ _eff   =    1.2663e+13  Hz

BB(ν_eff)  =  BB(1.2663e+13)  =  4.7694e-7

Then the uncalibrated flux from the blackbody spectrum is computed:

uncalibrated_flux_bb =  ∫ BB(ν) ν R_ν dν   /    ∫ ν R_ν dν  = 4.9275e-7

Finally,  we get the color correction factor by dividing into blackbody flux density at the effective wavelength:

CC  =  BB(ν_eff)  / uncalibrated_flux_bb  =  0. 9679

The uncertainty adjustment factors are discussed in more detail in Section 9.3.2.