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_{initial} ^{2} + (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.