IRAC Instrument Handbook - IRSA - California Institute of Technology

IRAC Instrument Handbook
In this convention, the overall normalization of R is unimportant. Observers can correct the photometry to
the spectrum of their source by either performing the integral in this equation or looking up the color
corrections for sources with similar spectra. Note that our definition of the color correction looks slightly
different from that in the IRAS Explanatory Supplement [4], because we used the system spectral
response R in electrons/photon, instead of ergs/photon.
We selected nominal wavelengths that minimize the need for color corrections, such that the quoted flux
densities in IRAC data products are minimally sensitive to the true shape of the source spectrum. (This
paragraph can be skipped by most readers; the table is given below.) First, let us expand the source
spectrum in a Taylor series about the nominal wavelength:
⎡ ⎛ λ − λ ⎤
0 ⎞
F ⎢ ⎜
⎟
ν = F 1+
β + ... ⎥
(4.9)
ν 0
⎣ ⎝ λ0
⎠ ⎦
Using equation 4.8, the color correction for a source with spectrum F ν is
1 λ λ0
−1
K 1 β ( ν / ν 0 ) Rdν
ν ∫ λ0
⎥ ⎡ ⎛ − ⎞⎤
= ⎢ +
⎜
⎟
(4.10)
∆ ⎢⎣
⎝ ⎠⎦
The choice of λ 0 that makes K minima lly sensitive to β is the one for which
Solving for λ 0 we get
λ =< λ >=
0
∫
∫
dK
= 0.
dβ
λ(
ν / ν ) Rdν
= C
( ν / ν Rdν
−1
0
−1
0 )
Calibration 39 Color Correction
∫
∫
ν
−2
Rdν
−1
ν Rdν
So the optimum choice of 0
λ for insensitivity to spectral slope is the weighted average wavelength.
Using the nominal wavelengths from Table 4.2, the color corrections for a wide range of spectral shapes
are less than 3%. Thus, when comparing IRAC fluxes to a theoretical model, placing the data points on
(4.11)