Color Correction of IRAS Flux Densities

[Adapted from the Explanatory Supplement]

In the catalogs, flux densities are quoted for the effective wavelengths of the IRAS bands (12, 25, 60, 100 microns) and an input energy distribution which is constant in the flux per logarithmic frequency interval (essentially the flux per octave); i.e., the flux density f(nu) with frequency nu is proportional to 1/nu and the flux density f(lambda) with wavelength lambda is proportional to 1/lambda. No loss in generality is incurred by such a procedure, nor does it prejudice subsequent correction for the true spectral distribution of the source.

If the input spectral distribution is not constant in flux per octave then a correction, the "color correction", must be applied to the quoted flux densities. This correction depends on the shape of the intrinsic energy distribution and on the details of the wavelength response of the system. The color corrections for a number of input energy distributions are given in Tables 1 and 2 below. Tabulated are the factors K(nu) such that f(nu)[actual] = f(nu)[quoted]/K(nu). K(nu) is written as a function of frequency because it is band-dependent. The response functions for the four bands are tabulated here; for a more detailed discussion see the Explanatory Supplement.

The sensitivity of the color corrections to uncertainties in the spectral bandpasses was checked by numerical simulations. For many sources of interest in the catalog, the 60 micron band flux densities are especially sensitive to errors caused by lack of knowledge of the spectral pass bands. Specifically, in this band, uncertainties in the short wavelength parameters of the transmission of the optics, and in the detector efficiency, affect the response for extremely cold objects (T ~ 60 K) in a significantly different way than for the stellar energy distribution of the calibrating sources. The numerical tests show that the sensitivity of the color corrections to wavelength shifts of the entire response is approximately 7%/micron; pre-launch measurements of the spectral shape should be accurate to ~0.3 micron. On the other hand, if the effective responsivity of the system increases by an additive 1% over the entire bandwidth, starting at 24 microns, the calibration for 60 K sources changes by 16% relative to the stellar calibration. Uncertainties of this magnitude in the effective response are the maximum expected from pre-flight measurements. Errors in the long wave cutoff of the 100 micron band could also result in significant errors in the flux densities of objects colder than 30 K.

It should be emphasized that there is no prejudice in the procedure or assumptions for color correction. The uncertainty in the quoted flux densities results directly from the lack of knowledge of the spectral response of the system. Deriving true flux densities requires a knowledge of the intrinsic energy distribution of the astronomical sources.

Note that in the tables R(i,j) = f(nu)[band i]/f(nu)[band j].

Table 1.  K(nu) for a power-law spectral energy distribution
[f(nu) proportional to nu^alpha]

alpha  R(12,25)  R(25,60)  R(60,100)  K(12)  K(25)  K(60)  K(100 micron)
------------------------------------------------------------------------
-3.0    0.113     0.063     0.21      0.91   0.89   1.02   1.02
-2.5    0.162     0.102     0.275     0.92   0.91   1.00   1.01
-2.0    0.232     0.164     0.355     0.94   0.93   0.99   1.00
-1.5    0.333     0.262     0.460     0.97   0.96   0.99   1.00
-1.0    0.480     0.417     0.600     1.00   1.00   1.00   1.00
-0.5    0.694     0.662     0.786     1.04   1.04   1.02   1.00
 0.0    1.005     1.045     1.037     1.10   1.10   1.05   1.01
 0.5    1.459     1.642     1.378     1.17   1.16   1.09   1.02
 1.0    2.123     2.567     1.843     1.25   1.23   1.15   1.04
 1.5    3.094     3.992     2.484     1.35   1.32   1.23   1.06
 2.0    4.519     6.170     3.373     1.47   1.41   1.32   1.09
 2.5    6.610     9.480     4.617     1.61   1.53   1.44   1.12
 3.0    9.681    14.475     6.370     1.78   1.67   1.59   1.16


Table 2.  K(nu) for a blackbody spectral energy distribution
characterized by a temperature T

T (K)  R(12,25)  R(25,60)  R(60,100)  K(12)  K(25)  K(60)  K(100 micron)
------------------------------------------------------------------------
10000   4.345     6.050     3.350     1.45   1.41   1.32   1.09
 5000   4.172     5.931     3.327     1.43   1.40   1.32   1.09
 4000   4.086     5.872     3.316     1.42   1.40   1.31   1.09
 3000   3.944     5.773     3.297     1.41   1.39   1.31   1.09
 2000   3.666     5.578     3.259     1.38   1.38   1.31   1.09
 1000   2.891     5.005     3.145     1.27   1.34   1.29   1.08
  800   2.545     4.730     3.088     1.22   1.32   1.28   1.08
  600   2.036     4.287     2.995     1.15   1.29   1.27   1.08
  500   1.692     3.950     2.920     1.09   1.26   1.26   1.08
  400   1.272     3.478     2.810     1.01   1.22   1.24   1.08
  300   0.785     2.780     2.630     0.92   1.15   1.21   1.07
  290   0.734     2.693     2.606     0.91   1.15   1.21   1.07
  280   0.684     2.602     2.580     0.90   1.14   1.20   1.07
  270   0.633     2.506     2.553     0.89   1.13   1.20   1.07
  260   0.583     2.407     2.523     0.88   1.12   1.19   1.07
  250   0.534     2.304     2.491     0.87   1.11   1.19   1.07
  240   0.486     2.196     2.457     0.86   1.09   1.18   1.07
  230   0.438     2.084     2.420     0.85   1.08   1.18   1.07
  220   0.392     1.967     2.381     0.85   1.07   1.17   1.07
  210   0.347     1.845     2.338     0.84   1.06   1.16   1.06
  200   0.304     1.719     2.291     0.83   1.04   1.16   1.06
  190   0.263     1.589     2.240     0.83   1.02   1.15   1.06
  180   0.224     1.455     2.184     0.83   1.01   1.14   1.06
  170   0.188     1.317     2.124     0.83   0.99   1.13   1.06
  160   0.154     1.176     2.057     0.84   0.97   1.12   1.06
  150   0.124     1.034     1.983     0.85   0.95   1.11   1.05
  140   0.097     0.892     1.901     0.87   0.93   1.09   1.05
  130   0.073     0.751     1.810     0.90   0.91   1.08   1.05
  120   0.053     0.614     1.709     0.94   0.89   1.06   1.04
  110   0.036     0.484     1.595     1.01   0.86   1.04   1.04
  100   0.023     0.363     1.468     1.12   0.84   1.02   1.04
   95   0.018     0.307     1.400     1.19   0.83   1.01   1.03
   90   0.014     0.256     1.326     1.28   0.83   1.00   1.03
   85   0.010     0.208     1.249     1.39   0.82   0.99   1.03
   80   0.007     0.165     1.168     1.54   0.81   0.97   1.02
   75   0.005     0.127     1.082     1.74   0.81   0.96   1.02
   70   0.003     0.095     0.993     2.01   0.81   0.95   1.01
   65   0.002     0.067     0.898     2.40   0.82   0.94   1.01
   60   0.001     0.045     0.801     2.97   0.83   0.93   1.00
   55   ----      0.028     0.700     3.86   0.86   0.92   1.00
   50   ----      0.016     0.597     5.25   0.90   0.91   0.99
   45   ----      0.008     0.493     8.09   0.97   0.92   0.98
   40   ----      0.003     0.391    13.79   1.08   0.93   0.98