VI.C.2.b Asteroid Calibration

IRAS Explanatory Supplement
VI. Flux Reconstruction and Calibration
C. Absolute Calibration
C.2 Point Source Calibration

C.2.b Asteroid Calibration

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The fluxes from the asteroids Hygiea, Europa and Bamberga were observed on eight occasions using the pointed mode of IRAS. Ten individual crossing of the focal plane were measured for Hygiea and Europa while 20 crossings were recorded for Bamberga. Color temperatures were derived for each observation using the stellar calibration at 25 and 60 µm, and the assumption was then made that these color temperatures would remain unchanged between 60 and 100 µm. The flux at 100 µm was then calculated for each observation from the appropriate blackbody function and the stellar calibration at 60 µm. The average of the predicted 100 µm fluxes for the three asteroids was then adopted as the basis of the 100 µm absolute calibration. The average color temperatures and the ratio of the predicted 100 µm flux to that adopted are given in Table VI.C.4.

The asteroids Hygiea, Europa and Bamberga were selected for the basis of the 100 µm calibration because the analysis of ground based observations (Lebofsky, 1984) indicated that the standard asteroid model was a good fit out to 25 µm and could thus reasonably be expected to fit the longer IRAS wavelengths as well. This expectation was in fact borne out by the IRAS observations.

Several other asteroids were observed with IRAS. These are included in Table VI.C.4 in order to show the dispersion in the method. It should be emphasized that those selected as the basis of the 100 µm calibration were those which a priori fit the "standard asteroid model" described below between 12 and 60 µm.

As a check on the above procedure and the simple assumptions concerning asteroid colors, the observed flux densities for all the asteroids measured already, including the three used in the 60 to 100 µm extrapolation, were compared to calculations based on the "standard asteroid model" of Morrison (1973) and Jones and Morrison (1974). The infrared emissivity of the surface was taken to be 0.9 independent of wavelength and the thermal modeling constant  beta was 0.9; the albedo was taken from the TRIAD file (Zellner, 1979). The temperature distribution on the surface was assumed to follow:

T = Tss cos¼ z

(VI.C.3)

Table VI.C.4 Color Temperatures of Asteroids between 25 and 60 µm

Asteroid Color Temp.1,3
K		 Obs./Pred. Flux2,3
Europa 228 ± 15 0.97 ± 0.12
Bamberga 243 ± 10 1.01 ± 0.15
Hygeia 232 ± 16 1.01 ± 0.13
Eukrate 292 ± 29 1.19 ± 0.12
Egeria 259 ± 19 0.95 ± 0.13
Ceres 234 ± 12 1.13 ± 0.12
Flora 297 ± 40 1.43 ± 0.25
Berberic 301 ± 32 1.52 ± 0.26
Pallas 232 ± 7 1.05 ± 0.08
  1. The color temperature is based on the 25 and 60 µm fluxes
  2. The predicted 100 µm flux is extrapolated from the 60 µm flux density obtained from the stellar calibration and the color temperature.
  3. The uncertainties are the population standard deviations

where Tss is the subsolar point temperature and is the zenith angle of the Sun. The temperature of the dark side was taken to be 0 K; this assumption does not lead to a significant error since mainly the sunlit sides of the asteroids were observed by IRAS.

The asteroid diameters were adjusted for each observation to match the 60 µm stellar calibration exactly, i.e. all ratios of observed/model fluxes at 60 µm are identical to unity. The 100 µm calibration was adjusted such that for the asteroids the mean of the ratio of the observed flux to the model flux was equal to unity. The resultant ratios of observed fluxes to those derived from the model are given in Table VI.C.5.

Ratio of Observed to Model Fluxes of Asteroids
Table VI.C.5
Asteroid Observed/Model Fluxes(1)
25 µm 60 µm(2) 100 µm
Europa 1.026 1.000 1.000
  1.026 1.000 0.965
Hygiea 1.052 1.000 1.005
  1.062 1.000 1.015
Bamberga 1.000 1.000 0.980
  1.000 1.000 1.035
  1.082 1.000 1.015
  1.066 1.000 1.025
Average Asteroid 1.039 1.000 1.000(3)
Population Dispersion ±0.031   ±0.029
  1. Observed 25 and 60 µm fluxes are based on stellar calibration. The model fluxes are based on the standard asteroid model (Morrison, 1973; Jones and Morrison, l974) with the beaming factor = 0.9, emissivity = 0.9, and albedo from the TRIAD file (Zellner, l979).
  2. The asteroid diameter is used to normalize the model flux to the observed flux at 60 µm, i.e. observed/model = 1.000 for each asteroid.
  3. By definition of the calibration procedure, the mean ratio of observed/model = 1.000.
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