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ALLEN (in reply to a question by KenKnight): In the rotation calculation, I assumed Earth to be on the asteroid's equator. If we look pole-on, rotation has no effect. The corrections to infrared diameters are reduced if we do not face their equators. BRECHER: F. C. Gillett of UCSD has communicated to me the results of his independent observations of the three largest asteroids in the infrared, namely that high surface temperatures of 245 to 270 K were obtained. The blackbody temperature in that region of the belt should be ~170 K. What sort of assumptions about albedos, etc., does one have to make to account for such a large discrepancy between expected and observed surface temperature of asteroids? ALLEN: There are two points... first, I do not agree with your calculated temperature and find values around 240 K more appropriate. Secondly, the apparent temperature for a spread of temperatures from subsolar point to limb varies with observing wavelengths, and this effect must be taken into account. ALLEN (in reply to a question by Bender): I use as the basic temperature the subsolar point temperature equivalent to a flat body facing the Sun; the temperature varies across the disk. If an asteroid rotates, the temperature is reduced. ANONYMOUS: I am worried by the low densities implied by the diameter for Ceres. To get densities down to 1.6 g-cm-3 or so you must assume a proportion of ice, and this has important consequences for the stability of Ceres or any body of that size. ALLEN: Do not overinterpret the densities I give; I was a bit hesitant about including them in the slide at all. The figure for Ceres was 1.6, but this varies as the third power of the diameter; when you take into account the uncertainties, it could be anywhere from 0 to 4. SCHUBART (in reply to a request by Chairman Dubin to comment on this paper): The infrared diameters are very valuable because they indicate the sign of possible errors in the diameters measured earlier. GEHRELS (editorial comment added after the conference): Barnard's value for Vesta may need some revision: Using the diameters of Dollfus” and the masses of Schubart" one obtains 5 g-cm-3 for both Ceres and Vesta. Also see the discussion after the diameter paper of Dollfus.” As for the smaller bodies behaving as solid rocks, this may be an incorrect concept. (See the paper by Hapke,” the polarization paper of Dollfus,” and discussion remarks by Anders.”) Of course, one needs a much thicker layer of dust against infrared penetration than for visual light.

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California Institute of Technology

This paper is a brief preliminary report about a program of reconnaissance photometry designed to study the thermal radiation emitted from asteroids. Observations of thermal radiation, and their subsequent interpretation, can provide new knowledge that presently cannot be gained by any other method. The emitted thermal power is by and large that portion of the insolation which is absorbed. Part of the asteroid's emission spectrum can be observed through windows in Earth's atmosphere. With the aid of models for the details of energy transfer at the asteroid's surface, and accurate visual photometry, reliable estimates can be made for some of the important parameters in the models. Of particular interest are Bond albedo, size, emissivity, and thermal inertia.

Infrared observations were made through bandpasses centered at 8.5, 10.5, and 11.6 pum (AA = 0.5,0.5, and 1.0 pm, respectively). The observations were made from July 21, 1969, to July 27, 1970, using the Hale Observatories' 1.52 m telescope at Mt. Wilson. A total of 26 objects was observed: 1 Ceres, 2 Pallas, 3 Juno, 4 Vesta, 5 Astraea, 6 Hebe, 7 Iris, 8 Flora, 9 Metis, 15 Eunomia, 16 Psyche, 18 Melpomene, 19 Fortuna, 20 Massalia, 25 Phocaea, 27 Euterpe, 39 Laetitia, 44 Nysa, 68 Leto, 80 Sappho, 145 Adeona, 163 Erigone, 192 Nausikaa, 313 Chaldaea, 324 Bamberga, and 674 Rachele. Most of the program asteroids were observed through the 11.6 pm bandpass, and bright objects were measured at all three wavelengths. The observational coverage varies from good for the bright objects, which were observed at a number of phase angles, to poor for those asteroids observed only once.

Phase data for 4 Vesta and 7 Iris are shown in figures 1 and 2. Each point represents the weighted nightly mean. The curve in each of these figures is the average using both the 4 Vesta and 7 Iris data. This curve is used to correct all the 11.6 pum thermal emission observations to zero phase angle. For any given angle, the phase variation is a function of the temperature distribution, which in turn is a function of the thermal properties of the asteroidal surface, the orbit, the rotational period, and the aspect geometry. The regions on each side of opposition where the phase angle is large are the two most important critical regions for testing thermal models. Under the proper circumstances, additional

*This paper is contribution no. 2039 of the Division of Geological and Planetary Sciences.

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Figure 1.-Phase data for 4 Vesta. The curve through the 11.6 um data is the phase function used for the reduction of the data presented in figure 3. Errors for some of the data are less than the size of the plotted symbol. Allen's (1970) data for the same opposition have not yet been reduced to the present photometry systems.

critical regions can be provided by aspect differences from one opposition to another.

The ordinate on the phase plots is calibrated by the assumption that o-Bootis has a flux per unit area at Earth of 4.1, 1.8, and 1.2 X 10-15 W-cm-2 per micrometer for 8.5, 10.5, and 11.6 pm, respectively. The accuracy of this calibration is not known. The calibrations currently for use in the 8 to 14 pum region have a range of about 20 percent.

All measurements reported here were made with respect to three new stellar photometry systems that were established from observations obtained concurrently with the asteroid program and using the same equipment (Matson, 1971).

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Figure 2. —Phase data for 7 Iris. Some of the scatter is due to the lightcurve.

The scatter shown by the 7 Iris data is due to the lightcurve variation of that asteroid. In fact, enough data are available to construct a composite lightcurve of the thermal emission at 10.5 p.m. Correlation of these data with the phase of the visible lightcurve will enable one to differentiate between a spotted asteroid and an irregularly shaped object. This can also be accomplished with the infrared data alone by using observations from two bandpasses to obtain the color temperature as a function of the rotational phase angle. For this method the propagation of observational errors is not as favorable as when using the visible and infrared data.

The error bars on the two phase variation plots represent the propagation of all random and nominal errors incurred in transferring the asteroid observation to o-Bootis. The bounds are intended to delimit the region where the probability of the “true value” is two-thirds or greater.

Table I tabulates some simple models that have been used to analyze the same 4 Vesta data. The parameters, as it can be seen, vary as the model is changed. The common assumption of the three models in table I is that each elemental area on the surface radiates like a blackbody. Phase effects, other than for the corrections applied to the observational data, have been ignored. The albedo parameter has been assumed to be independent of wavelength. This parameter is a weighted average over the solar spectrum. The weight is the amount of energy absorbed at each wavelength.

TABLE I.—Simple Models for 4 Vesta

Method of handling Model Model Description temperature T distribution albedo o ius, m Flat disk T = constant 0.13 264 1/4

Smooth, nonrotating T {-yes .085 328

(1 - a)Sl!/4

“Rough,” nonrotating r- o ) | (coso)1/6 .098 306


a = Stefan-Boltzmann constant; p = angle between heliocentric radius vector and local surface normal; and S = solar constant at the asteroid.

The albedos provided by the models are surprisingly low and the corresponding sizes are large compared to disk measurements. The models and the absolute calibration of the photometry have a systematic error of unknown size and it is premature to assume that the albedo anomaly is due to some unexpected property of asteroidal surfaces. Currently, detailed thermal models that take rotation and the direction of the pole into account are being examined. The simple models (table I) err chiefly in their treatment of the infrared phase integral and are used only for a differential comparison of the data. Table I shows that the changes in parameters from model to model are small enough that it is safe to draw some conclusions at this time. For this purpose, the “rough,” nonrotating sphere model is employed because it represents the Moon better than the other two. Normalization to 4 Vesta enables a differential comparison to be made between asteroids. The arbitrary normalization is set at 210 km radius and 0.3 albedo. In this way systematic errors from many diverse sources are mitigated, but other errors are introduced. For example, error from the visible phase integral q for 4 Vesta is introduced if the result is interpreted as the Bond albedo. The 11.6 pm infrared data are corrected to zero phase angle and the visible data, B(1,0), are taken from Gehrels (1970). The resulting model radius and model albedo are plotted in figure 3. The first things to note are the infrared points for 1 Ceres and 2 Pallas. Already they are in reasonable agreement with published data. Part of the difference is the result of the adopted normalization and the model. The asteroids vary in the albedo parameter from about 0.03 for 324 Bamberga to about 0.3 for several objects. 324 Bamberga is extremely dark. Presently it is the darkest member of a group of large, dark asteroids. By contrast, 4 Vesta appears to be unique—the only known large, light-colored asteroid. Objects of comparable albedo are not encountered until the 50 to 90km radius interval is reached. Type I bias is the discrimination against small,

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Figure 3.—Differential comparison of the model parameters for selected asteroids. The error bars are for the infrared photometry only. The errors in albedo and radius are correlated and lie along trajectories defined by B(1,0) = constant. Errors in B(1,0) and the phase correction are not plotted. The lightcurves appear to be responsible for much of the scatter of values for the smaller asteroids. The ordinate for the data from the literature is the Bond albedo, which is approximately equivalent to the normalized model albedo. Data for Icarus is from Gehrels et al. (1970) and Veverka and Liller (1969).

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