Harris A. W. (1), Wisniewski W.Z.(2)(deceased)

(1) Jet Propulsion Laboratory, Caltech, Pasadena, CA 91109 USA,
(2) University of Arizona, Tucson, AZ 85721 USA

The application of CCD photometry to monitoring the light variations of very small asteroids has led to an explosion of data available, and perhaps as importantly, has made it possible to probe fainter, and hence smaller asteroids. In this paper, we review several new results from the analysis of such lightcurve data, much of it taken by the late W. Z. Wisniewski, a native of Poland who studied at Poznan University.

At the time of the last close pass of the asteroid 4179 Toutatis by the Earth in 1992, it became apparent from radar observations that the asteroid was in a bizarre rotation state, and that the rotation rate was extremely slow. A re-evaluation of a work by Burns and Safronov (MNRAS 165, 403, 1973) indicated that very small and slowly rotating asteroids can have a time scale of damping into a principal-axis rotation state which is long compared to their expected collisional lifetime, or for that matter, the age of the solar system, thus such a small, slowly spinning body might be expected to be in an undamped, or ''tumbling'' rotation state. Lightcurve observations confirmed that Toutatis is indeed in such a rotation state. Lightcurve observations of several other small Earth-approaching asteroids indicate that they too are in ''tumbling'' rotation states. Perhaps most interesting among these is the asteroid 253 Mathilde, which is a flyby target of the Near-Earth Asteroid Rendezvous (NEAR) space mission. As yet, we have no understanding of why some asteroids have such very slow spins (with rotation periods of many days or even weeks). Perhaps the NEAR flyby may reveal some clue.

At the other end of the rotation rate spectrum are some small asteroids which are spinning so rapidly that they are nearly in a state of tension, with centrifugal acceleration at the equator nearly equal to the self-gravitational acceleration. We have recently re-analyzed the distribution of spin rates of small (<10 km diameter) asteroids. With the benefit of the larger data set now available, it appears that the distribution of spins is truncated, rather than smoothly decreasing to zero (population) with decreasing spin period, with the threshold being at a period of ~2 1/4 hours. This suggests that indeed the spin rate of asteroids is limited by the rate at which the body would become in a state of tension, which in turn implies that even such small asteroids are not monolithic bodies. Furthermore, the threshold spin rate implies that the bulk density of these asteroids is ~2.5 g/cm&179;, which corresponds to significant porosity for silicate rock. Thus we infer that most small asteroids are ''rubble piles'', rather than single rocky bodies.

A third investigation which has resulted from observations by Wisniewski does not involve rotations, but rather the population of near-Earth asteroids. Wisniewski obtained photometric observations of many asteroids recently discovered by photographic methods, as well as by his colleagues using the Spacewatch Camera with a CCD detector. In comparing the carefully calibrated magnitudes observed by Wisniewski with the discovery estimates, we find that the magnitudes from photographs are underestimated by an average of 0.8 magnitudes, while the Spacewatch magnitudes are quite accurate. We suggest that this has led to a bias in the NEA population statistics. The very largest NEAs (>3 km) have for the most part been re-observed by photometric techniques, so magnitudes used to estimate populations have been corrected from their discovery reports. The very smallest asteroids (<0.3 km) have mostly been discovered by Spacewatch, thus again the magnitudes are correct. In the mid range, however, most discoveries have been made by photography and have not been re-observed with electronic detectors, so many of the magnitudes still contain the average bias mentioned above. This leads to an over-estimation in the size range 3 >D>0.3 km. In comparing with published population curves of NEAs, we find a ''bump'' in exactly this range, and thus suggest that it is an artifact of the observational bias which we have found.