On the Slow Rotation of Asteroids

Asteroids with very slow rotation rates, up to 100 times slower than the mean for ordinary asteroids, are clearly a statistically distinct population from the rest. The cause of such slow rotation has remained a mystery since the discovery of the population about 20 years ago. The expected distribution of slow rotations for three-dimensional rotation vectors f→ if uniform near the origin (e.g., a three-dimensional Maxwellian distribution) would be N (<f)∝f3, where f is the rotation frequency (inverse period of rotation) and N (<f) is the cumulative number of asteroids with spin rate less than f. In this paper I show that the statistics of the slow-rotation population as currently known is well fit as a uniform distribution of the one-dimensional parameter f, that is N (<f)∝f. I offer as a possible explanation for slow rotations that they result from disintegration of high mass ratio (∼1:5) binaries through the rapid transfer of rotational energy of the primary into the orbit of the secondary due to the irregular gravity field of the primary. A troubling aspect of this hypothesis is that it would seem to predict a distribution of residual spins of the approximate form N (<f)∝f2, which does not fit the available data.