A Statistical Mechanics Model for Stable Rings Outside the Roche Limit

Abstract

Stellar occultations have revealed two rings around the dwarf planet Quaoar outside the Roche limit. Simulations suggest that the rings are sustained by large velocity dispersions. We present the first analytical, first-principles theory that extends the Roche limit to describe planetary rings with large velocity dispersion. The underlying principle is an analogy between a liquid/gas phase transition and the moon/ring transition: just as high temperatures can boil a liquid under pressure, high velocity dispersions can stabilize ring systems beyond the Roche limit. We employ statistical mechanics to derive a modification to the Roche limit that treats rings with nonzero velocity dispersion. We demonstrate the new model's consistency with previous simulations of Quaoar's outermost ring. We also note that dense regions of the ring experience negative pressure, which would cause them to shrink over time if the assumptions of the model continue to hold. This could help explain the rings' azimuthal asymmetry.