Tidal disruption of dissipative planetesimals

Tidal disruption is a potentially important process for the accumulation of the planets from planetesimals. The fact that stable equilibria do not exist for circular orbits inside the Roche limit has often been hypothesized to mean that any object that passes within the Roche limit is totally disrupted. We have disproven this hypothesis by solving the dynamic problem of the tidal disruption of a dissipative planetestimal during a close encounter with a protoplanet. The solution consists of a numerical integration of the three-dimensional, nonlinear equations of motion, including an approximate treatment of viscous dissipation in the solid regions of the planetesimal. The numerical methods have been extensively tested on a series of one-, two- (Jeans), and three-(Roche) dimensional test problems involving the equilibrium of a body subjected to tidal forces. The results may be scaled to planetesimals of arbitrary size, providing that the scaled equation of state applied. The calculations show that a strongly dissipative planetesimal which passes by the Earth on a parabolic orbit with a perigee within the Roche limit (≈3R_Earth) is not tidally disrupted (even for grazing incidence), and loses no more than a few percent of its mass. This result applies to bodies of radius R which have a kinematic viscosity ν ? 10¹²(R/1000km)² cm²sec^?1. Less dissipative planetesimals (ν ≈ 10¹³(R/1000 km)² cm²sec^?1) may lose up to about 20% of their mass. There are two coupled reasons why this result differs from previous hypotheses: (1) in a dynamic encounter, there is insufficient time to disrupt the planetesimal, and (2) even in circular orbit, the small velocities in the solid region imply that many orbital periods are necessary to completely disrupt the planetesimal. Hence solid and partially molten planetesimals will not experience substantial tidal disruption; completely molten bodies may be sufficiently inviscid to undergo tidal disruption.