Tidal disruption of inviscid planetesimals

Abstract

A planetesimal passing within the Roche limit of a more massive body is subject to tidal forces that could result in disruption of the planetesimal into a spray of debris. The possible occurence of tidal disruption is of considerable importance for planetary accumulation in general and for the origin of the Moon in particular. Previous work has shown that strongly dissipative planetesimals are immune to tidal disruption. We have now examined the effects of tidal forces in the other extreme case, inviscid planetesimals that might arise from collisions energetic enough to result in total melting of the resultant planetesimal and debris. First, a simple analytical calculation implies that massive planetesimals avoid tidal disruption, with the critical mass for disruption being roughly a lunar mass. Second, in order to relax the assumptions inherent in this analysis, we have numerically simulated tidal disruption with the smoothed particle hydrodynamics (SPH) code previously used by two of us to model impacts between protoplanets. SPH models by Cameron and Benz (1991) show that relatively massive (Marssized), inviscid protoplanets do not undergo complete tidal disruption, even in near-grazing incidence collisions. Hence we have concentrated on studying tidal disruption of 0.01 M⦶ planetesimals passing by the Earth with variations in the impact parameter at perigee ( r p ) and velocity at infinity ( ν ∞). Even for these relatively small bodies, significant tidal disruption requires r p < 1.5R ⦶ and ν ∞ < 2 kmsec −1 . The SPH models also show that tidal forces during a close encounter efficiently convert orbital angular momentum into spin angular momentum, initiating equatorial mass-shedding in inviscid planetesimals that have been spun up beyond the limit of rotational stability. This rotational disruption occurred for 1.5R ⦶ < r p < 1.9R ⦶ when ν ∞ = 2 km sec −1 but not at all for ν ∞ = 0, implying that rotational disruption may be more important than purely tidal disruption for planetary accumulation. Neither disruption process leads to capture of sufficient material in Earth orbit to permit lunar formation from the debris of a single encounter.