RESONANT TRAPPING IN A SELF-GRAVITATING PLANETESIMAL DISK

The effects of collective particle behavior on the trapping strength o f a perturber's mth order outer Lindblad resonance in a planetesimal d isk are examined. We find that if the particle disk supports density w aves, the spiral disk potential generated in response to forcing by th e perturber shields particles from the perturber and may greatly dimin ish the perturber's ability to trap particles undergoing orbit decay v ia aerodynamic drag. The density waves can transport away from the res onance much of the angular momentum deposited in the disk by the pertu rber. If these waves are modestly damped by gas drag and/or particle c ollisions, the energy and angular momentum delivered to particles at r esonance is greatly reduced (relative to the isolated particle treatme nt of resonant trapping commonly employed in the literature) and canno t compensate for the losses the particles suffer due to drag. Hence wa ve propagation, when combined with a moderate degree of wave damping, weakens the perturber's trapping barrier. We describe the range of dis k conditions (i.e., the range of perturber masses and disk particle si zes) for which waves in the planetesimal disk propagate away from reso nance without return and thus exclude resonant particle trapping. Plan etary embryos formed by runaway accretion in the solar nebula are like ly to satisfy these conditions. However, we also find that wave action weakens the trapping barrier only if the perturber's mass is not too large; for a minimum mass solar nebula at 5 AU, a perturber exceeding similar to 4 Earth masses/m will force a nonlinear wave response which likely damps rapidly to the planetesimal disk in the vicinity of the resonance. This heats the disk and eventually shuts off the waves, res toring the possibility of resonant trapping by embryos this size and l arger. (C) 1995 Academic Press, Inc.