Nebular Gas Drag and Planetary Accretion

Abstract

We have studied the orbital dynamics of planetesimals whose decay due to gas drag in the primordial solar nebula causes them to spiral sunward and approach a growing planet. The planet is assumed to be on a circular orbit unaffected by gas drag. Particles (planetesimals) originate in circular orbits external to the planet's orbit and are usually coplanar with it. The trajectories of these particles are studied using three-body numerical simulations. Trapping of particles at mean motion resonances with the planet sets a maximum size on the particles which can reach the planet's orbit (Weidenschilling and Davis 1985, Icarus 62, 16-29). We find that the stability of resonance locks depends on a variety of factors, including the strength of the resonance in question, the proximity of other resonances and in some cases a period-doubling transition to chaos as the drag rate is increased.When the particles are small enough to pass through all of the resonances and approach the planet, we find that for realistic solid planet densities only a small fraction (typically 10 to 40%) of the material not trapped in resonances hits the planet. The remainder is transferred into inferior orbits. A planet with a dense extended atmosphere capable of trapping planetesimals may be able to accrete a much larger fraction of the approaching planetesimals. At large orbital decay rates, the impact probability varies as the inverse of the drag parameter. For particles whose vertical motions relative to the plane of the planet's orbit are large compared to the planet's radius, the impact probability varies inversely with the inclination of the particle's orbit.The axial rotation induced by those particles which hit the planet is dependent on the rate of orbital decay. Particles with low orbital decay rates (i.e., the particle semimajor axes evolve by less than a planetary Hill sphere radius in a synodic period when they are 23 Hill spheres from the planet's orbit) produce prograde rotation, as expected for particles accreted from the edge of the planet's accretion zone (Lissauer and Kary 1991, Icarus 94, 126-159). Particles whose orbits decay rapidly produce retrograde rotation, since these particles can approach the planet from anywhere in the accretion zone, and their eccentricities are damped down to near zero on a synodic time scale.