Nebular Gas Drag and Planetary Accretion: II. Planet on an Eccentric Orbit

Abstract

We study the trajectories of planetesimals whose orbits decay starward as a result of gas drag and are perturbed by the gravity of a massive planet on an eccentric orbit. Each planetesimal ultimately suffers one of three possible fates: (1) trapping in a mean motion resonance with the planet, (2) accretion by the planet, or (3) passage by the planet and continued orbital decay. At moderate to large planetary eccentricity, numerical 3-body integrations of the motion of a planetesimal in the solar nebula demonstrate that migrating planetesimals can become trapped in the 1/1 resonance. These bodies initially have large libration amplitudes (approaching 2π) which decay down to 0 at the trailing Lagrange point. With some combinations of drag rate and planetary eccentricity, over 15% of the planetesimals which encounter the planet are trapped in the 1/1 resonance. Bodies trapped in the this way could be the precursors of the Trojan asteroids. Migrating planetesimals can be caught in both pure Lindblad and combined Lindblad/corotation resonances exterior to the planet's orbit. Trapping has been found in several j/( j + k) resonances with k's ranging from 1 to 4. As one considers larger planetary eccentricities, corotation resonances become more important than Lindblad resonances, and (for a given drag rate) trapping can occur at higher k's and farther from the planet. At large planetary eccentricities, planetesimals can also be caught in ( j + 1)/ j Lindblad/corotation resonances interior to the planet. Interior trapping, which is dynamically forbidden in the case of a planet on a circular orbit, requires planetary eccentricity to increase both the planetesimal's semimajor axis and its eccentricity near conjunction to counter gas drag. Provided the planetesimal's and planet's apoapses are roughly aligned, and conjunction occurs while both bodies are approaching apoapse, then the planetesimal can become trapped in an interior resonance. The probability of a planetesimal avoiding accretion while migrating past the planet can be described as the probability of not being accreted in a single conjunction to the power of the number of conjunctions that a planetesimal has with the planet while passing through its feeding zone. In the nongravitating planet limit (which is valid for a low mean density planet on a highly eccentric orbit), the accretion probability increases with planetary eccentricity due to the growth of the planet's feeding zone. When the planet's gravity is considered using the 2+2-body approximation (which is valid for a dense planet on a moderately eccentric orbit), the accretion rate is nearly independent of planetary eccentricity. Numerical simulations show that at small planetary eccentricities, the 2+2-body approximation breaks down, and the accretion probability gradually increases with decreasing eccentricity in this regime.