Planetesimal Dynamics in the Presence of a Giant Planet II: Dependence on Planet Mass and Eccentricity

Abstract: The presence of an early-formed giant planet in the protoplanetary disk has mixed influence on the growth of other planetary embryos. Gravitational perturbation from the planet can increase the relative velocities of planetesimals at the mean motion resonances to very high values and impede accretion at those locations. However, gas drag can also align the orbital pericenters of equal-size planetesimals in certain disk locations and make them dynamically quiet and "accretion-friendly" locations for planetesimals of similar sizes. Following the previous paper, where we investigated the effect of a Jupiter-like planet on an external planetesimal disk, we generalize our findings to extrasolar planetary systems by varying the planet parameters. In particular, we focus on the dependence of the planetesimal relative velocities on the mass and eccentricity of the existing planet. We found that the velocity dispersion of identical-mass particles increases monotonically with increasing planet mass. Meanwhile, the dependence of the relative velocity between different-mass planetesimals on their mass ratio becomes weaker as the planet mass increases. While the relative velocities generally increases with increasing planet eccentricity, the velocity dispersion of smaller-mass particles ($m \lesssim 10^{18}~\rm{g}$) is almost independent of planet eccentricity owing to their strong coupling to gas. We find that the erosion limits are met for a wider range of parameters (planet mass/eccentricity, planetesimal mass ratio) when the planetesimal size decreases. Our results could provide some clues for the formation of Saturn's core as well as the architecture of some exoplanetary systems with multiple cold giant planets.