Formation of inner planets in the presence of a Cold Jupiter: orbital evolution and relative velocities of planetesimals

Abstract

We investigate the orbital evolution of planetesimals in the inner disk in the presence of nebula gas and a (proto-) cold Jupiter. By varying the mass, eccentricity, and semi-major axis of the planet, we study the dependence of the relative velocities of the planetesimals on these parameters. For classic small planetesimals ($10^{16}-10^{20} $g) whose mutual gravitational interaction is negligible, gas drag introduces a size-dependent alignment of orbits and keeps the relative velocity low for similar-size bodies, while preventing orbital alignment for different-size planetesimals. Regardless of the location and the mass ratio of the planetesimals, increasing the mass and eccentricity or decreasing the orbital distance of the planet always leads to higher relative velocities of planetesimals. However, for massive planetesimals, the interplay of viscous stirring, gas damping, and secular perturbation results in lower velocity dispersion of equal-size planetesimals when the planet is more massive or when it is located on a closer or more eccentric orbit. The random velocities of such planetesimals remain almost unperturbed when the planet is located beyond Jupiter's current orbit, or when it is less massive or less eccentric than Jupiter. Unlike small planetesimals, such large planetesimals can grow in a runaway fashion as in the unperturbed case. Our results imply that the presence of a cold Jupiter does not impede the formation of inner rocky planets through planetesimal accretion, provided that the planetesimals are initially large.