Eccentricity Evolution Through Accretion of Protoplanets

TL;DR

This study uses N-body simulations to show that collision damping during in situ protoplanet accretion leads to super-Earths with smaller eccentricities and aligned orbital planes, matching observations from Kepler and RV surveys.

Contribution

It provides detailed insights into eccentricity and inclination damping mechanisms during in situ protoplanet accretion, a topic not thoroughly studied before.

Findings

Merged planets have smaller eccentricities than escape eccentricities due to collision damping.

Orbital inclinations are also damped, leading to shared orbital planes.

The model reproduces observed eccentricity and inclination distributions of super-Earths.

Abstract

Most of super-Earths detected by the radial velocity (RV) method have significantly smaller eccentricities than the eccentricities corresponding to velocity dispersion equal to their surface escape velocity ("escape eccentricities"). If orbital instability followed by giant impacts among protoplanets that have migrated from outer region is considered, it is usually considered that eccentricities of the merged bodies become comparable to those of orbital crossing bodies, which are excited up to their escape eccentricities by close scattering. However, the eccentricity evolution in the {\it in situ} accretion model has not been studied in detail. Here, we investigate the eccentricity evolution through {\it N}-body simulations. We have found that the merged planets tend to have much smaller eccentricities than the escape eccentricities due to very efficient collision damping. If the protoplanet orbits are initially well separated and their eccentricities are securely increased, an inner protoplanet collides at its apocenter with an outer protoplanet at its pericenter. The eccentricity of the merged body is the smallest for such configuration. Orbital inclinations are also damped by this mechanism and planets tend to share a same orbital plane, which is consistent with {\it Kepler} data. Such efficient collision damping is not found when we start calculations from densely packed orbits of the protoplanets. If the protoplanets are initially in the mean-motion resonances, which corresponds to well separated orbits, the {\it in situ} accretion model well reproduces the features of eccentricities and inclinations of multiple super-Earths/Earth systems discovered by RV and {\it Kepler} surveys.