Planetary Growth with Collisional Fragmentation and Gas Drag

TL;DR

This paper develops analytical models and simulations to understand how collisional fragmentation and gas drag influence planetary embryo growth, highlighting challenges and conditions for forming gas giant cores within the protoplanetary disk.

Contribution

It introduces analytical formulae for final embryo masses considering planetesimal depletion and validates them with statistical simulations, advancing understanding of planetary formation processes.

Findings

Final embryo mass at several AU can reach ~0.1 Earth mass in 10^7 years.

More massive disks and larger initial planetesimals can produce embryos of ~10 Earth masses.

Atmospheric enhancement could enable formation of gas giant cores at 5-10 AU.

Abstract

As planetary embryos grow, gravitational stirring of planetesimals by embryos strongly enhances random velocities of planetesimals and makes collisions between planetesimals destructive. The resulting fragments are ground down by successive collisions. Eventually the smallest fragments are removed by the inward drift due to gas drag. Therefore, the collisional disruption depletes the planetesimal disk and inhibits embryo growth. We provide analytical formulae for the final masses of planetary embryos, taking into account planetesimal depletion due to collisional disruption. Furthermore, we perform the statistical simulations for embryo growth (which excellently reproduce results of direct $N$-body simulations if disruption is neglected). These analytical formulae are consistent with the outcome of our statistical simulations. Our results indicate that the final embryo mass at several AU in the minimum-mass solar nebula can reach about $\sim 0.1$ Earth mass within $10^7$ years. This brings another difficulty in formation of gas giant planets, which requires cores with $\sim 10$ Earth masses for gas accretion. However, if the nebular disk is 10 times more massive than the minimum-mass solar nebula and the initial planetesimal size is larger than 100 km, as suggested by some models of planetesimal formation, the final embryo mass reaches about 10 Earth masses at 3-4 AU. The enhancement of embryos' collisional cross sections by their atmosphere could further increase their final mass to form gas giant planets at 5-10 AU in the solar system.