The Growth of Protoplanets via the Accretion of Small Bodies in Disks Perturbed by the Planetary Gravity

TL;DR

This study uses 3D hydrodynamic simulations to analyze how gas flow and atmospheric effects influence the accretion of small bodies onto protoplanets, providing new formulas for collision rates and insights into gas-giant core formation.

Contribution

It introduces a new analytic formula for collision rates considering atmospheric and gas flow effects, improving understanding of protoplanet growth in disks.

Findings

Meter-sized particles have high collision rates due to atmospheric gas drag.

Gas flow significantly affects smaller particles' orbital evolution.

Rapid core formation (~0.005 Myr) at 5 au with high accretion efficiency (~1).

Abstract

Planets grow via the collisional accretion of small bodies in a protoplanetary disk. Such small bodies feel strong gas drag and their orbits are significantly affected by the gas flow and atmospheric structure around the planet. We investigate the gas flow in the protoplanetary disk perturbed by the gravity of the planet by three-dimensional hydrodynamic simulation. We then calculate the orbital evolutions of particles in the gas structure obtained from the hydrodynamic simulation. Based on the orbital calculations, we obtain the collision rate between the planet and centimeter to kilometer sized particles. Our results show that meter-sized or larger particles effectively collide with the planet due to the atmospheric gas drag, which significantly enhances the collision rate. On the other hand, the gas flow plays an important role for smaller particles. Finally, considering the effects of the atmosphere and gas flow, we derive the new analytic formula for the collision rate, which is in good agreement with our simulations. We estimate the growth timescale and accretion efficiency of drifting bodies for the formation of a gas-giant solid core using the formula. We find the accretion of sub-kilometer sized bodies achieve a short growth timescale (~0.005 Myr) and a high accretion efficiency (~1) for the core formation at 5 au in the minimum mass solar nebula model.