Accretion Rates of Planetesimals by Protoplanets Embedded in Nebular Gas

TL;DR

This paper investigates how atmospheres around protoplanets enhance their growth by capturing planetesimals through gas drag, providing numerical and analytical models for accretion rates across various conditions.

Contribution

It introduces a semi-analytical formula for planetesimal accretion rates considering atmospheric gas drag, validated by numerical simulations and applicable to protoplanets of one to ten Earth-masses.

Findings

Gas drag significantly increases accretion rates.

The semi-analytical formula accurately reproduces numerical results.

Atmospheric effects depend on planetesimal size and orbital parameters.

Abstract

When protoplanets growing by accretion of planetesimals have atmospheres, small planetesimals approaching the protoplanets lose their energy by gas drag from the atmospheres, which leads them to be captured within the Hill sphere of the protoplanets. As a result, growth rates of the protoplanets are enhanced. In order to study the effect of an atmosphere on planetary growth rates, we performed numerical integration of orbits of planetesimals for a wide range of orbital elements and obtained the effective accretion rates of planetesimals onto planets that have atmospheres. Numerical results are obtained as a function of planetesimals' eccentricity, inclination, planet's radius, and non-dimensional gas-drag parameters which can be expressed by several physical quantities such as the radius of planetesimals and the mass of the protoplanet. Assuming that the radial distribution of the gas density near the surface can be approximated by a power-law, we performed analytic calculation for the loss of planetesimals' kinetic energy due to gas drag, and confirmed agreement with numerical results. We confirmed that the above approximation of the power-law density distribution is reasonable for accretion rate of protoplanets with one to ten Earth-masses, unless the size of planetesimals is too small. We also calculated the accretion rates of planetesimals averaged over a Rayleigh distribution of eccentricities and inclinations, and derived a semi-analytical formula of accretion rates, which reproduces the numerical results very well. Using the obtained expression of the accretion rate, we examined the growth of protoplanets in nebular gas. We found that the effect of atmospheric gas drag can enhance the growth rate significantly, depending on the size of planetesimals.