Hydrodynamics of Embedded Planets' First Atmospheres. II. A Rapid Recycling of Atmospheric Gas

TL;DR

This study uses 3D hydrodynamical simulations to show that embedded protoplanet atmospheres are rapidly replenished by nebular gas, preventing contraction and influencing planet composition.

Contribution

It extends previous 2D models to 3D, revealing open, dynamic atmospheres with rapid gas exchange, and links replenishment timescales to planetary atmosphere growth limits.

Findings

Atmospheres are open systems with high-latitude inflow and midplane outflow.

Replenishment timescales are shorter than cooling times, halting atmosphere contraction.

Replenishment rate aligns with a modified Bondi accretion rate.

Abstract

Following Paper I we investigate the properties of atmospheres that form around small protoplanets embedded in a protoplanetary disc by conducting hydrodynamical simulations. These are now extended to three dimensions, employing a spherical grid centred on the planet. Compression of gas is shown to reduce rotational motions. Contrasting the 2D case, no clear boundary demarcates bound atmospheric gas from disc material; instead, we find an open system where gas enters the Bondi sphere at high latitudes and leaves through the midplane regions, or, vice versa, when the disc gas rotates sub-Keplerian. The simulations do not converge to a time-independent solution; instead, the atmosphere is characterized by a time-varying velocity field. Of particular interest is the timescale to replenish the atmosphere by nebular gas, $t_\mathrm{replenish}$. It is shown that the replenishment rate, $M_\mathrm{atm}/t_\mathrm{replenish}$, can be understood in terms of a modified Bondi accretion rate, $\sim$$R_\mathrm{Bondi}^2\rho_\mathrm{gas}v_\mathrm{Bondi}$, where $v_\mathrm{Bondi}$ is set by the Keplerian shear or the magnitude of the sub-Keplerian motion of the gas, whichever is larger. In the inner disk, the atmosphere of embedded protoplanets replenishes on a timescale that is shorter than the Kelvin-Helmholtz contraction (or cooling) timescale. As a result, atmospheric gas can no longer contract and the growth of these atmospheres terminates. Future work must confirm whether these findings continue to apply when the (thermodynamical) idealizations employed in this study are relaxed. But if shown to be broadly applicable, replenishment of atmospheric gas provides a natural explanation for the preponderance of gas-rich but rock-dominant planets like super-Earths and mini-Neptunes.