Protoplanets with core masses below the critical mass fill in their Roche lobe

TL;DR

This paper demonstrates that low-mass protoplanets develop atmospheres filling their Roche lobe, challenging traditional models based on Bondi radius and impacting calculations of disc torque effects.

Contribution

It introduces a model showing protoplanets with masses of a few Earth masses have atmospheres extending to their Roche lobe, contrasting with previous Bondi radius-based assumptions.

Findings

Protoplanet atmospheres fill their Roche lobe during rapid accretion.

Atmosphere extension is independent of the Bondi radius in this regime.

Tidal torque calculations should exclude Roche lobe-bound material.

Abstract

We study the evolution of a protoplanet of a few earth masses embedded in a protoplanetary disc. If we assume that the atmosphere of the protoplanet, i.e. the volume of gas in hydrostatic equilibrium bound to the core, has a surface radius smaller than the Roche lobe radius, we show that it expands as it accretes both planetesimals and gas at a fixed rate from the nebula until it fills in the Roche lobe. The evolution occurs on a timescale shorter than the formation or migration timescales. Therefore, we conclude that protoplanets of a few earth masses have an atmosphere that extends to the Roche lobe surface, where it matches to the nebula. This is true even when the Bondi radius is smaller than the Roche lobe radius. This is in contrast to the commonly used models in which the static atmosphere extends up to the Bondi radius and is surrounded by a cold accretion flow. As a result, any calculation of the tidal torque exerted by the disc onto the protoplanet should exclude the material present in the Roche lobe, since it is bound to the protoplanet.