Growing planet envelopes in spite of recycling flows

ABSTRACT The hydrodynamic exchange of a protoplanet’s envelope material with the background protoplanetary disc has been proposed as one mechanism to account for the diversity of observed planet envelopes that range in mass fractions from $\sim\!\! 1{{\ \rm per\, cent}}$ for super-Earths to $\sim\!\! 90{{\ \rm per\, cent}}$ for giants. Here, we present 3D radiation-hydrodynamics models of protoplanet envelopes applicable to gas-giant cores at intermediate distances and a subset of close-in super-Earths in hot or low-density discs. We analyse how hydrodynamic mass and energy exchange impact the formation process. Our protoplanet envelope simulations show an exchange of material bringing the outer $\gtrsim\!\! 0.4R_\mathrm{ b}$ envelope to steady state. This exchange provides a continuous source of energy, which acts to increase the observed luminosity beyond that inferred from the binding energy liberated from Kelvin–Helmholtz contraction alone – a finding important for potential protoplanet observations. The inner envelope at $\lesssim\!\! 0.4R_\mathrm{ b}$ remains insulated, however – growing in accordance with 1D quasi-static theory. We incorporate these 3D hydrodynamic effects into an extensible 1D framework with a physically motivated three-layer recycling parametrization. Specializing to the case of Jupiter, recycling produces minimal changes to the growth rate with the planet still entering runaway accretion and becoming a gas giant in $\sim\!\! 1$ Myr. Even in the inner disc (0.1 au), our 1D models suggest that recycling is not so robust and ubiquitous as to stop all cores from becoming giants. At the same time, however, this recycling can delay a runaway phase by an order of magnitude depending on the inner disc conditions and core mass.