Recycling of the first atmospheres of embedded planets: Dependence on core mass and optical depth

¹ Institut für Astronomie und Astrophysik, Universität Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany
e-mail: tobias.moldenhauer@uni-tuebingen.de
² Zentrum für Astronomie der Universität Heidelberg, Institut für Theoretische Astrophysik, Albert-Ueberle-Straße 2, 69120 Heidelberg, Germany
³ Department of Astronomy, Tsinghua University, 30 Shuangqing Rd, 100080 Haidian District, Beijing, PR China

Received: 4 August 2021
Accepted: 7 February 2022

Abstract

Context. Recent observations found close-in planets with significant atmospheres of hydrogen and helium in great abundance. These are the so-called super-Earths and mini-Neptunes. Their atmospheric composition suggests that they formed early during the gas-rich phase of the circumstellar disk and were able to avoid becoming hot Jupiters. As a possible explanation, recent studies explored the recycling hypothesis and showed that atmosphere-disk recycling is able to fully compensate for radiative cooling and thereby halt Kelvin-Helmholtz contraction to prevent runaway gas accretion.

Aims. To understand the parameters that determine the efficiency of atmospheric recycling, we extend our earlier studies by exploring the effects of the core mass, the effect of circumstellar gas on sub-Keplerian orbits (headwind), and the optical depth of the surrounding gas on the recycling timescale. Additionally, we analyze their effects on the size and mass of the forming atmosphere.

Methods. We used three-dimensional (3D) radiation-hydrodynamic simulations to model a local shearing box centered on the planet. Our planet is located at a separation of a_p = 0.1 au from its solar-type host star, and we scanned the core mass range from 1 to 10 M_Earth. In order to measure and track the recycling of the atmosphere, we employed tracer particles as well as tracer fluids after thermodynamic equilibrium was reached.

Results. For the explored parameter space, all simulations eventually reach an equilibrium where heating due to hydrodynamic recycling fully compensates radiative cooling. In this equilibrium, the atmosphere-to-core mass ratio stays well below 10%, preventing the atmosphere from becoming self-gravitating and entering runaway gas accretion. Higher core masses cause the atmosphere to become turbulent, which further enhances recycling. Compared to the core mass, the effect of the headwind on the recycling timescale is negligible. The opacity has no significant effect on the recycling timescale, which demonstrates that the Kelvin-Helmholtz contraction timescale and the atmosphere-disk recycling timescale are independent of each other.

Conclusions. Even for our highest core mass of 10 M_Earth, atmosphere-disk recycling is efficient enough to fully compensate for radiative cooling and prevent the atmosphere from becoming self-gravitating. Hence, in-situ formation of hot Jupiters is very unlikely, and migration of gas giants is a key process required to explain their existence. Our findings imply that atmosphere-disk recycling is the most natural explanation for the prevalence of close-in super-Earths and mini-Neptunes.