How planets grow by pebble accretion

V. Silicate rainout delays the contraction of sub-Neptunes

¹ Astrophysics Research Center (ARCO), Department of Natural Sciences, The Open University of Israel, Raanana 4353701, Israel
e-mail: vazan@openu.ac.il
² Department of Astronomy, Tsinghua University, 30 Shuangqing Rd, 100084 Beijing, PR China
³ Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK

Received: 31 December 2023
Accepted: 16 May 2024

Abstract

The characterization of super-Earth- to Neptune-sized exoplanets relies heavily on our understanding of their formation and evolution. In this study, we link a model of planet formation by pebble accretion to the planets’ long-term observational properties by calculating the interior evolution, starting from the dissipation of the protoplanetary disk. We investigate the evolution of the interior structure in 5–20 M_⊕ planets, accounting for silicate redistribution caused by convective mixing, rainout (condensation and settling), and mass loss. Specifically, we have followed the fate of the hot silicate vapor that remained in the planet’s envelope after planet formation as the planet cools. We find that disk dissipation is followed by a rapid contraction of the envelope from the Hill or Bondi radius to about one-tenth of that size within 10 Myr. Subsequent cooling leads to substantial growth of the planetary core through silicate rainout accompanied by inflated radii, in comparison to the standard models of planets that formed with core-envelope structure. We examined the dependence of rainout on the planet’s envelope mass, on the distance from its host star, on its silicate mass, and on the atmospheric opacity. We find that the population of planets that formed with polluted envelopes can be roughly divided into three groups based on the mass of their gas envelopes: bare rocky cores that have shed their envelopes, super-Earth planets with a core-envelope structure, and Neptune-like planets with diluted cores that undergo gradual rainout. For polluted planets that formed with envelope masses below 0.4 M_⊕, we anticipate that the inflation of the planet’s radius caused by rainout will enhance the mass loss by a factor of 2–8 compared to planets with unpolluted envelopes. Our model bridges the gap between the predicted composition gradients in massive planets and the core-envelope structure in smaller planets.