A primordial radius valley as a consequence of planet formation

¹ Center for Star and Planet Formation, Globe Institute, University of Copenhagen, Øster Voldgade 5–7, 1350 Copenhagen, Denmark
² Lund Observatory, Department of Physics, Lund University, Box 43, 22100 Lund, Sweden
³ Institute for Particle Physics and Astrophysics, ETH Zürich, Otto-Stern-Weg 5, 8093 Zürich, Switzerland

^★ Corresponding author; jesper.nielsen@sund.ku.dk

Received: 11 April 2024
Accepted: 14 February 2025

Abstract

The radius distribution of close-in planets has been observed to have a bimodal distribution, with a dearth of planets around ~1.5–2.0 R_⊕ commonly referred to as the ‘radius valley’. The origin of the valley is normally attributed to mass-loss processes such as photoevaporation or core-powered mass loss. Recent work, however, has suggested that the radius valley may instead arise as a consequence of gas accretion by low-mass planets. Therefore in this work, we aim to investigate the formation of a primordial radius valley from the formation of planet cores through pebble accretion up until the dissipation of the protoplanetary disc and subsequent contraction of accreted atmospheres. The goal of this work is to explore the conditions for forming a primordial radius valley from the first principles of planet formation theory, rather than attempting to explain the detailed structure of the observed valley. We used an analytical model with minimal assumptions to estimate the contraction rate of atmospheres and find the formation of a primordial radius valley. The planets smaller than the valley did not reach the pebble isolation mass, which is required for the planets to cool down sufficiently to be able to accrete a significant amount of gas. We also estimated the slopes of the radius gap as a function of orbital period for the intrinsic population as well as for planets with orbital periods of less than 100 days. For the intrinsic population, the radius gap follows the pebble isolation mass and increases with increasing orbital period, but for close-in planets, the direction of the slope reverses and decreases with increasing orbital period. We find that planets smaller than the radius valley are predominantly rocky, while the population of planets larger than the valley comprises a mixture of rocky and water-rich planets.