Creating the Radius Gap without Mass Loss

Abstract

The observed exoplanet population features a gap in the radius distribution that separates the smaller super-Earths ( 1.7𝑅 ⊕ ) from the larger sub-Neptunes (∼1.7-4𝑅 ⊕ ). While mass loss theories can explain many of the observed features of this radius valley, it is difficult to reconcile them with a potentially rising population of terrestrials beyond orbital periods of 30 days. We investigate the ability of initial gas accretion to reproduce both the location of the observed radius gap and the existence of long-period terrestrials. We first update the analytic scalings of gas accretion rate accounting for the shrinking of the bound radius by hydrodynamic effects. From the cooling evolution of planetary envelope with realistic opacity and equation of state, we find that the envelope mass fraction depends only weakly with the radius shrinking factor (𝑀 gas /𝑀 core ∝ 𝑓 0.31 𝑅 ). Co-evolving planetary masses and disk structures, focussing on dust-free opacity, we find that gas accretion alone is able to carve out the observed radius gap, with slopes 𝑅 gap ∝ 𝑃 −0.11 and 𝑅 gap ∝ 𝑀 0.24 ★ for top-heavy; and 𝑅 gap ∝ 𝑃 −0.10 and 𝑅 gap ∝ 𝑀 0.21 ★ for bottom-heavy core mass distributions, in good agreement with observations. Our model reconciles the location of the radius gap with the existence of long period terrestrials. The peaks and valleys in the radius distribution were likely set in place primordially while post-formation processes further tune the exoplanetary population. We provide potential observational tests that may be possible with PLATO and Roman Space Telescope.

The Demographics of Kepler's Earths and Super-Earths into the Habitable Zone

“…However, this method may underestimate the occurrence of sub-Earth planets in the size regime where sensitivity is low (Zhu & Dong 2021). Other methods (e.g., the approximate Bayesian approach of Hsu et al 2019) may be more accurate in their predictions of increasing occurrence at smaller sizes, as discussed in Lee et al (2022). As there is not yet a clear consensus for the functional form of this complex size distribution for small close-in planets, we do not adopt any functional dependence on the planet radius outside of what is described below.…”

The K2-3 System Revisited: Testing Photoevaporation and Core-powered Mass Loss with Three Small Planets Spanning the Radius Valley

“…It it not certain how this picture would change for planetary formation in M-dwarf disks. Recent planetary formation work demonstrates that super-Earth-sized planets can indeed be formed at periods >30 days (K2-3b has a period of 44 days), where the influence of photoevaporation and core-powered mass loss is diminished (Lee et al 2022). However, this still does not easily explain the sub-Neptune K2-3b orbiting well interior to K2-3d.…”

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“…Kite & Barnett 2020). Other mechanisms, such as in-situ formation in gas-poor disks, may naturally carve out the current period-radius distribution of small planets (Lee & Connors 2021;Lee et al 2022), and the radii of small planets may evolve much slower than predicted from run-away mass loss models (David et al 2021).…”