Creating the Radius Gap without Mass Loss

Abstract

Abstract The observed exoplanet population features a gap in the radius distribution that separates the smaller super-Earths (≲1.7 Earth radii) from the larger sub-Neptunes (∼1.7–4 Earth radii). While mass-loss theories can explain many of the observed features of this radius valley, it is difficult to reconcile them with the potentially rising population of terrestrials beyond orbital periods of ∼30 days. We investigate the ability of gas accretion during the gas-poor phase of disk evolution to reproduce both the location of the observed radius gap and the existence of long-period terrestrial planets. Updating the analytic scaling relations of gas accretion rate accounting for the shrinking of the bound radius by hydrodynamic effects and deriving a more realistic disk temperature profile, we find that the late-stage gas accretion alone is able to carve out the observed radius gap, with slopes R gap ∝ P −0.096 and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>R</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>gap</mml:mi> </mml:mrow> </mml:msub> <mml:mo>∝</mml:mo> <mml:msubsup> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>⋆</mml:mo> </mml:mrow> <mml:mrow> <mml:mn>0.15</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> for top-heavy; and R gap ∝ P −0.089 and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>R</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>gap</mml:mi> </mml:mrow> </mml:msub> <mml:mo>∝</mml:mo> <mml:msubsup> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>⋆</mml:mo> </mml:mrow> <mml:mrow> <mml:mn>0.22</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> for bottom-heavy core mass distributions, in good agreement with observations. The general morphology of the primordial radius gap is stable against a range of disk gas density and disk accretion rate with the latter affecting mostly the population of large planets (≳3–4 R ⊕ ). The peaks and valleys in the radius distribution were likely set in place primordially while post-formation mass loss further tunes the exoplanetary population. We provide potential observational tests that may be possible with TESS, PLATO, and Roman Space Telescope.

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