The radius distribution of small, close-in exoplanets has recently been shown to be bimodal. The photoevaporation model predicted this bimodality. In the photoevaporation scenario, some planets are completely stripped of their primordial H/He atmospheres, whereas others retain them. Comparisons between the photoevaporation model and observed planetary populations have the power to unveil details of the planet population inaccessible by standard observations, such as the core mass distribution and core composition. In this work, we present a hierarchical inference analysis on the distribution of close-in exoplanets using forward-models of photoevaporation evolution. We use this model to constrain the planetary distributions for core composition, core mass and initial atmospheric mass fraction. We find that the core-mass distribution is peaked, with a peak-mass of ∼4 M⊕. The bulk core-composition is consistent with a rock/iron mixture that is ice-poor and “Earth-like”; the spread in core-composition is found to be narrow ($\lesssim 16\%$ variation in iron-mass fraction at the 2σ level) and consistent with zero. This result favours core formation in a water/ice poor environment. We find the majority of planets accreted a H/He envelope with a typical mass fraction of $\sim 4\%$; only a small fraction did not accrete large amounts of H/He and were “born-rocky”. We find four-times as many super-Earths were formed through photoevaporation, as formed without a large H/He atmosphere. Finally, we find core-accretion theory over-predicts the amount of H/He cores would have accreted by a factor of ∼5, pointing to additional mass-loss mechanisms (e.g. “boil-off”) or modifications to core-accretion theory.

In 2017, the California-Kepler Survey (CKS) published its first data release (DR1) of high-resolution optical spectra of 1305 planet hosts. Refined CKS planet radii revealed that small planets are bifurcated into two distinct populations, super-Earths (smaller than 1.5 R ⊕) and sub-Neptunes (between 2.0 and 4.0 R ⊕), with few planets in between (the “radius gap”). Several theoretical models of the radius gap predict variation with stellar mass, but testing these predictions is challenging with CKS DR1 due to its limited M ⋆ range of 0.8–1.4 M ⊙. Here we present CKS DR2 with 411 additional spectra and derived properties focusing on stars of 0.5–0.8 M ⊙. We found that the radius gap follows R p ∝ P m with m = −0.10 ± 0.03, consistent with predictions of X-ray and ultraviolet- and core-powered mass-loss mechanisms. We found no evidence that m varies with M ⋆. We observed a correlation between the average sub-Neptune size and M ⋆. Over 0.5–1.4 M ⊙, the average sub-Neptune grows from 2.1 to 2.6 R ⊕, following R p ∝ M ⋆ α with α = 0.25 ± 0.03. In contrast, there is no detectable change for super-Earths. These M ⋆–R p trends suggest that protoplanetary disks can efficiently produce cores up to a threshold mass of M c , which grows linearly with stellar mass according to M c ≈ 10 M ⊕(M ⋆/M ⊙). There is no significant correlation between sub-Neptune size and stellar metallicity (over −0.5 to +0.5 dex), suggesting a weak relationship between planet envelope opacity and stellar metallicity. Finally, there is no significant variation in sub-Neptune size with stellar age (over 1–10 Gyr), which suggests that the majority of envelope contraction concludes after ∼1 Gyr.

The EUV/X-ray photoevaporation and core-powered mass-loss models are both capable of reproducing the bimodality in the sizes of small, close-in exoplanets observed by the Kepler space mission, often referred to as the ‘radius gap’. However, it is unclear which of these two mechanisms dominates the atmospheric mass-loss which is likely sculpting the radius gap. In this work, we propose a new method of differentiating between the two models, which relies on analysing the radius gap in 3D parameter space. Using models for both mechanisms, and by performing synthetic transit surveys we predict the size and characteristics of a survey capable of discriminating between the two models. We find that a survey of ≳ 5000 planets, with a wide range in stellar mass and measurement uncertainties at a $\lesssim 5{{\ \rm per\ cent}}$ level is sufficient. Our methodology is robust against moderate false positive contamination of $\lesssim 10{{\ \rm per\ cent}}$. We perform our analysis on two surveys (which do not satisfy our requirements): the California Kepler Survey and the Gaia-Kepler Survey and find, unsurprisingly, that both data-sets are consistent with either model. We propose a hypothesis test to be performed on future surveys which can robustly ascertain which of the two mechanisms formed the radius gap, provided one dominates over the other.

The population of small, close-in exoplanets is bifurcated into super-Earths and sub-Neptunes. We calculate physically motivated mass–radius relations for sub-Neptunes, with rocky cores and H/He-dominated atmospheres, accounting for their thermal evolution, irradiation, and mass loss. For planets ≲10 M ⊕, we find that sub-Neptunes retain atmospheric mass fractions that scale with planet mass and show that the resulting mass–radius relations are degenerate with results for “water worlds” consisting of a 1:1 silicate-to-ice composition ratio. We further demonstrate that our derived mass–radius relation is in excellent agreement with the observed exoplanet population orbiting M dwarfs and that planet mass and radii alone are insufficient to determine the composition of some sub-Neptunes. Finally, we highlight that current exoplanet demographics show an increase in the ratio of super-Earths to sub-Neptunes with both stellar mass (and therefore luminosity) and age, which are both indicative of thermally driven atmospheric escape processes. Therefore, such processes should not be ignored when making compositional inferences in the mass–radius diagram.

<p>Recent Kepler data has shown that the radius distribution of small, close-in exoplanets is bimodal. Such bimodality was expected from photoevaporation models of close-in super-Earths, where some planets are stripped of their primordial H/He atmospheres, whilst others retain them. We present a hierarchical inference model on the distribution of Kepler planets using the photoevaporation evolution model. This approach is used to place key constraints on the planetary distributions for core composition, core mass and initial envelope mass-fraction, as well as test other models of planet evolution such as core-powered mass-loss. This new information has interesting implications on planet formation models and also hints at additional atmopsheric mass-loss mechanisms.</p>