Recent observations revealed a bimodal radius distribution of small, short-period exoplanets with a paucity in their occurrence, a radius 'valley', around 1.5−2.0 R ⊕ . In this work, we investigate the effect of a planet's own cooling luminosity on its thermal evolution and atmospheric mass-loss (core-powered mass-loss) and determine its observational consequences for the radius distribution of small, close-in exoplanets. Using simple analytical descriptions and numerical simulations, we demonstrate that planetary evolution based on the core-powered mass-loss mechanism alone (i.e., without any photoevaporation) can produce the observed valley in the radius distribution. Our results match the valley's location, shape and slope in planet radius-orbital period parameter space, and the relative magnitudes of the planet occurrence rate above and below the valley. We find that the slope of the valley is, to first order, dictated by the atmospheric mass-loss timescale at the Bondi radius and given by d logR p /d logP 1/ (3(1 − β)) which evaluates to −0.11 for β 4, where M c /M ⊕ = (R c /R ⊕ ) β (ρ c * /ρ ⊕ ) β/3 is the massradius relation of the core. This choice for β yields good agreement with observations and attests to the significance of internal compression for massive planetary cores. We further find that the location of the valley scales as ρ −4/9 c * and that the observed planet population must have predominantly rocky cores with typical water-ice fractions of less than ∼ 20%. Furthermore, we show that the relative magnitude of the planet occurrence rate above and below the valley is sensitive to the details of the planet-mass distribution but that the location of the valley is not.

Recent studies have shown that atmospheric mass-loss powered by the cooling luminosity of a planet's core can explain the observed radius valley separating super-Earths and sub-Neptunes, even without photoevaporation. In this work, we investigate the dependence of this core-powered mass-loss mechanism on stellar mass (M * ), metallicity (Z * ) and age (τ * ). Without making any changes to the underlying planet population, we find that the core-powered mass-loss model yields a shift in the radius valley to larger planet sizes around more massive stars with a slope given by d logR p /d logM * 0.35, in agreement with observations. To first order, this slope is driven by the dependence of core-powered mass-loss on the bolometric luminosity of the host star and is given by d logR p /d logM * (3α − 2)/36 0.36, where (L * /L ) = (M * /M ) α is the stellar mass-luminosity relation and α 5 for the CKS dataset. We therefore find, contrary to photoevaporation models, no evidence for a correlation between planet and stellar mass. In addition, we show that the location of the radius valley is, to first order, independent of stellar age and metallicity. In contrast, assuming that the atmospheric opacity scales linearly with stellar metallicity, we determine that that the size of sub-Neptune population increases with metallicity and decreases with age with a slope given by d logR p /d logZ * 0.1 and d logR p /d logτ * −0.1, respectively. This implies that the abundance of super-Earths relative to sub-Neptunes increases with age but decreases with stellar metallicity. We conclude with a series of observational tests that can differentiate between core-powered mass-loss and photoevaporation models.

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.