Signatures of the core-powered mass-loss mechanism in the exoplanet population: dependence on stellar properties and observational predictions

ABSTRACT 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 dlog Rp/dlog M* ≃ 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 dlog Rp/dlog M* ≃ (3α − 2)/36 ≃ 0.33, where (L*/L⊙) = (M*/M⊙)α is the stellar mass–luminosity relation and α ≃ 4.6 for the CKS data set. We therefore find, in contrast to photoevaporation models, no evidence for a linear correlation between planet and stellar mass, but cannot rule it out either. In addition, we show that the location of the radius valley is, to first order, independent of stellar age and metallicity. Since core-powered mass-loss proceeds over Gyr time-scales, the abundance of super-Earths relative to sub-Neptunes increases with age but decreases with stellar metallicity. Finally, due to the dependence of the envelope’s cooling time-scale on metallicity, we find that the radii of sub-Neptunes increase with metallicity and decrease with age with slopes given by dlog Rp/dlog Z* ≃ 0.1 and dlog Rp/dlog τ* ≃ −0.1, respectively. We conclude with a series of observational tests that can differentiate between core-powered mass-loss and photoevaporation models.