Core-powered mass-loss and the radius distribution of small exoplanets

Recent observations identify a valley in the radius distribution of small exoplanets, with planets in the range 1.5-2.0 R_⊕ significantly less common than somewhat smaller or larger planets. This valley may suggest a bimodal population of rocky planets that are either engulfed by massive gas envelopes that significantly enlarge their radius, or do not have detectable atmospheres at all. One explanation of such a bimodal distribution is atmospheric erosion by high-energy stellar photons. We investigate an alternative mechanism: the luminosity of the cooling rocky core, which can completely erode light envelopes while preserving heavy ones, produces a deficit of intermediate sized planets. We evolve planetary populations that are derived from observations using a simple analytical prescription, accounting self-consistently for envelope accretion, cooling and mass-loss, and demonstrate that core-powered mass-loss naturally reproduces the observed radius distribution, regardless of the high-energy incident flux. Observations of planets around different stellar types may distinguish between photoevaporation, which is powered by the high-energy tail of the stellar radiation, and core-powered mass-loss, which depends on the bolometric flux through the planet's equilibrium temperature that sets both its cooling and mass-loss rates.