Aeronomical constraints to the minimum mass and maximum radius of hot low-mass planets

Abstract

Stimulated by the discovery of a number of close-in low-density planets, we generalise the Jeans escape parameter taking hydrodynamic and Roche lobe effects into account. We furthermore define Λ as the value of the Jeans escape parameter calculated at the observed planetary radius and mass for the planet's equilibrium temperature and considering atomic hydrogen, independently of the atmospheric temperature profile.We consider 5 and 10 M⊕ planets with an equilibrium temperature of 500 and 1000 K, orbiting early G-, K-, and M-type stars. Assuming a clear atmosphere and by comparing escape rates obtained from the energy-limited formula, which only accounts for the heating induced by the absorption of the high-energy stellar radiation, and from a hydrodynamic atmosphere code, which also accounts for the bolometric heating, we find that planets whose Λ is smaller than 15-35 lie in the "boil-off" regime, where the escape is driven by the atmospheric thermal energy and low planetary gravity. We find that the atmosphere of hot (i.e. Teq ≥ 1000 K) low-mass (Mpl / 5 M⊕) planets with Λ < 15-35 shrinks to smaller radii so that their Λ evolves to values higher than 15-35, hence out of the boil-off regime, in less than ∼500 Myr. Because of their small Roche lobe radius, we find the same result also for hot (i.e. Teq ≥ 1000 K) higher mass (Mpl / 10 M⊕) planets with Λ < 15-35, when they orbit M-dwarfs. For old, hydrogen-dominated planets in this range of parameters, Λ should therefore be ≥15-35, which provides a strong constraint on the planetary minimum mass and maximum radius and can be used to predict the presence of aerosols and/or constrain planetary masses, for example.