The Nature of the Radius Valley: Hints from Formation and Evolution Models

Abstract

The existence of a Radius Valley in the Kepler size distribution stands as one of the most important observational constraints to understand the origin and composition of exoplanets with radii between that of Earth and Neptune. The goal of this work is to provide insights into the existence of the Radius Valley from, first, a pure formation point of view, and second, a combined formation-evolution model. We run global planet formation simulations including the evolution of dust by coagulation, drift and fragmentation; and the evolution of the gaseous disc by viscous accretion and photoevaporation. A planet grows from a moon-mass embryo by either silicate or icy pebble accretion, depending on its position with respect to the water ice line. We account for gas accretion and type-I/II migration. We perform an extensive parameter study evaluating a wide range in disc properties and embryo's initial location. We account for photoevaporation driven mass-loss after formation. We find that due to the change in dust properties at the water ice line, rocky cores form typically with $\sim$3 M$_{\oplus}$ and have a maximum mass of $\sim$5 M$_{\oplus}$, while icy cores peak at $\sim$10 $M_{\oplus}$, with masses lower than 5 M$_{\oplus}$ being scarce. When neglecting the gaseous envelope, rocky and icy cores account naturally for the two peaks of the Kepler size distribution. The presence of massive envelopes for cores more massive than $\sim$10 M$_{\oplus}$ inflates the radii of those planets above 4 R$_{\oplus}$. While the first peak of the Kepler size distribution is undoubtedly populated by bare rocky cores, the second peak can host water-rich planets with thin H-He atmospheres. Some envelope-loss mechanism should operate efficiently at short orbital periods to explain the presence of $\sim$10-40 M$_{\oplus}$ planets falling in the second peak of the size distribution.