Tracking the evolution of sub-Neptunes. II. The radius valley on gyrochronological ages

Abstract

The radius valley separating super-Earths from sub-Neptunes is understood as a signature of atmospheric mass loss, but the timescale over which it develops remains poorly constrained. We investigate the age evolution of the radius valley and the super-Earth population around FGK stars using gyrochronological ages. We select $746$ planets around $510$ FGK hosts with reliable gyrochronological ages between $0.1$ and $4$ Gyr. A subset of $581$ planets around $404$ hosts, for which detection and confirmation completeness can be characterised, forms the reference sample. We measure the valley morphology and its locus in the period-radius plane, and infer the intrinsic super-Earth fraction with a selection-conditioned mixture model that accounts for stellar-age uncertainties. The intrinsic super-Earth fraction increases primarily during the first $\sim2$ Gyr, with no significant subsequent evolution. An exponential approach-to-plateau model places $90\%$ of this increase within $1.9$ Gyr at $90\%$ credibility. The radius valley is consistently resolved from $\sim1.5$ Gyr onwards, with no significant evolution in its depth or width. Its minimum may shift from $\sim1.5\,R_\oplus$ before $\sim2$ Gyr to $\sim1.8\,R_\oplus$ at older ages, accompanied by a change in the shape of the super-Earth radius distribution, although these changes are only suggestive. This evolution is consistent with atmospheric loss continuing up to approximately $1$-$2$ Gyr for a fraction of planets. The tentative shift of the valley minimum towards larger radii may indicate that planets with more massive cores complete envelope loss later, although the present data do not uniquely distinguish between atmospheric-loss mechanisms.