The Relationship of Stellar Radius Inflation to Rotation and Magnetic Starspots at 10--670 Myr

Active, low-mass stars are widely observed to have radii that are larger than predicted by standard stellar models. Proposed mechanisms for this radius inflation generally involve stellar magnetism, either in the form of added pressure support in the outer layers and/or suppression of convection via starspots. We have assembled a large sample of 261 low-mass stars in the young clusters Upper Scorpius, $α$ Persei, Pleiades, and Praesepe (spanning ages 10--670 Myr) for which the data exist to empirically measure the stellar radii, rotation periods, and starspot covering fractions. We find a clear, strong relationship between the degree of radius inflation and stellar rotation as represented by the Rossby number; this inflation-rotation relationship bears striking resemblance to canonical activity-rotation relationships, including both the so-called linear and saturated regimes. We also demonstrate here for the first time that the radius inflation depends directly on the starspot covering fraction. We furthermore find that the stars' effective temperatures decrease with decreasing Rossby number as well, and that this temperature suppression balances the radius inflation so as to preserve the stellar bolometric luminosity. These relationships are consistent across the age range sampled here, which spans from the pre--main-sequence to the zero-age main sequence. The favorable comparison of our findings to the predictions of modern starspot-based stellar evolution models suggests that, while rotation is clearly the underlying driver, magnetism may be the most likely direct cause of the radius inflation phenomenon.