Evidence of radius inflation in stars approaching the slow-rotator sequence

Abstract

Average stellar radii in open clusters can be estimated from rotation periods and projected rotational velocities under the assumption of random orientation of the spin axis. Such estimates are independent of distance, interstellar absorption, and models, but their validity can be limited by missing data (truncation) or data that only represent upper/lower limits (censoring). We present a new statistical analysis method to estimate average stellar radii in the presence of censoring and truncation. We use theoretical distribution functions of the projected stellar radius $R \sin i$ to define a likelihood function in the presence of censoring and truncation. Average stellar radii in magnitude bins are then obtained by a maximum likelihood parametric estimation procedure. This method is capable of recovering the average stellar radius within a few percent with as few as $\approx$ 10 measurements. Here it is applied for the first time to the dataset available for the Pleiades. We find an agreement better than $\approx$ 10 percent between the observed $R$ vs $M_K$ relationship and current standard stellar models for 1.2 $\ge M/M_{\odot} \ge$ 0.85 with no evident bias. Evidence of a systematic deviation at $2\sigma$ level are found for stars with 0.8 $\ge M/M_{\odot} \ge$ 0.6 approaching the slow-rotator sequence. Fast-rotators ($P$ < 2 d) agree with standard models within 15 percent with no systematic deviations in the whole 1.2 $\ge M/M_{\odot} \ge$ 0.5 range. The evidence found of a possible radius inflation just below the lower mass limit of the slow-rotator sequence indicates a possible connection with the transition from the fast to the slow-rotator sequence.