2021ApJ...913...75B

We apply for the first time a two-dimensional fitting statistic, τ², to rotational-evolution models (REMs) of stars (0.1-1.3 M_☉) on the period-mass plane. The τ² statistic simultaneously considers all cluster rotation data to return a goodness of fit, allowing for data-driven improvement of REMs. We construct data sets for Upper Sco, the Pleiades, and Praesepe, to which we tune our REMs. We use consistently determined stellar masses (calculated by matching K_s magnitudes to isochrones) and literature rotation periods. As a first demonstration of the τ² statistic, we find the best-fitting gyrochronology age for Praesepe, which is in good agreement with the literature. We then systematically vary three parameters that determine the dependence of our stellar wind torque law on the Rossby number in the saturated and unsaturated regimes, and the location of the transition between the two. By minimizing τ², we find best-fit values for each parameter. These values vary slightly between clusters, mass determinations, and initial conditions, highlighting the precision of τ² and its potential for constraining REMs, gyrochronology, and our understanding of stellar physics. Our resulting REMs, which implement the best-possible fitting form of a broken-power-law torque, are statistically improved on previous REMs using similar formulations, but still do not simultaneously describe the observed rotation distributions of the lowest masses, which have both slow and fast rotators by the Praesepe age, and the shape of the converged sequence for higher masses. Further complexity in the REMs is thus required to accurately describe the data.