To better understand the observed distributions of rotation rate and magnetic activity of sun-like and low-mass stars, we derive a physically motivated scaling for the dependence of the stellar-wind torque on Rossby number. The torque also contains an empirically-derived scaling with stellar mass (and radius), which provides new insight into the mass-dependence of stellar magnetic and wind properties. We demonstrate that this new formulation explains why the lowest mass stars are observed to maintain rapid rotation for much longer than solar-mass stars, and simultaneously, why older populations exhibit a sequence of slowly rotating stars, in which the low-mass stars rotate more slowly than solar-mass stars. The model also reproduces some previously unexplained features in the period-mass diagram for the Kepler field, notably: the particular shape of the upper envelope of the distribution, suggesting that ~95% of Kepler field stars with measured rotation periods are younger than ~4 Gyr; and the shape of the lower envelope, corresponding to the location where stars transition between magnetically saturated and unsaturated regimes.
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