  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.
