Forward Modeling of the Kepler Stellar Rotation Period Distribution: Interpreting Periods from Mixed and Biased Stellar Populations

Stellar surface rotation carries information about stellar parameters---particularly ages---and thus the large rotational datasets extracted from Kepler timeseries represent powerful probes of stellar populations. In this article, we address the challenge of interpreting such datasets with a forward-modeling exercise. We combine theoretical models of stellar rotation, a stellar population model for the galaxy, and prescriptions for observational bias and confusion to predict the rotation distribution in the Kepler field under standard "vanilla" assumptions. We arrive at two central conclusions: first, that standard braking models fail to reproduce the observed distribution at long periods, and second, that the interpretation of the period distribution is complicated by mixtures of unevolved and evolved stars and observational uncertainties. By assuming that the amplitude and thus detectability of rotational signatures is tied to the Rossby number, we show that the observed period distribution contains an apparent "Rossby edge" at $\textrm{Ro}_{thresh} = 2.08$, above which long-period, high-Rossby number stars are either absent or undetected. This $\textrm{Ro}_{thresh}$ is comparable to the Rossby number at which van Saders et al. (2016) observed the onset of weakened magnetic braking, and suggests either that this modified braking is in operation in the full Kepler population, or that stars undergo a transition in spottedness and activity at a very similar Rossby number. We discuss the observations necessary to disentangle these competing scenarios. (abridged)