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

Abstract

Stellar surface rotation carries information about stellar parameters—particularly ages—and thus the large rotational data sets extracted from Kepler time series represent powerful probes of stellar populations. In this article, we address the challenge of interpreting such data sets with a forward-modeling exercise. We combine theoretical models of stellar rotation, a stellar population model for the galaxy, and prescriptions for observational bias 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 a mixture of evolutionary states and observational uncertainties. If we assume that the detectability of rotational signatures scales with the Rossby number, we can show that the observed period distribution contains an apparent "Rossby edge" at ${{\rm{Ro}}}_{\mathrm{thresh}}=2.08$, above which long-period, high Rossby number stars are either absent or undetected. This threshold suggests either that weakened magnetic braking is in operation in the full Kepler population or that stars undergo a transition in spottedness and activity. We discuss the observations necessary to disentangle these competing scenarios. Regardless of the physical origin of the edge, it biases the inferred age distributions, affecting stars older than ~9 Gyr at ${T}_{\mathrm{eff}}=5100\,{\rm{K}}$, older than $\sim 4.2\,\mathrm{Gyr}$ at solar temperatures, and $1.5\,\mathrm{Gyr}$ at 6500 K. Below $5100\,{\rm{K}}$, rotation periods should be viable age diagnostics in even the oldest stars in the population.