Study of Kepler's FGKM stars

Alternatively, the P_rot_ distribution of stars can be inferred from their projected rotation velocities vsin i and radii R, without being biased against photometrically quiet stars. We solve this inference problem using a hierarchical Bayesian framework, which (i) is applicable to heteroscedastic measurements of vsin(i) and R with non-Gaussian uncertainties and (ii) does not require a simple parametric form for the true P_rot_ distribution.

We test the method on simulated data sets and show that the true P_rot_ distribution can be recovered from ~> 100 sets of vsin i and R measured with precisions of 1 km.s^-1^ and 4 per cent, respectively, unless the true distribution includes sharp discontinuities. We apply the method to a sample of 144 late-F/early-G dwarfs in the Kepler field with vsin(i) measured from Keck/HIRES spectra, and find that the typical rotation periods of these stars are similar to the photometric periods measured from Kepler light curves: we do not find a large population of slow rotators that are missed in the photometric sample, although we find evidence that the photometric sample is biased for young, rapidly rotating stars.