Inferring the rotation period distribution of stars from their projected rotation velocities and radii: Application to lateF/earlyG Kepler stars
Abstract
While stellar rotation periods P_{rot} may be measured from broadband photometry, the photometric modulation becomes harder to detect for slower rotators, which could bias measurements of the longperiod tail of the P_{rot} distribution. 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 nonGaussian 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 $1\, \mathrm{km\, s}^{1}$ and 4 per cent, respectively, unless the true distribution includes sharp discontinuities. We apply the method to a sample of 144 lateF/earlyG 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. Our results also agree with asteroseismic measurements of P_{rot} for Kepler stars with similar ages and effective temperatures, and show that $\approx 1.1\, \mathrm{M}_\odot$ stars beyond the middle of their mainsequence lifetimes rotate faster than predicted by standard magnetic braking laws.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 March 2022
 DOI:
 10.1093/mnras/stab3650
 arXiv:
 arXiv:2112.07162
 Bibcode:
 2022MNRAS.510.5623M
 Keywords:

 methods: data analysis;
 methods: statistical;
 techniques: spectroscopic;
 stars: rotation;
 Astrophysics  Solar and Stellar Astrophysics;
 Astrophysics  Instrumentation and Methods for Astrophysics
 EPrint:
 17 pages, 15 figures, accepted for publication in MNRAS