Inferring the Rotation Period Distribution of Stars from their Projected Rotation Velocities and Radii: Application to late-F/early-G Kepler Stars

TL;DR

This paper introduces a hierarchical Bayesian method to infer stellar rotation period distributions from projected velocities and radii, overcoming biases in photometric measurements, and applies it to Kepler stars, revealing insights into stellar rotation evolution.

Contribution

The paper develops a novel Bayesian framework that accurately infers rotation periods from $v\sin i$ and radii, handling complex uncertainties and avoiding parametric assumptions.

Findings

The method reliably recovers true rotation distributions from simulated data.

Applied to Kepler stars, it shows no large bias against slow rotators in photometric samples.

Stars beyond mid-main-sequence rotate faster than standard models predict.

Abstract

While stellar rotation periods $P_\mathrm{rot}$ may be measured from broadband photometry, the photometric modulation becomes harder to detect for slower rotators, which could bias measurements of the long-period tail of the $P_\mathrm{rot}$ distribution. Alternatively, the $P_\mathrm{rot}$ distribution of stars can be inferred from their projected rotation velocities $v\sin i$ 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 $v\sin i$ and $R$ with non-Gaussian uncertainties and (ii) does not require a simple parametric form for the true $P_\mathrm{rot}$ distribution. We test the method on simulated data sets and show that the true $P_\mathrm{rot}$ distribution can be recovered from $\gtrsim 100$ sets of $v\sin i$ and $R$ measured with precisions of $1\,\mathrm{km/s}$ and $4\%$, 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 $v\sin i$ 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 $P_\mathrm{rot}$ for Kepler stars with similar ages and effective temperatures, and show that $\approx 1.1\,M_\odot$ stars beyond the middle of their main-sequence lifetimes rotate faster than predicted by standard magnetic braking laws.