Calibrating Gyrochronology using Kepler Asteroseismic targets

Abstract: Among the available methods for dating stars, gyrochronology is a powerful one because it requires knowledge of only the star's mass and rotation period. Gyrochronology relations have previously been calibrated using young clusters, with the Sun providing the only age dependence, and are therefore poorly calibrated at late ages. We used rotation period measurements of 310 Kepler stars with asteroseismic ages, 50 stars from the Hyades and Coma Berenices clusters and 6 field stars (including the Sun) with precise age measurements to calibrate the gyrochronology relation, whilst fully accounting for measurement uncertainties in all observable quantities. We calibrated a relation of the form $P=A^n\times(B-V-c)^b$, where $P$ is rotation period in days, $A$ is age in Myr, $B$ and $V$ are magnitudes and $a$, $b$ and $n$ are the free parameters of our model. We found $a = 0.40^{+0.3}_{-0.05}$, $b = 0.31^{+0.05}_{-0.02}$ and $n = 0.55^{+0.02}_{-0.09}$. Markov Chain Monte Carlo methods were used to explore the posterior probability distribution functions of the gyrochronology parameters and we carefully checked the effects of leaving out parts of our sample, leading us to find that no single relation beween rotation period, colour and age can adequately describe all the subsets of our data. The Kepler asteroseismic stars, cluster stars and local field stars cannot all be described by the same gyrochronology relation. The Kepler asteroseismic stars may be subject to observational biases, however the clusters show unexpected deviations from the predicted behaviour, providing concerns for the overall reliability of gyrochronology as a dating method.