  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.
