A Monte Carlo Method for Evaluating Empirical Gyrochronology Models and
  its Application to Wide Binary Benchmarks
  Accurate stellar ages are essential for our understanding of the star
formation history of the Milky Way, Galactic chemical evolution, and to
constrain exoplanet formation models. Gyrochronology, a relationship between
stellar rotation and age, appears to offer a reliable age indicator for main
sequence (MS) stars over the mass range of approximately 0.6 to 1.3 $M_\odot$.
Those stars lose their angular momentum due to magnetic braking and as a
result, their rotation speeds decrease with age. Although current
gyrochronology relations are fairly well tested for young MS stars with masses
greater than 1 $M_\odot$, primarily in young open clusters, insufficient tests
exist for older and lower mass MS stars. Binary stars offer the potential to
expand and fill in the range of ages and metallicity over which gyrochronology
can be empirically tested. In this paper, we demonstrate a Monte Carlo approach
to evaluate gyrochronology models using binary stars. As examples, we used five
previously published wide binary pairs. We also demonstrate a Monte Carlo
approach to assess the precision and accuracy of ages derived from each
gyrochronology model. For the traditional Skumanich models, the age
uncertainties are $\sigma_{age}$/$age$ = 15-20\% for stars with $B-V$ = 0.65,
and $\sigma_{age}$/$age$ = 5-10\% for stars with $B-V$ = 1.5 and rotation
period P $\leq$ 20 days.
