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.