The TIME Table: Rotation and Ages of Cool Exoplanet Host Stars

Abstract

Age is a stellar parameter that is both fundamental and difficult to determine. Among middle-aged M dwarfs, the most prolific hosts of close-in and detectable exoplanets, gyrochronology is the most promising method to assign ages, but requires calibration by rotation-temperature sequences (gyrochrones) in clusters of known ages. We curated a catalog of 249 late K- and M-type (($T_{eff}$=3200-4200K) exoplanet host stars with established rotation periods, and applied empirical, temperature-dependent rotation-age relations based on relevant published gyrochrones, including one derived from observations of the 4 Gyr-old open cluster M67. We estimated ages for 227 of these stars, and upper limits for 8 others, excluding 14 which have too rapidly rotating or are otherwise outside the valid parameter range of our gyrochronology. We estimated uncertainties based on observed scatter in rotation periods in young clusters, error in the gyrochrones, and uncertainties in temperature and non-solar metallicity. For those stars with measured metallicities, we provide but do not incorporate a correction for the effects of deviation from solar metallicity. The age distribution of our sample declines to near zero at 10 Gyr, the age of the Galactic disk, with the handful of outliers explainable by large uncertainties. Continued addition or extension of cluster rotation sequences to more thoroughly calibrate the gyrochronology in time and temperature space, more precise and robust measurement of rotation periods, and more accurate stellar parameter measurements will enable continued improvements in the age estimates of these important exoplanet host stars.