Relations of Rotation and Chromospheric Activity to Stellar Age for FGK Dwarfs from Kepler and LAMOST

Abstract

The empirical relations between rotation period, chromospheric activity, and age can be used to estimate stellar age. To calibrate these relations, we present a catalog, including the masses and ages of 52,321 FGK dwarfs, 47,489 chromospheric activity index $\mathrm{log}{R}_{\mathrm{HK}}^{+}$ , 6077 rotation periods P _rot, and variability amplitudes S _ph, based on data from LAMOST DR7, Kepler, and Gaia Data Release 3. We find a pronounced correlation among P _rot, age, and [Fe/H] throughout the main-sequence phase for F dwarfs. However, the decrease of $\mathrm{log}{R}_{\mathrm{HK}}^{+}$ over time is not significant except for those with [Fe/H] < ‑0.1. For G dwarfs, both P _rot and $\mathrm{log}{R}_{\mathrm{HK}}^{+}$ are reliable age probes in the ranges ∼2–11 Gyr and ∼2–13 Gyr, respectively. K dwarfs exhibit a prominent decrease in $\mathrm{log}{R}_{\mathrm{HK}}^{+}$ within the age range of ∼3–13 Gyr when the relation of P _rot–τ is invalid. These relations are very important for promptly estimating the age of a vast number of stars, thus serving as a powerful tool in advancing the fields of exoplanet properties, stellar evolution, and Galactic archeology.