Ensemble Kinematic Ages for 1.5 Million LAMOST Stars

We present a framework for inferring stellar ages from spectroscopic stellar parameters, calibrated with ensemble kinematics by averaging over the median vertical action, $J_z$, for stars with similar atmospheric and chemical properties, yielding self-consistent age estimates across the Hertzsprung-Russell (HR) diagram. We refer to these ages as ensemble kinematic ages as the age scale is calibrated from the average kinematics of ensembles of stars with similar stellar parameters. Individual stellar kinematics are not used in assigning ages. We validate the method against subgiant ages, achieving an accuracy of ~30%, comparable to [C/N]-based estimates. We find a clear age-$J_z$ relations that enable age inference up to ~10 Gyr for both the high- and low-$\alpha$ disks. Applying this framework to 1.5 million LAMOST stars, we derive ages for subgiants and giants with typical uncertainties of ~2 Gyr. The inferred ages agree well with literature age catalogs, with no significant systematic trends as a function of $\log g$. We also demonstrate the potential of empirical isochrones to calibrate theoretical stellar models. We identify an old (~7 Gyr) population within the low-$\alpha$ disk but draw no firm conclusions. Although ensemble kinematic ages are statistical and sensitive to selection effects, Galactic potential assumptions, and Galactic location, they provide a robust population-level tool for Galactic archaeology, complementing traditional age indicators and extending age estimates across the full HR diagram.