Spectroscopic age estimates for APOGEE red-giant stars: Precise spatial and kinematic trends with age in the Galactic disc

Over the last few years, many studies have found an empirical relationship between the abundance of a star and its age. Here we estimate spectroscopic stellar ages for 178 825 red-giant stars observed by the APOGEE survey with a median statistical uncertainty of 17%. To this end, we use the supervised machine learning technique XGBoost , trained on a high-quality dataset of 3060 red-giant and red-clump stars with asteroseismic ages observed by both APOGEE and Kepler . After verifying the obtained age estimates with independent catalogues, we investigate some of the classical chemical, positional, and kinematic relationships of the stars as a function of their age. We find a very clear imprint of the outer-disc flare in the age maps and confirm the recently found split in the local age-metallicity relation. We present new and precise measurements of the Galactic radial metallicity gradient in small age bins between 0.5 and 12 Gyr, confirming a steeper metallicity gradient for ∼2 − 5 Gyr old populations and a subsequent flattening for older populations mostly produced by radial migration. In addition, we analyse the dispersion about the abundance gradient as a function of age. We find a clear power-law trend (with an exponent β ≈ 0.15) for this relation, indicating a relatively smooth radial migration history in the Galactic disc over the past 7 − 9 Gyr. Departures from this power law may possibly be related to the Gaia Enceladus merger and passages of the Sagittarius dSph galaxy. Finally, we confirm previous measurements showing a steepening in the age-velocity dispersion relation at around ∼9 Gyr, but now extending it over a large extent of the Galactic disc (5 kpc < R Gal < 13 kpc). To establish whether this steepening is the imprint of a Galactic merger event, however, detailed forward modelling work of our data is necessary. Our catalogue of precise stellar ages and the source code to create it are publicly available.