Isochrone ages for ∼3 million stars with the second Gaia data release

We present a catalogue of distances, masses, and ages for similar to 3 million stars in the second Gaia data release with spectroscopic parameters available from the large spectroscopic surveys: APOGEE, Gaia-ESO, GALAH, LAMOST, RAVE, and SEGUE. We use a Bayesian framework to characterize the probability density functions of distance, mass, and age using photometric, spectroscopic, and astrometric information, supplemented with spectroscopic masses where available for giant stars. Furthermore, we provide posterior extinction estimates (AV) to every star using published extinction maps as a prior input. We provide an appendix with extinction coefficients for Gaia photometry derived from stellar models, which account for variation with intrinsic colour and total extinction. Our pipeline provides output estimates of the spectroscopic parameters, which can be used to inform improved spectroscopic analysis. We complement our catalogues with Galactocentric coordinates and actions with associated uncertainties. As a demonstration of the power of our catalogue, we produce velocity dispersion profiles of the disc separated by age and Galactocentric radius (between 3 and 15 kpc from the Galactic centre). This suggests that the velocity dispersion profiles flatten with radius in the outer Galaxy (> 8 kpc) and that at all radii the velocity dispersion follows the smooth power law with age observed in the solar neighbourhood.