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

We present a catalogue of distances, masses and ages for $\sim3$ 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 characterise 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 ($A_V$) 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 $15\,\mathrm{kpc}$ from the Galactic centre). This suggests that the velocity dispersion profiles flatten with radius in the outer Galaxy ($>8\,\mathrm{kpc}$) and that at all radii the velocity dispersion follows the smooth power law with age observed in the solar neighbourhood.