Simultaneous calibration of spectro-photometric distances and the Gaia DR2 parallax zero-point offset with deep learning

Gaia measures the five astrometric parameters for stars in the Milky Way, but only four of them (positions and proper motion, but not parallax) are well measured beyond a few kpc from the Sun. Modern spectroscopic surveys such as APOGEE cover a large area of the Milky Way disk and we can use the relation between spectra and luminosity to determine distances to stars beyond Gaia's parallax reach. Here, we design a deep neural network trained on stars in common between Gaia and APOGEE that determines spectro-photometric distances to APOGEE stars, while including a flexible model to calibrate parallax zero-point biases in Gaia DR2. We determine the zero-point offset to be $-52.3 \pm 2.0uas$ when modeling it as a global constant, but also train a multivariate zero-point offset model that depends on $G$, $G_{BP} - G_{RP}$ color, and $T_\mathrm{eff}$ and that can be applied to all 139 million stars in Gaia DR2 within APOGEE's color--magnitude range. Our spectro-photometric distances are more precise than Gaia at distances $\approx 2kpc$ from the Sun. We release a catalog of spectro-photometric distances for the entire APOGEE DR14 data set which covers Galactocentric radii $2kpc\lesssim R \lesssim19kpc$; $\approx 150,000$ stars have <10% uncertainty, making this a powerful sample to study the chemo-dynamical structure of the disk. We use this sample to map the mean [Fe/H] and 15 abundance ratios [X/Fe] from the Galactic center to the edge of the disk. Among many interesting trends, we find that the bulge and bar region at $R \lesssim 5kpc$ clearly stands out in [Fe/H] and most abundance ratios.