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

## TL;DR

This paper presents a deep learning method to simultaneously calibrate Gaia DR2 parallax zero-point biases and determine spectro-photometric distances for APOGEE stars, improving distance estimates and enabling detailed chemo-dynamical mapping of the Milky Way.

## Contribution

It introduces a neural network that calibrates Gaia parallax zero-point offsets while deriving precise spectro-photometric distances for a large stellar sample, including a multivariate zero-point model.

## Key findings

- Zero-point offset of -52.3 ± 2.0 μas identified.
- Distances more precise than Gaia at ~2 kpc.
- Catalog of distances for ~150,000 stars with <10% uncertainty.

## Abstract

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.