# Improving \textsl{Gaia} parallax precision with a data-driven model of stars

## TL;DR

This paper introduces a data-driven, empirical prior for stellar distances using Gaia and 2MASS data, significantly improving parallax precision by leveraging a large, noise-deconvolved color-magnitude model.

## Contribution

It develops a novel noise-deconvolved empirical prior based on 2MASS colors and Gaia data, enhancing parallax estimates without relying on stellar physics or Galactic models.

## Key findings

- Median parallax precision improved by 20% over Gaia TGAS
- 14% of estimates are more than twice as precise
- Validated with star cluster M67, revealing clearer cluster structure

## Abstract

Converting a noisy parallax measurement into a posterior belief over distance requires inference with a prior. Usually this prior represents beliefs about the stellar density distribution of the Milky Way. However, multi-band photometry exists for a large fraction of the \textsl{\small{Gaia}} \textsl{\small{TGAS}} Catalog and is incredibly informative about stellar distances. Here we use \textsl{\small{2MASS}} colors for 1.4 million \textsl{\small{TGAS}} stars to build a noise-deconvolved empirical prior distribution for stars in color--magnitude space. This model contains no knowledge of stellar astrophysics or the Milky Way, but is precise because it accurately generates a large number of noisy parallax measurements under an assumption of stationarity; that is, it is capable of combining the information from many stars. We use the Extreme Deconvolution (\textsl{\small{XD}}) algorithm---an Empirical Bayes approximation to a full hierarchical model of the true parallax and photometry of every star---to construct this prior. The prior is combined with a \textsl{\small{TGAS}} likelihood to infer a precise photometric parallax estimate and uncertainty (and full posterior) for every star. Our parallax estimates are more precise than the \textsl{\small{TGAS}} catalog entries by a median factor of 1.2 (14% are more precise by a factor >2) and are more precise than previous Bayesian distance estimates that use spatial priors. We validate our parallax inferences using members of the Milky Way star cluster M67, which is not visible as a cluster in the \textsl{\small{TGAS}} parallax estimates, but appears as a cluster in our posterior parallax estimates. Our results, including a parallax posterior pdf for each of 1.4 million \textsl{\small{TGAS}} stars, are available in companion electronic tables.