Bayesian Cross-Matching of High Proper Motion Stars in Gaia DR2 and Photometric Metallicities for $\sim$1.7 million K and M Dwarfs

We present a Bayesian method to cross-match 5,827,988 high proper motion Gaia sources ($\mu>40 \ mas \ yr^{-1}$) to various photometric surveys: 2MASS, AllWISE, GALEX, RAVE, SDSS and Pan-STARRS. To efficiently associate these objects across catalogs, we develop a technique that compares the multidimensional distribution of all sources in the vicinity of each Gaia star to a reference distribution of random field stars obtained by extracting all sources in a region on the sky displaced 2$^\prime$. This offset preserves the local field stellar density and magnitude distribution allowing us to characterize the frequency of chance alignments. The resulting catalog with Bayesian probabilities $>$95% has a marginally higher match rate than current internal Gaia DR2 matches for most catalogs. However, a significant improvement is found with Pan-STARRS, where $\sim$99.8% of the sample within the Pan-STARRS footprint is recovered, as compared to a low $\sim$20.8% in Gaia DR2. Using these results, we train a Gaussian Process Regressor to calibrate two photometric metallicity relationships. For dwarfs of $3500

Keywords:

• Sky
• Stellar density
• Astrophysics
• Proper motion
• Photometry (optics)
• Random field
• Stars
• Physics
• Gaussian process
• Metallicity

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