Cross-Identification of Stars with Unknown Proper Motions

The cross-identification of sources in separate catalogs is one of the most basic tasks in observational astronomy. It is, however, surprisingly difficult and generally ill-defined. Recently Budavári & Szalay (2008) formulated the problem in the realm of probability theory, and laid down the statistical foundations of an extensible methodology. In this paper, we apply their Bayesian approach to stars that, we know, can move measurably on the sky, with detectable proper motion, and show how to associate their observations. We study models on a sample of stars in the Sloan Digital Sky Survey, which allow for an unknown proper motion per object, and demonstrate the improvements over the analytic static model. Our models and conclusions are directly applicable to upcoming surveys such as PanSTARRS, the Dark Energy Survey, Sky Mapper, and the LSST, whose data sets will contain hundreds of millions of stars observed multiple times over several years.

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