Comprehensive Spatial Cross-matching and Application to the Chandra Source Catalog

Cross-matching of sources between catalogs, purely on the basis of their positions, can be (and has been) performed with varying degrees of sophistication, accuracy, and reliability. The following properties can successively be taken into account to improve the reliability of the match results, from a simple nearest neighbor criterion to a near-perfect match probability: - Spatial separation - Positional uncertainty - Source density - Point Spread Function (PSF) - Self-consistent probability threshold - Matching ambiguity We have developed a spatial cross-match tool that is based on the Bayesian algorithms described by Budavari, Heinis, and Szalay (ApJ 679, 301 and 705, 739) that were extended to allow the application of elliptical errors and the consideration of the PSF associated with the source detections. Subsequently, the self-consistent threshold criterion proposed by Budavari and Szalay is applied to the derived match probabilities in order to decide on the acceptance of the match; ambiguous matches are identified and separated out. The new elements are the generalization to elliptical position errors, the consideration of the role played by the PSFs, the self-consistent probability thresholding, and the explicit identification of ambiguous matches. This has allowed us to derive cross-matches that are far more authoritative between catalogs that are based on observational data with widely different PSF characteristics and covering different parts of the electro-magnetic spectrum. Additionally, we expect to be able to extend the tool to perform cross-matching across a large number of multiple catalogs simultaneously. This is feasible since the underlying cross-match algorithm is based on pair-wise probabilities, from which it will be straightforward to identify the connected components of an undirected graph developed from graph theory, thus drastically limiting the number of combinations that need to be considered. We will present authoritative cross-match catalogs of CSC Release 2.0 with SDSS, AllWISE, and Gaia. This work has been supported by NASA under contract NAS 8-03060 to the SAO for operation of the Chandra X-ray Center.