XID:: Cross-association of ROSAT/Bright Source Catalog X-ray sources with USNO A-2 optical point sources

We quantitatively cross-associate the 18,811 ROSAT Bright Source Catalog (RASS/BSC) X-ray sources with optical sources in the USNO A-2 catalog, calculating the probability of unique association (P-id) between each candidate within 75 " of the X-ray source position, on the basis of optical magnitude and proximity. We present catalogs of RASS/BSC sources for which P-id > 98%, P-id > 90%, and P-id > 50%, which contain 2705, 5492, and 11,301 unique USNO A-2 optical counterparts respectively down to the stated level of significance. Together with identifications of objects not cataloged in USNO A-2 due to their high surface brightness (M31, M32,...) and optical pairs, we produced a total of 11,803 associations to a probability of P-id > 50%. We include in this catalog a list of objects in the SIMBAD database within 10 " of the USNO A-2 position, as an aid to identification and source classification. This is the first RASS/BSC counterpart catalog which provides a probability of association between each X-ray source and counterpart, quantifying the certainty of each individual association. The catalog is more useful than previous catalogs which either rely on plausibility arguments for association or do not aid in selecting a counterpart between multiple off-band sources in the field. Sources of high probability of association can be separated out, to produce high-quality lists of classes (Seyfert 1/2s, QSOs, RS CVns) desired for targeted study, or for discovering new examples of known classes (or new classes altogether) through the spectroscopic classification of securely identified but unclassified USNO A-2 counterparts. Low P-id associations can be used for statistical studies and follow-on investigation-for example, performing follow-up spectroscopy of the many low-mass stars to search for signatures of coronal emission, or to investigate the relationship between X-ray emission and classes of sources not previously well-studied for their X-ray emissions (such as pulsating variable stars). We find that a fraction similar to 65.8% of RASS/BSC sources have an identifiable optical counterpart, down to the magnitude limit of the USNO A-2 catalog which could be identified by their spatial proximity and high optical brightness.