We quantitatively cross-associate the 18811 ROSAT Bright Source Catalog ( RASS/BSC ) X-ray sources with optical sources in the USNO A-2 catalog , calculating the the probability of unique association ( P _ { id } ) between each candidate within 75 \arcsec 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 11301 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 11803 associations to a probability of P _ { id } > 50 % .
We include in this catalog a list of objects in the SIMBAD database within 10 \arcsec 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 \sim 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 .