XID II: Statistical Cross-Association of ROSAT Bright Source Catalog X-ray Sources with 2MASS Point Source Catalog Near-Infrared Sources

The 18,806 ROSAT All Sky Survey Bright Source Catalog (RASS/BSC) X-ray sources are quantitatively cross-associated with near-infrared (NIR) sources from the Two Micron All Sky Survey Point Source Catalog (2MASS/PSC). An association catalog is presented, listing the most likely counterpart for each RASS/BSC source, the probability P _id that the NIR source and X-ray source are uniquely associated, and the probability P _no-id that none of the 2MASS/PSC sources are associated with the X-ray source. The catalog includes 3853 high quality (P _id>0.98) X-ray-NIR matches, 2280 medium quality (0.98 >= P _id>0.9) matches, and 4153 low quality (0.9 >= P _id>0.5) matches. Of the high quality matches, 1418 are associations that are not listed in the SIMBAD database, and for which no high quality match with a USNO-A2 optical source was presented for the RASS/BSC source in previous work. The present work offers a significant number of new associations with RASS/BSC objects that will require optical/NIR spectroscopy for classification. For example, of the 6133 P _id>0.9 2MASS/PSC counterparts presented in the association catalog, 2411 have no classification listed in the SIMBAD database. These 2MASS/PSC sources will likely include scientifically useful examples of known source classes of X-ray emitters (white dwarfs, coronally active stars, active galactic nuclei), but may also contain previously unknown source classes. It is determined that all coronally active stars in the RASS/BSC should have a counterpart in the 2MASS/PSC, and that the unique association of these RASS/BSC sources with their NIR counterparts thus is confusion limited.