  Identifying the infrared counterparts of X-ray sources in Galactic Plane
fields such as those of the MYStIX project presents particular difficulties due
to the high density of infrared sources. This high stellar density makes it
inevitable that a large fraction of X-ray positions will have a faint field
star close to them, which standard matching techniques may incorrectly take to
be the counterpart. Instead we use the infrared data to create a model of both
the field star and counterpart magnitude distributions, which we then combine
with a Bayesian technique to yield a probability that any star is the
counterpart of an X-ray source. In our more crowded fields, between 10 and 20%
of counterparts that would be identified on the grounds of being the closest
star to X-ray position within a 99% confidence error circle are instead
identified by the Bayesian technique as field stars. These stars are
preferentially concentrated at faint magnitudes. Equally importantly the
technique also gives a probability that the true counterpart to the X-ray
source falls beneath the magnitude limit of the infrared catalog. In deriving
our method, we place it in the context of other procedures for matching
astronomical catalogs.
