The Effect of Unresolved Contaminant Stars on the Cross-Matching of
  Photometric Catalogues
  A fundamental process in astrophysics is the matching of two photometric
catalogues. It is crucial that the correct objects be paired, and that their
photometry does not suffer from any spurious additional flux. We compare the
positions of sources in WISE, IPHAS, 2MASS, and APASS with Gaia DR1 astrometric
positions. We find that the separations are described by a combination of a
Gaussian distribution, wider than naively assumed based on their quoted
uncertainties, and a large wing, which some authors ascribe to proper motions.
We show that this is caused by flux contamination from blended stars not
treated separately. We provide linear fits between the quoted Gaussian
uncertainty and the core fit to the separation distributions.
  We show that at least one in three of the stars in the faint half of a given
catalogue will suffer from flux contamination above the 1% level when the
density of catalogue objects per PSF area is above approximately 0.005. This
has important implications for the creation of composite catalogues. It is
important for any closest neighbour matches as there will be a given fraction
of matches that are flux contaminated, while some matches will be missed due to
significant astrometric perturbation by faint contaminants. In the case of
probability-based matching, this contamination affects the probability density
function of matches as a function of distance. This effect results in up to 50%
fewer counterparts being returned as matches, assuming Gaussian astrometric
uncertainties for WISE-Gaia matching in crowded Galactic plane regions,
compared with a closest neighbour match.
