SIMBAD references

The matching of sources between photometric catalogues can lead to cases where objects of differing brightness are incorrectly assumed to be detections of the same source. The rejection of unphysical matches can be achieved through the inclusion of information about the sources' magnitudes. The method described here uses the additional photometric information from both catalogues in the process of accepting or rejecting counterparts, providing approximately a factor of 10 improvement in Bayes' factor with its inclusion. When folding in the photometric information we avoid using prior astrophysical knowledge. Additionally, the method allows for the possibility of no counterparts to sources and the possibility that sources overlap multiple potential counterparts. We formally describe the probability of two sources being the same astrometric object, allowing systematic effects of astrometric perturbation (by e.g. contaminant objects) to be accounted for. We apply the method to two cases. First, we test INT Photometric Hα Survey of the Northern Galactic Plane (IPHAS)-Gaia matches to compare the resulting matches in two catalogues of similar wavelength coverage but differing dynamical ranges. Second, we apply the method to matches between IPHAS and Two Micron All Sky Survey and show that the method holds when considering two catalogues with approximately equal astrometric precision. We discuss the importance of including the magnitude information in each case. Additionally, we discuss extending the method to multiple catalogue matches through an iterative matching process. The method allows for the selection of high-quality matches by providing an overall probability for each pairing, giving the flexibility to choose stars known to be good matches.