A General Formulation of the Source Confusion Statistics and Application to Infrared Galaxy Surveys

Source confusion has been a long-standing problem in the astronomicalhistory. In the previous formulation, sources are assumed to be distributedhomogeneously on the sky. This fundamental assumption is not realistic in manyapplications. In this work, by making use of the point field theory, we derivegeneral analytic formulae for the confusion problems with arbitrarydistribution and correlation functions. As a typical example, we apply thesenew formulae to the source confusion of infrared galaxies. We first calculatethe confusion statistics for power-law galaxy number counts as a test case.When the slope of differential number counts, \gamma, is steep, the confusionlimits becomes much brighter and the probability distribution function (PDF) ofthe fluctuation field is strongly distorted. Then we estimate the PDF andconfusion limits based on the realistic number count model for infraredgalaxies. The gradual flattening of the slope of the source counts makes theclustering effect rather mild. Clustering effects result in an increase of thelimiting flux density with \sim 10%. In this case, the peak probability of thePDF decreases up to \sim 15% and its tail becomes heavier.Comment: ApJ in press, 21 pages, 9 figures, using aastex.cls, emulateapj5.sty. Abstract abridge