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

Source confusion has been a long-standing problem in the astronomical history. In the previous formulation, sources are assumed to be distributed homogeneously on the sky. This fundamental assumption is not realistic in many applications. In this work, by making use of the point field theory, we derive general analytic formulae for the confusion problems with arbitrary distribution and correlation functions. As a typical example, we apply these new formulae to the source confusion of infrared galaxies. We first calculate the confusion statistics for power-law galaxy number counts as a test case. When the slope of differential number counts, \gamma, is steep, the confusion limits becomes much brighter and the probability distribution function (PDF) of the fluctuation field is strongly distorted. Then we estimate the PDF and confusion limits based on the realistic number count model for infrared galaxies. The gradual flattening of the slope of the source counts makes the clustering effect rather mild. Clustering effects result in an increase of the limiting flux density with \sim 10%. In this case, the peak probability of the PDF 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

The Phoenix Deep Survey: Extremely Red Galaxies and Cluster Candidates

We present the results of a study of a sample of 375 Extremely Red Galaxies (ERGs) in the Phoenix Deep Survey, 273 of which constitute a subsample which is 80% complete to K_s = 18.5 over an area of 1160 arcmin^2. The angular correlation function for ERGs is estimated, and the association of ERGs with faint radio sources explored. We find tentative evidence that ERGs and faint radio sources are associated at z > 0.5. A new overdensity-mapping algorithm has been used to characterize the ERG distribution, and identify a number of cluster candidates, including a likely cluster containing ERGs at 0.5 < z < 1. Our algorithm is also used in an attempt to probe the environments in which faint radio sources and ERGs are associated. We find limited evidence that the I - K_s > 4 criterion is more efficient than R - K_s > 5 at selecting dusty star-forming galaxies, rather than passively evolving ERGs.Comment: 14 emulateapj pages, 15 figures, 1 table, accepted for publication in Astronomical Journal. A version with full resolution figures is available at http://www.physics.usyd.edu.au/~asmith/research/ERGpaper.pd