A statistical test of emission from unresolved point sources

Abstract

We describe a simple test of the spatial uniformity of an ensemble of discrete events. Given an estimate for the point-source luminosity function and an instrumental point spread function, a robust upper bound on the fractional point-source contribution to a diffuse signal can be found. We verify with Monte Carlo tests that the statistic has advantages over the two-point correlation function for this purpose, and derive analytic estimates of the statistic’s mean and variance as a function of the point-source contribution. As a case study, we apply this statistic to recent gamma-ray data from the Fermi Large Area Telescope, and demonstrate that at energies above 10 GeV the contribution of unresolved point sources to the diffuse emission is small in the region relevant for study of the WMAP Haze.