A statistical test of emission from unresolved point sources

TL;DR

This paper introduces a statistical test to evaluate the contribution of unresolved point sources to diffuse signals, demonstrating its effectiveness with gamma-ray data from Fermi LAT and showing minimal unresolved source contribution above 10 GeV.

Contribution

The paper presents a new statistical method for assessing the fractional contribution of unresolved point sources to diffuse emissions, outperforming traditional correlation functions.

Findings

Unresolved point sources contribute minimally to diffuse gamma-ray emission above 10 GeV.

The proposed statistic has advantages over the two-point correlation function.

Analytic estimates of the statistic's mean and variance are derived.

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 (PSF), 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 (LAT), 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.