Inference of Unresolved Point Sources At High Galactic Latitudes Using Probabilistic Catalogs

TL;DR

This paper introduces a Bayesian probabilistic cataloging method to detect and characterize faint and overlapping point sources in astrophysical images, improving sensitivity and covariance tracking over traditional techniques.

Contribution

The authors develop a novel Bayesian framework for probabilistic cataloging that accurately infers properties of unresolved point sources, validated on gamma-ray data near the North Galactic Pole.

Findings

Identified approximately 270 point sources above the detection threshold.

Estimated that point sources contribute about 18% to the total gamma-ray emission.

Inferred the flux distribution slope of point sources as approximately -1.92.

Abstract

Detection of point sources in images is a fundamental operation in astrophysics, and is crucial for constraining population models of the underlying point sources or characterizing the background emission. Standard techniques fall short in the crowded-field limit, losing sensitivity to faint sources and failing to track their covariance with close neighbors. We construct a Bayesian framework to perform inference of faint or overlapping point sources. The method involves probabilistic cataloging, where samples are taken from the posterior probability distribution of catalogs consistent with an observed photon count map. In order to validate our method we sample random catalogs of the gamma-ray sky in the direction of the North Galactic Pole (NGP) by binning the data in energy and Point Spread Function (PSF) classes. Using three energy bins spanning $0.3 - 1$, $1 - 3$ and $3 - 10$ GeV, we identify $270\substack{+30 \\ -10}$ point sources inside a $40^\circ \times 40^\circ$ region around the NGP above our point-source inclusion limit of $3 \times 10^{-11}$/cm$^2$/s/sr/GeV at the $1-3$ GeV energy bin. Modeling the flux distribution as a power law, we infer the slope to be $-1.92\substack{+0.07 \\ -0.05}$ and estimate the contribution of point sources to the total emission as $18\substack{+2 \\ -2}$\%. These uncertainties in the flux distribution are fully marginalized over the number as well as the spatial and spectral properties of the unresolved point sources. This marginalization allows a robust test of whether the apparently isotropic emission in an image is due to unresolved point sources or of truly diffuse origin.