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