Distinguishing Dark Matter from Unresolved Point Sources in the Inner
  Galaxy with Photon Statistics
  Data from the Fermi Large Area Telescope suggests that there is an extended
excess of GeV gamma-ray photons in the Inner Galaxy. Identifying potential
astrophysical sources that contribute to this excess is an important step in
verifying whether the signal originates from annihilating dark matter. In this
paper, we focus on the potential contribution of unresolved point sources, such
as millisecond pulsars (MSPs). We propose that the statistics of the
photons---in particular, the flux probability density function (PDF) of the
photon counts below the point-source detection threshold---can potentially
distinguish between the dark-matter and point-source interpretations. We
calculate the flux PDF via the method of generating functions for these two
models of the excess. Working in the framework of Bayesian model comparison, we
then demonstrate that the flux PDF can potentially provide evidence for an
unresolved MSP-like point-source population.
