The Enigmatic Galactic Center Excess: Spurious Point Sources and Signal
  Mismodeling
  The Galactic Center GeV excess (GCE) has garnered great interest as a
possible signal of either dark matter annihilation or some novel astrophysical
phenomenon, such as a new population of gamma-ray emitting pulsars. In a
companion paper, we showed that in a $10^\circ$ radius region of interest (ROI)
surrounding the Galactic Center, apparent evidence for GCE point sources (PSs)
from non-Poissonian template fitting (NPTF) is actually an artifact of
unmodeled north-south asymmetry of the GCE. In this work, we develop a
simplified analytic description of how signal mismodeling can drive an apparent
preference for a PS population, and demonstrate how the behavior pointed out in
the companion paper also appears in simpler simulated datasets that contain no
PS signals at all. We explore the generality of this behavior in the real
gamma-ray data, and discuss the implications for past and future studies using
NPTF techniques. While the drop in PS preference once north-south asymmetry is
included is not ubiquitous in larger ROIs, we show that any overly-rigid signal
model is expected to yield a spurious PS signal that can appear very
convincing: as well as apparent significance comparable to what one would
expect from a true PS population, the signal can exhibit stability against a
range of variations in the analysis, and a source count function that is very
consistent with previous apparent NPTF-based detections of a GCE PS population.
This contrasts with previously-studied forms of systematic mismodeling which
are unlikely to mimic a PS population in the same way. In the light of this
observation, and its explicit realization in the region where the GCE is
brightest, we argue that a dominantly smooth origin for the GCE is not in
tension with existing NPTF analyses.
