Luminosity functions consistent with a pulsar-dominated Galactic Center
  Excess
  A new population of millisecond pulsars is a long-standing proposed
explanation for the excess of GeV-scale gamma rays emanating from the region
surrounding the center of the Milky Way (the "Galactic Center excess"). We
examine several simple parameterizations of possible luminosity functions for
this population, as well as several benchmark luminosity functions proposed in
the literature, and compare the predicted populations of resolved point sources
to the Fermi 4FGL-DR2 point source catalog and a sub-population recently
identified using wavelet-based methods. We provide general results that can be
used to translate upper limits on the number of resolved point sources
associated with the excess, and the fraction of the flux in the excess that can
be attributed to resolved sources, into limits on the luminosity function
parameter space. We discuss a number of important systematic uncertainties,
including in the detection threshold model and the total flux attributed to the
excess. We delineate regions of parameter space (containing existing benchmark
models) where there is no apparent tension with current data, and the number of
total pulsars needed to explain the excess is in the range of
O(10,000-100,000). Forecasting the effects of lowered point source detection
thresholds, we show that novel analysis methods that probe sub-threshold point
source populations can hope to resolve more than 30% of the flux of the excess.
