  The unexplained excess gamma-ray emission from the Milky Way's Galactic
Center has puzzled astronomers for nearly a decade. Two theories strive to
explain the origin of this excess: self-annihilating dark matter particles or
an unresolved population of radio millisecond pulsars. We examine the
plausibility of a pulsar origin for the GeV excess using N-body simulations. We
simulated millisecond pulsars in a realistic dynamical environment: (i) pulsars
were born from the known stellar mass components of our Galaxy; (ii) pulsars
were given natal velocity kicks as empirically observed from two different
studies (or, for comparison, without kicks); (iii) pulsars were evolved in a
Galactic gravitational potential consistent with observations. Multiple
populations of pulsars (with different velocity kicks) were simulated over 1
Gyr. With final spatial distributions of pulsars, we constructed synthetic
gamma-ray surface brightness profiles. From comparisons with published
Fermi-LAT surface brightness profiles, our pulsar simulations cannot reproduce
the concentrated emission in the central degrees of the Bulge, though models
without natal velocity kicks approach the data. We considered additive
combinations of our (primordial MSP) simulations with models where pulsars are
deposited from destroyed globular clusters in the Bulge, and a simple model for
pulsars produced in the nuclear star cluster. We can reasonably reproduce the
measured central gamma-ray surface brightness distribution of Horiuchi and
collaborators using several combinations of these models, but we cannot
reproduce the measured distribution of Di Mauro with any combination of models.
Our fits provide constraints on potential pathways to explain the gamma-ray
excess using MSPs.
