  The paucity of old millisecond pulsars observed at the galactic center of the
Milky Way could be the result of dark matter accumulating in and destroying
neutron stars. In regions of high dark matter density, dark matter clumped in a
pulsar can exceed the Schwarzschild limit and collapse into a natal black hole
which destroys the pulsar. We examine what dark matter models are consistent
with this hypothesis and find regions of parameter space where dark matter
accumulation can significantly degrade the neutron star population within the
galactic center while remaining consistent with observations of old millisecond
pulsars in globular clusters and near the solar position. We identify what dark
matter couplings and masses might cause a young pulsar at the galactic center
to unexpectedly extinguish. Finally, we find that pulsar collapse age scales
inversely with the dark matter density and linearly with the dark matter
velocity dispersion. This implies that maximum pulsar age is spatially
dependent on position within the dark matter halo of the Milky Way. In turn,
this pulsar age spatial dependence will be dark matter model dependent.
