The gamma-ray luminosity function of millisecond pulsars and implications for the GeV excess

It has been proposed that a large population of unresolved millisecond pulsars (MSPs) could potentially account for the excess of GeV-scale gamma-rays observed from the region surrounding the Galactic Center. The viability of this scenario depends critically on the gamma-ray luminosity function of this source population, which determines how many MSPs Fermi should have already detected as resolved point sources. In this paper, we revisit the gamma-ray luminosity function of MSPs, without relying on uncertain distance measurements. Our determination, based on a comparison of models with the observed characteristics of the MSP population, suggests that Fermi should have already detected a significant number of sources associated with such a hypothesized Inner Galaxy population. As a result, we cannot rule out a scenario in which the MSPs residing near the Galactic Center are systematically less luminous than those present in the Galactic Plane or within globular clusters.