New determination of the millisecond pulsar gamma-ray luminosity function and implications for the Galactic Center gamma-ray excess

It has been suggested that the Galactic Center gamma-ray excess (GCE) could be produced by a large number of centrally located millisecond pulsars. The fact that no such pulsar population has been detected implies that these sources must be very faint and very numerous. In this study, we use the contents of Fermi's recently released Third Pulsar Catalog (3PC) to measure the luminosity function of the millisecond pulsars in the Milky Way's disk. We find that this source population exhibits a luminosity function with a mean $\ensuremath{\gamma}$-ray luminosity of $⟨{L}_{\ensuremath{\gamma}}⟩\ensuremath{\sim}6\ifmmode\times\else\texttimes\fi{}{10}^{32}\text{ }\text{ }\mathrm{erg}/\mathrm{s}$ (integrated above 0.1 GeV). If the GCE were generated by millisecond pulsars with the same luminosity function, we find that $\ensuremath{\sim}20$ such sources from the inner Galaxy population should have already been detected by Fermi and included in the 3PC. Given the lack of such observed sources, we exclude the hypothesis that the GCE is generated by pulsars with the same luminosity function as those in the Galactic disk with a significance of $3.4\ensuremath{\sigma}$. We conclude that either less than 39% of the GCE is generated by pulsars, or that the millisecond pulsars in the inner Galaxy are at least 5 times less luminous on average than those found in the Galactic disk.