The gamma-ray pulsar population of globular clusters: implications for the GeV excess

It has been suggested that the GeV excess, observed from the region surrounding the Galactic Center, might originate from a population of millisecond pulsars that formed in globular clusters. With this in mind, we employ the publicly available Fermi data to study the gamma-ray emission from 157 globular clusters, identifying a statistically significant signal from 25 of these sources (ten of which are not found in existing gamma-ray catalogs). We combine these observations with the predicted pulsar formation rate based on the stellar encounter rate of each globular cluster to constrain the gamma-ray luminosity function of millisecond pulsars in the Milky Way's globular cluster system. We find that this pulsar population exhibits a luminosity function that is quite similar to those millisecond pulsars observed in the field of the Milky Way (i.e. the thick disk). After pulsars are expelled from a globular cluster, however, they continue to lose rotational kinetic energy and become less luminous, causing their luminosity function to depart from the steady-state distribution. Using this luminosity function and a model for the globular cluster disruption rate, we show that millisecond pulsars born in globular clusters can account for only a few percent or less of the observed GeV excess. Among other challenges, scenarios in which the entire GeV excess is generated from such pulsars are in conflict with the observed mass of the Milky Way's Central Stellar Cluster.