Millisecond Pulsars in Globular Clusters and Implications for the Galactic Center Gamma-Ray Excess

We study the gamma-ray emission from millisecond pulsars within the Milky Way's globular cluster system in order to measure the luminosity function of this source population. We find that these pulsars have a mean luminosity of $\langle L_{\gamma}\rangle \sim (1-8)\times 10^{33}\, {\rm erg/s}$ (integrated between 0.1 and 100 GeV) and a log-normal width of $\sigma_L \sim 1.4-2.8$. If the Galactic Center Gamma-Ray Excess were produced by pulsars with similar characteristics, Fermi would have already detected $N \sim 17-37$ of these sources, whereas only three such pulsar candidates have been identified. We conclude that the excess gamma-ray emission can originate from pulsars only if they are significantly less bright, on average, than those observed within globular clusters or in the Galactic Plane. This poses a serious challenge for pulsar interpretations of the Galactic Center Gamma-Ray Excess.