Millisecond Pulsars in Dense Star Clusters: Evolution, Scaling Relations, and the Galactic-Center Gamma-ray Excess
The number of millisecond pulsars (MSPs) observed in Milky Way globular clusters has increased explosively in recent years, but the underlying population is still uncertain due to observational biases. We use state-of-the-art $N$-body simulations to study the evolution of MSP populations in dense star clusters. These cluster models span a wide range in initial conditions, including different initial masses, metallicities, and virial radii, which nearly cover the full range of properties exhibited by the population of globular clusters in the Milky Way. We demonstrate how different initial cluster properties affect the number of MSPs, for which we provide scaling relations as a function of cluster age and mass. As an application, we use our formulae to estimate the number of MSPs delivered to the Galactic Center from inspiralling globular clusters to probe the origin of the Galactic-Center gamma-ray excess detected by Fermi. We predict about $400$ MSPs in the Galactic Center from disrupted globular clusters, which can potentially explain most of the observed gamma-ray excess.