A Fermi-LAT Study of Globular Cluster Dynamical Evolution in the Milky Way: Millisecond Pulsars as the Probe

Using archival Fermi-LAT data with a time span of similar to 12 yr, we study the population of Millisecond Pulsars (MSPs) in Globular Clusters (GlCs) and investigate their dependence on cluster dynamical evolution in the Milky Way. We show that the gamma-ray luminosity (L-gamma) and emissivity (i.e., epsilon(gamma) = L-gamma/M, with M the cluster mass) are good indicators of the population and abundance of MSPs in GlCs, and they are highly dependent on the dynamical evolution history of the host clusters. Specifically speaking, the dynamically older GlCs with more compact structures are more likely to have larger L-gamma and epsilon(gamma), and these trends can be summarized as strong correlations with cluster stellar encounter rate Gamma and the specific encounter rate (Lambda = Gamma/M), with L-gamma proportional to Gamma(0.70 +/- 0.11) and epsilon(gamma) proportional to Lambda(0.73 +/- 0.13) for dynamically normal GlCs. However, as GlCs evolve into deep core collapse, these trends are found to be reversed, implying that strong encounters may have lead to the disruption of Low-Mass X-ray Binaries and ejection of MSPs from core-collapsed systems. Besides, the GlCs are found to exhibit larger epsilon(gamma) with increasing stellar mass function slope (epsilon(gamma) proportional to 10((0.57 +/- 0.1)alpha)), decreasing tidal radius (epsilon(gamma) proportional to R-t(-1.0 +/- 0.22)) and distances from the Galactic Center (GC, epsilon(gamma) proportional to R-gc(-1.13 +/- 0.21) ). These correlations indicate that, as GlCs losing kinetic energy and spiral in toward the GC, tidal stripping and mass segregation have a preference in leading to the loss of normal stars from GlCs, while MSPs are more likely to concentrate to cluster center and be deposited into the GC. Moreover, we gauge epsilon(gamma) of GlCs is similar to 10-1000 times larger than the Galactic bulge, the latter is thought to reside thousands of unresolved MSPs and may be responsible for the GC gamma-ray excess, which supports that GlCs are generous contributors to the population of MSPs in the GC.