The Galactic Millisecond Pulsar Population: Implications for the Galactic Center Excess

The Galactic Center Excess (GCE) is an extended gamma-ray source in the central region of the Galaxy found in Fermi Large Area Telescope data. In recent years it has become apparent that the GCE may not be spherically symmetric, but may be spatially correlated with the distribution of stellar mass in the Galactic bulge, potentially favoring an unresolved population of millisecond pulsars (MSPs) scenario. In this thesis, we perform detailed modelling of the Galactic MSP population. Including in our model the spin down between formation and observation, we find a model in which luminosity $L \propto E_{\rm cut}^{1.2 \pm 0.3} B^{0.1 \pm 0.4} \dot{E}^{0.5 \pm 0.1}$ provides the best fit to the data, where $E_{\rm cut}$ is spectral energy cutoff, $B$ is magnetic field strength, and $\dot{E}$ is the spin-down power. Due to differing star formation histories it is expected that the MSPs in the Galactic bulge are older and therefore dimmer than those in the Galactic disk. Our results demonstrate that we do not require that there is anything systematically different about the inner Galaxy MSPs to explain the GCE. In the "recycling" channel of MSP formation the neutron star forms from a core collapse supernovae that undergoes a random "kick" due to the asymmetry of the explosion. This would imply a smoothing out of the spatial distribution of the MSPs. We use N-body simulations to model how the MSP spatial distribution changes. We estimate the probability distribution of natal kick velocities using the resolved gamma-ray MSP proper motions, where MSPs have velocities relative to circular motion of 77 +/- 6 km/s, as determined as part of our Galactic MSP population model. We find that, due to the natal kicks, there is an approximately 10% increase in each of the bulge MSP spatial distribution dimensions and also the bulge MSP distribution becomes less boxy but is still far from being spherical.