The Fermi Large Area Telescope has observed a gamma-ray excess toward the center of the Galaxy at ~ GeV energies. The spectrum and intensity of the excess are consistent with the annihilation of dark matter with a mass of ~100 GeV and a velocity-averaged cross section of ~ 1e-26 cubic centimeter per second. In the meantime, a population of unresolved millisecond pulsars (MSPs) in the Galactic center remains a possible source of the excess. Furthermore, recent analyses have shown that the excess prefers the spatial morphology of the stellar bulge distribution in the Galactic center, supporting a MSP origin. The new discovery makes it imperative to further study the signals from MSPs.

This dissertation studies the gamma-ray emission from Galactic millisecond pulsars to provide new insights into the origin of the Galactic center excess. Using the GALPROP code, we simulate the propagation of e± injected by the putative MSPs in the Galactic bulge and calculate the inverse Compton (IC) emission caused by the e± losing energy in the interstellar radiation field. We find recognizable features in the spatial maps of the IC. Above TeV energies, the IC morphology tends to follow the distribution of the injected e±. Then, we study the Cherenkov Telescope Array (CTA) sensitivity to the IC signal from MSPs. We find that the CTA has the potential to robustly discover the IC signature when the MSP e± injection efficiencies are in the range ≈ 2.9-74.1%. The CTA can also discriminate between an MSP and a dark matter origin for the radiating e± based on their different spatial maps.

Next, we analyze the Fermi data from directions of Galactic globular clusters. The globular clusters are thought to be shining in gamma rays because of the MSP population they host. By analyzing their gamma-ray spectra, we reveal evidence for an IC component in the high-energy tail of Fermi data. Based on the IC component in the globular cluster spectra, the e± injection efficiency of millisecond pulsars is estimated to be slightly smaller than 10%.

Finally, we study the spatial morphology of the 511 keV signal toward the Galactic center using data from INTEGRAL/SPI. We confirm that the 511 keV signal also traces the old stellar population in the Galactic bulge, which is similar to the Fermi GeV excess. Using a 3D smoothing kernel, we find that the signal is smeared out over a characteristic length scale of 150 ± 50 pc. We show that positron propagation prior to annihilation can explain the overall phenomenology of the 511 keV signal.