Gamma-ray Analysis of Pulsar Environments and Their Theoretical Explanation

Pulsars and their pulsar wind nebulae (PWNe) are unique laboratories for extreme astrophysical processes. This dissertation combines Fermi-LAT observations with a time-dependent leptonic PWN model (TIDE) to explore their gamma-ray emission. The model was validated on benchmark PWNe and applied to a systematic LAT search, leading to the discovery of new MeV-GeV candidates and the first population-level characterization. Several sources were modeled in detail, and predictions for potential TeV-emitting PWNe were tested against current and future observatories. Ultra-high-energy gamma-ray sources were also examined, revealing limits of standard leptonic scenarios. Beyond PWNe, stringent upper limits were obtained for the binary pulsar 1A 0535+262, and steady emission was detected from the globular cluster M5. Together, these results advance our understanding of pulsar environments and establish a framework for future multi-wavelength and next-generation gamma-ray studies.