Nature's particle accelerators, such as Pulsars, Pulsar Wind Nebulae, Active GalacticNuclei and Supernova Remnants accelerate charged particles to very high energies that thenproduce high energy photons. The particle acceleration mechanisms and the high energyphoton emission mechanisms are poorly understood phenomena. These mechanisms canbe understood either by studying individual sources in detail or, alternatively, using thecollective properties of a sample of sources. Recent development of GeV survey instruments,such as Fermi-LAT, and TeV survey instruments, such as Milagro, provides a large sampleof high energy gamma-ray flux measurements from galactic and extra-galactic sources. Inthis thesis I provide constraints on GeV and TeV radiation mechanisms using the X-ray-TeVcorrelations and GeV-TeV correlations.My data sample was obtained from three targeted searches for extragalactic sourcesand two targeted search for galactic sources, using the existing Milagro sky maps. The firstextragalactic candidate list consists of Fermi-LAT GeV extragalactic sources, and the secondextragalactic candidate list consists of TeVCat extragalactic sources that have been detectedby Imaging Atmospheric Cerenkov Telescopes (IACTs). In both extragalactic candidatelists Markarian 421 was the only source detected by Milagro. A comparison between theMarkarian 421 time-averaged flux, measured by Milagro, and the flux measurements oftransient states, measured by IACTs, is discussed. The third extragalactic candidate listis a list of potential TeV emitting BL Lac candidates that was synthesized using X-rayobservations of BL Lac objects and a Synchrotron Self-Compton model. Milagro's sensitivitywas not sufficient to detect any of those candidates. However, the 95% confidence fluxupper limits of those sources were above the predicted flux. Therefore, these results provideevidence to conclude that the Synchrotron Self-Compton model for BL Lac objects is still aviable model. Targeted searches for galactic candidates were able to measure TeV emissionassociated with 14 Fermi-LAT GeV pulsars.In this thesis I also presented a new multi-wavelength technique that I developed to isolatethe flux correlation factor (fΩ ) of pulsars as a function of pulsar spin down luminosity. Thecorrelation between fΩ and pulsar spin-down luminosity for a Fermi-LAT GeV pulsar samplewas measured using the measurements obtained in the Milagro targeted search performedfor galactic sources and from the literature. The measured correlation has some featuresthat favor the Outer Gap model over the Polar Cap, Slot Gap and One Pole Caustic modelsfor pulsar emission in the energy range of 0.1 to 100 GeV. However, these simulated modelsfailed to explain many other important pulsar population characteristics. Therefore, furtherimprovements on the galactic pulsar population simulations are needed to provide tighterconstraints.
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