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All of the extragalactic objects so far detected in high energy $\gamma$-rays ($>$50 MeV) by the EGRET instrument aboard CGRO are highly variable radio loud sources having compact core emission. These properties are thought to result from nonthermal radiation in a compact relativistic jet which is occassionally enhanced by propagating shock waves. At some level, the electrons which produce the synchrotron photons will scatter those photons up to $\gamma$-ray energies. We use numerical simulations to investigate the time evolution of the synchrotron self-Compton flux in a propagating shock. Our simulations include the effects of gradients in the magnetic field, electron density and electron energy, relativistic Doppler boosting, and time delays. We calculate the Compton emissivity throughout the jet, at each point integrating over the electron distribution and the frequency and angular dependence of the synchrotron photon distribution. We present the volume integrated Compton emissivity at several epochs.
We find that the $\gamma$-ray flare proceeds from a rapid onset to decay at a rate strongly dependent on photon energy. We present predictions of the expected amplitude, duration and spectral evolution of a $\gamma$-ray flare and its related synchrotron flare.
