arXiv1999
The time dependent synchrotron emission from relativistic jets, and the relation between the synchrotron and ERC emission is considered within the framework of the radiative front model. The timescale and profile of the optically thin emission are shown to be determined, in this model, by the shock formation radius, the thickness of expelled fluid slab and the variation of the front's parameters due to its transverse expansion. For a range of reasonable conditions, a variety of flare shapes can be produced, varying from roughly symmetric with exponential rises and decays, as often seen in blazars, to highly asymmetric with a fast rise and a much slower, power law decay, as seen in GRB afterglows. The onset, duration, and fluence of low-frequency (below the initial turnover frequency) and hard gamma-ray (above the initial gamma-spheric energy) outbursts are limited by opacity effects; the emission at these energies is quite generally delayed and, in the case of sufficiently short length outbursts, severely attenuated. The observational consequences are discussed. One distinctive prediction of this model is that in a single, powerful source, the upper cutoff of the gamma-ray spectrum should be correlated with the timescale of the outburst and with the amplitude of variations at long wavelengths (typically radio to millimeter).