On spectral and temporal variability in blazars and gamma-ray bursts

A simple model for variability in relativistic plasma outflows is studied, in which nonthermal electrons are continuously and uniformly injected in the comoving frame over a time interval Delta t. The evolution of the electron distribution is assumed to be dominated by synchrotron losses, and the energy and time dependence of the synchrotron and synchrotron self-Compton (SSC) fluxes are calculated for a power-law electron injection function with index s = 2. The mean time of a flare or pulse measured at photon energy E with respect to the onset of the injection event varies as E(-1/2) and E(-1/4) for synchrotron and SSC processes, respectively, until the time approaches the limiting intrinsic mean time (I + z)Delta t/(2D), where z is the redshift and D is the Doppler factor. This dependence is in accord with recent analyses of blazar and gamma-ray burst (GRB) emissions and suggests a method to discriminate between external Compton and SSC models of high-energy gamma radiation from blazars and GRBs. The qualitative behavior of the X-ray spectral index/flux relation observed from BL Lacertae objects can be explained with this model. This demonstrates that synchrotron losses are primarily responsible for the X-ray variability behavior and strengthens a new test for beaming from correlated hard X-ray/TeV observations.