Temporal and Spectral Variabilities of High-Energy Emission from Blazars Using Synchrotron Self-Compton Models

Multiwavelength observations of blazars such as Mrk 421 and Mrk 501 show that they exhibit strong short time variabilities in flarelike phenomena. Working from the homogeneous synchrotron self-Compton (SSC) model and assuming that time variability of the emission is initiated by changes in the injection of nonthermal electrons, we perform detailed temporal and spectral studies of a purely cooling plasma system using parameters appropriate to blazars. One important parameter is the total injected energy ℰ, and we show how the synchrotron and Compton components respond as ℰ varies. When the synchrotron and SSC components have comparable peak fluxes, we find that the SSC process contributes strongly to the electron cooling and that the whole system is nonlinear; thus, simultaneously solving electron and photon kinetic equations is necessary. In the limit of the injection-dominated situation when the cooling timescale is long, we find a unique set of model parameters that are fully constrained by observable quantities. In the limit of the cooling-dominated situation, TeV emissions arise mostly from a cooled electron distribution and the Compton scattering process is always in the Klein-Nishina regime, which gives the TeV spectrum a large curvature. Furthermore, even in a single-injection event, the multiwavelength light curves do not necessarily track each other because the electrons that are responsible for those emissions might have quite different lifetimes. We discuss in detail how one could infer important physical parameters using the observed spectra. In particular, we could infer the size of the emission region by looking for exponential decay in the light curves. We could also test the basic assumption of the SSC model by measuring the difference in the rate of peak energy changes of synchrotron and SSC peaks. We also show that the trajectory in the photon index-flux plane evolves clockwise or counterclockwise depending on the value of ℰ and the observed energy bands.