Variability in the synchrotron self-Compton model of blazar emission

We present a model of the spectra of gamma-ray emitting blazars in which a single homogeneous emission region both emits synchrotron photons directly and scatters them to high (gamma-ray) energy before emission (a ``synchrotron self-Compton'' or SSC model). In contrast to previous work, we follow the full time dependent evolution of the electron and photon spectra, assuming a power-law form of the electron injection and examine the predictions of the model with regard to variability of the source. We apply these computations to the object Mkn 421, which displayed rapid variability in its X-ray and TeV emission during a multiwavelength campaign in 1994. This observation strongly implies that the same population of electrons produces the radiation in both energy bands. By fitting first the observed quiescent spectrum over all 18 orders of magnitude in frequency, we show that the time dependence of the keV/TeV flare could have been the result of a sudden increase in the maximum energy of the injected electrons. We show also that different types of flare may occur in this object and others, and that the energy band most sensitive to the properties of the acceleration mechanism is the X-ray band.