Stochastic acceleration and the evolution of spectral distributions in SSC sources: A self consistent modeling of blazars' flares

Abstract

Broad-band spectral distributions of non-thermal sources, such as those of several known blazars, are well described by a log-parabolic fit. The second degree term in these fits measures the curvature in the spectrum. In this paper we investigate whether the curvature parameter observed in the spectra of the synchrotron emission can be used as a fingerprint of stochastic acceleration. We use a diffusion equation in momentum space to investigate the formation of log-parabolic shape in the electron distribution, and how it's curvature is related to the diffusion term. We apply these results to some observed trends, such as the anticorrelation between the peak energy and the curvature term observed in the spectra of Mrk 421, and a sample of BL Lac objects whose synchrotron emission peaks at X-ray energies.