Synchrotron self-Compton emission by relativistic electrons under stochastic acceleration: application to Mrk 421 and Mrk 501

Abstract

We examine the applicability of the stochastic electron acceleration to two high synchrotron peaked blazars, Mrk 421 and Mrk 501, assuming synchrotron self-Compton emission of gamma-rays. Our model considers an emitting region moving at relativistic speed, where non-thermal electrons are accelerated and attain a steady-state energy spectrum together with the photons they emit. The kinetic equations of the electrons and photons are solved numerically, given a stationary wave number spectrum of the magnetohydrodynamic (MHD) disturbances, which are responsible for the electron acceleration and escape. Our simple formulation appears to reproduce the two well-sampled, long-term averaged photon spectra. In order to fit the model to the emission component from the radio to the X-ray bands, we need both a steeper wave spectral index than the Kolmogorov spectrum and efficient particle escape. Although the model provides a natural explanation for the high-energy cutoff of the electron energy distribution, the derived physical parameters raise a problem with an energy budget if the MHD waves with the Alfv{\'e}n velocity are assumed to be the acceleration agent.