Synchrotron Self-Compton Emission by Relativistic Electrons under Stochastic Acceleration: Application to Mrk 421 and Mrk 501

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.