Verification of the diffusive shock acceleration in Mrk 501

Abstract: The present work considers a plane shock front propagating along a cylindrical jet. Electrons experience the diffusive shock acceleration around the shock front, and subsequently drift away into the downstream flow in which they emit most of their energy. Assuming a proper boundary condition at the interface between the shock zone and the downstream zone, we solve the transport equation for the electrons in the downstream flow zone, where the combined effects of escape, synchrotron and IC cooling in the Thomson regime are taken into account. Using the electron spectrum obtained in this manner we calculate the multi-wavelength spectral energy distribution of Mrk 501 in the synchrotron self-Compton scenario. We check numerically if the Klein-Nishina cross-section could be approximated to the Thomsom regime. We consider whether the model results yield physically reasonable parameters, and further discuss some of implications of the model results. It suggests that the process of diffusive shock acceleration operates in the outflow of Mrk 501.