TeV blazar gamma-ray emission produced by a cooling pileup particle energy distribution function

We propose a time-dependent one-zone model based on a quasi-Maxwellian pileup'' distribution in order to explain the time-averaged high-energy emission of TeV blazars. The instantaneous spectra are the result of the synchrotron and synchrotron self-Compton emission of ultrarelativistic leptons. The particle energy distribution function is computed in a self-consistent way, taking into account an injection term of fresh particles, a possible pair creation term, and the radiative cooling of the particles. The source term is not a usual power law but rather a pileup distribution, which can result from the combination of stochastic heating via second-order Fermi processes and radiative cooling. To validate this approach, we have performed time-averaged fits of the well-known TeV emitter Mrk 501 during the 1997 flaring activity period, taking into account the attenuation of the high-energy component by cosmic diffuse infrared background and intrinsic absorption via the pair creation process. The model can reproduce very satisfactorily the observed spectral energy distribution. A high Lorentz factor is required to avoid strong pair production; in the case of smaller Lorentz factor, an intense flare in the GeV range is predicted because of the sudden increase of soft photon density below the Klein-Nishina threshold. The possible relevance of such a scenario is discussed.