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

We propose a time-dependent one-zone model based on a quasi-Maxwellian pile-up' 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 (SSC) of ultra-relativistic leptons. The particle energy distribution function (EDF) is computed in a self-consistent way, taking into account an injection term of fresh particles, a possible pair creation term, and the particles radiative cooling. The source term is not a usual power-law but rather a pile-up’ distribution, which can result from the combination of a stochastic heating via second order Fermi process 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 (DIrB) and intrinsic absorption via the pair creation process. The model can reproduce very satisfactorily the observed spectral energy distribution (SED). 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 due to the sudden increase of soft photons density below the Klein-Nishina threshold. The possible relevance of such a scenario is discussed.