"Leading blob" model in a stochastic acceleration scenario: the case of the 2009 flare of Mkn~501

Evidence for very hard, intrinsic $\gamma$-ray source spectra, as inferred after correction for absorption in the extragalactic background light (EBL), has interesting implications for the acceleration and radiation mechanisms acting in blazars. A key issue so far has been the dependance of the hardness of the $\gamma$-ray spectrum on different existing EBL models. The recent {\it Fermi} observations of Mkn~501 now provide additional evidence for the presence of hard intrinsic $\gamma$-ray spectra independent of EBL uncertainties. Relativistic Maxwellian-type electron energy distributions that are formed in stochastic acceleration scenarios offer a plausible interpretation for such hard source spectra. Here we show that the combined emission from different components with Maxwellian-type distributions could in principle also account for more softer and broader, power law-like emission spectra. We introduce a “leading blob” scenario, applicable to active flaring episodes, when one (or few) of these components become distinct over the “background” emission, producing hard spectral features and/or hardening of the observed spectra. We show that this model can explain the peculiar high-energy characteristics of Mkn~501 in 2009, with evidence for flaring activity and strong spectral hardening at the highest $\gamma$-ray energies.