Formation of Very Hard Gamma-Ray Spectra of Blazars in Leptonic Models

The very high energy (VHE) γ-ray spectra of some TeV blazars, after being corrected for absorption in the extragalactic background light (EBL), appear unusually hard, which poses challenges to conventional acceleration and emission models. We investigate the parameter space that allows the production of such hard TeV spectra within time-dependent leptonic models, both for synchrotron self-Compton and external Compton scenarios. In the context of the interpretation of very hard γ-ray spectra, time-dependent considerations become crucial because even extremely hard, initial electron distributions can be significantly deformed due to radiative energy losses. We show that very steep VHE spectra can be avoided if adiabatic losses are taken into account. Another way to keep extremely hard electron distributions in the presence of radiative losses is to assume stochastic acceleration models that naturally lead to steady-state, relativistic, Maxwellian-type particle distributions. We demonstrate that in either case leptonic models can reproduce TeV spectra as hard as E _γ dN/dE _γvpropE _γ. Unfortunately, this limits, to a large extent, the potential of extracting EBL from γ-ray observations of blazars.