Formation of hard very-high energy spectra of blazars in leptonic models

TL;DR

This paper explores how leptonic models can produce very hard TeV gamma-ray spectra in blazars, considering time-dependent effects and different acceleration mechanisms, which impacts the use of such spectra to study the extragalactic background light.

Contribution

It demonstrates that leptonic models, including adiabatic losses and stochastic acceleration, can account for extremely hard VHE spectra in blazars, challenging previous assumptions.

Findings

Leptonic models can produce spectra as hard as Eγ dN/dEγ ∝ Eγ.

Adiabatic losses help avoid steep spectra in time-dependent models.

Stochastic acceleration leads to steady-state Maxwellian electron distributions.

Abstract

The very high energy (VHE) $\gamma$-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 (SSC) and external Compton (EC) scenarios. In the context of interpretation of very hard $\gamma$-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 $E_{\gamma} dN/dE_{\gamma} \propto E_{\gamma}$. Unfortunately this limits, to a large extend, the potential of extracting EBL from $\gamma$-ray observations of blazars.