Radiative signatures of electron-ion shocks in BL Lac type objects

¹ Max-Planck-Institut für Physik, Boltzmannstr. 8, DE-85748 Garching, Germany
² Max-Planck-Institut für Plasmaphysik, Boltzmannstr. 2, DE-85748 Garching, Germany

^⋆ Corresponding authors: aarbet@mpp.mpg.de; artem.bohdan@ipp.mpg.de; frank.rieger@ipp.mpg.de

Received: 10 April 2025
Accepted: 26 August 2025

Abstract

Aims. Plasma shock waves stand out as one of the most promising sites of efficient particle acceleration in extragalactic jets. In electron-ion plasma shocks, electrons can be heated up to large Lorentz factors, making them an attractive scenario to explain the high minimum electron Lorentz factors regularly needed to describe the emission of BL Lac type objects. Still, the (relativistic) thermal electron component is commonly neglected when modelling the observations, although it holds key information on the shock properties.

Methods. Considering a shock acceleration scenario, we modelled the broadband emission of the archetypal high synchrotron peaked blazar Markarian 421; we employed particle distributions that included a thermal (relativistic) Maxwellian component at low energies followed by a non-thermal power law, as motivated by particle-in-cell simulations. The observations, in particular in the optical/UV and MeV-GeV bands, efficiently restricted the non-thermal emission from the Maxwellian electrons, which we used to derive constraints on the basic properties, such as the fraction ϵ_e of the total shock energy stored in the non-thermal electrons.

Results. The best-fit model yields a non-thermal electron power law with an index of ∼2.4, close to predictions from shock acceleration. Successful fits are obtained when the ratio between the Lorentz factor at which the non-thermal distribution begins (γ_nth) and the dimensionless electron temperature (θ) satisfies γ_nth/θ ≲ 8. Since γ_nth/θ controls ϵ_e, the latter limit implies that at least ϵ_e ≈ 10% of the shock energy is transferred to the non-thermal electrons. These results are almost insensitive to the shock velocity γ_sh, but radio observations indicate γ_sh ≳ 5 since for lower shock velocities the fluxes in the millimetre band are overproduced by the Maxwellian electrons. Therefore, if shocks drive the particle energisation, our findings indicate that they operate in the mildly to fully relativistic regime with efficient electron acceleration. This paper lays the ground for future works, in which we will use plasma simulations to investigate if, and under which conditions, the findings presented here can be reproduced.