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

Shocks are promising sites of particle acceleration in extragalactic jets. In electron-ion 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 objects. Still, the thermal electron component is commonly neglected when modelling the observations, although it holds key informations on the shock properties. We model the broadband emission of the HSP blazar Mrk421 employing particle distributions that include a thermal relativistic Maxwellian component at low energies followed by a nonthermal power-law, as motivated by PIC simulations. The observations in the optical/UV and MeV-GeV bands efficiently restrict the nonthermal emission from the Maxwellian electrons, which we use to derive constraints on the basic properties, such as the fraction $\epsilon_e$ of the total shock energy stored in the nonthermal electrons. The best-fit model yields a nonthermal 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 nonthermal distribution begins ($\gamma_{\rm nth}$) and the dimensionless electron temperature ($\theta$) satisfies $\gamma_{\rm nth}/\theta \lesssim 8$. Since $\gamma_{\rm nth}/\theta$ controls $\epsilon_e$, the latter limit implies that at least $\epsilon_e \approx 10\%$ of the shock energy is transferred to the nonthermal electrons. These results are almost insensitive to the shock velocity $\gamma_{\rm sh}$, but radio observations indicate $\gamma_{\rm sh} \gtrsim 5$ since for lower shock velocities the radio fluxes are overproduced by the Maxwellian electrons. If shocks drive the particle energisation, our findings indicate that they operate in the mildly to fully relativistic regime with efficient electron acceleration.