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

A. Arbet-Engels, A. Bohdan, F. Rieger, D. Paneque, F. Jenko

TL;DR

This study investigates radiative signatures of electron–ion shocks in BL Lac jets by incorporating a PIC-motivated relativistic Maxwellian electron component alongside a nonthermal tail in the downstream distribution. Using a one-zone SSC model, the authors fit Mrk 421’s broadband SED and constrain the energy partition between thermal and nonthermal electrons through the ratio $γ_{ m nth}/θ$, finding $γ_{ m nth}/θ \lesssim 8$ and $θ \gtrsim 500$, which imply $Δ \gtrsim 0.4$ and $ε_e \gtrsim 0.1$; the best-fit case yields $γ_{ m sh} \approx 5.3$ and a modest jet power $L_{ m jet, kin} \lesssim 10^{45}$ erg s$^{-1}$. The results map onto shock parameters, linking $θ$ to the upstream Lorentz factor $γ_0$ and deriving an upstream magnetisation $σ \approx 0.15/a_B^2$, thereby providing a quantitative bridge to PIC simulations and supporting a scenario with mildly relativistic shocks and efficient electron acceleration. This framework advances the understanding of particle energisation in blazar jets and motivates future PIC-driven tests and multi-zone modelling to assess robustness across jet conditions.

Abstract

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 $ε_e$ 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 ($γ_{\rm nth}$) and the dimensionless electron temperature ($θ$) satisfies $γ_{\rm nth}/θ\lesssim 8$. Since $γ_{\rm nth}/θ$ controls $ε_e$, the latter limit implies that at least $ε_e \approx 10\%$ of the shock energy is transferred to the nonthermal electrons. These results are almost insensitive to the shock velocity $γ_{\rm sh}$, but radio observations indicate $γ_{\rm sh} \gtrsim 5$ 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.

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

TL;DR

This study investigates radiative signatures of electron–ion shocks in BL Lac jets by incorporating a PIC-motivated relativistic Maxwellian electron component alongside a nonthermal tail in the downstream distribution. Using a one-zone SSC model, the authors fit Mrk 421’s broadband SED and constrain the energy partition between thermal and nonthermal electrons through the ratio , finding and , which imply and ; the best-fit case yields and a modest jet power erg s. The results map onto shock parameters, linking to the upstream Lorentz factor and deriving an upstream magnetisation , thereby providing a quantitative bridge to PIC simulations and supporting a scenario with mildly relativistic shocks and efficient electron acceleration. This framework advances the understanding of particle energisation in blazar jets and motivates future PIC-driven tests and multi-zone modelling to assess robustness across jet conditions.

Abstract

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 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 () and the dimensionless electron temperature () satisfies . Since controls , the latter limit implies that at least of the shock energy is transferred to the nonthermal electrons. These results are almost insensitive to the shock velocity , but radio observations indicate 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.

Paper Structure

This paper contains 7 sections, 15 equations, 5 figures, 1 table.

Table of Contents

  1. Introduction
  2. Model setup
  3. Application to the TeV BL Lac object Mrk 421
  4. Results
  5. Relationship to shock parameters
  6. Conclusions
  7. SED scans

Figures (5)

  • Figure 1: Sample of electron distributions using Eq. \ref{['eq:electron_distribution']} for different $\gamma_{\rm nth} / \theta$ values ranging from 6 to 15. The black dashed line represents $\theta$, which is fixed to 500. The colored dotted lines give the location of $\gamma_{\rm nth}$ where the transition from the Maxwellian to the nonthermal component occurs. Here, we arbitrarily set $\gamma_{\rm br}=2\times10^5$ and $\gamma_{\rm cut}=7\times10^5$ and $p_1=2.4$.
  • Figure 2: SED models for $\theta=100$ (left) and $\theta=500$ (right), corresponding to a shock velocity (in the upstream frame) of $\gamma_{\rm sh}=1.8$ and $\gamma_{\rm sh}=5.3$, respectively. We refer the reader to Sect. \ref{['sec:shock_simul']} for more details on the connection between $\theta$ and $\gamma_{\rm sh}$. Solid lines, from light violet to dark violet, cover three different $\gamma_{\rm nth}/\theta$ ratios, 4, 7, and 10. The SED from abdo:2011 is plotted with grey markers.
  • Figure 3: $\chi^2-\chi^2_{\rm min}$ as a function of $\gamma_{\rm nth}/\theta$, for $\theta ~=~[100, 300, 500, 1500]$, equivalent to a shock velocity of $\gamma_{\rm sh}~=~[1.8, 3.5, 5.3, 13.9]$. We refer the reader to Sect. \ref{['sec:shock_simul']} for more details on the connection between $\theta$ and $\gamma_{\rm sh}$. $\chi^2_{\rm min}$ is the minimum $\chi^2$ for a given $\theta$. The vertical dashed lines mark the $\gamma_{\rm nth}/\theta$ value beyond which $\chi^2-\chi^2_{\rm min}>9$.
  • Figure 4: $\Delta$ (top panel) and $\epsilon_e$ (lower panel) as functions of $\gamma_{\rm nth}/\theta$ computed using Eq. \ref{['eq:Delta_def']} and Eq. \ref{['eq:epsilon_e']}, respectively. The allowed region lies left from the black vertical dashed line placed at $\gamma_{\rm nth}/\theta=8$, which is roughly the maximum value that we found compatible with the measurements.
  • Figure 5: SED models for $\theta=[100,300,500, 1500]$. Solid lines, from light violet to dark violet, cover three different $\gamma_{\rm nth}/\theta = [6, 8, 9, 9]$, i.e. the transition region where the fit degrades. For each $\theta$, the corresponding shock velocity $\gamma_{\rm sh}$ is also given. We refer the reader to Sect. \ref{['sec:shock_simul']} for more details on the connection between $\theta$ and $\gamma_{\rm sh}$. The SED from abdo:2011 is plotted with grey markers.