Magnetized Shocks Mediated by Radiation from Leptonic and Hadronic Processes

TL;DR

The paper tackles radiation-mediated shocks in mildly magnetized relativistic outflows by solving steady-state hydrodynamics and radiative transfer with explicit leptonic and hadronic emission, for $Γ_u = 10$ and $σ_u$ spanning from 0 to 0.3. It demonstrates that synchrotron self-absorption reshapes the upstream and accelerates subshock formation at higher magnetizations, while proton acceleration introduces a high-energy photon tail that has little impact on the shock dynamics. By incorporating hadronic channels through AM$^3$ and a downstream feedback loop, it shows that $pp$ and $pγ$ processes primarily affect the high-energy spectrum rather than the shock structure, with leptonic processes remaining the dominant driver of the radiative feedback. These results underscore the need to couple shock physics to full particle- and photon-transport to forecast the multi-messenger emission from transients.

Abstract

Shocks in astrophysical transients are key sites of particle acceleration. If the shock upstream is optically thick, radiation smoothens the velocity discontinuity at the shock (radiation-mediated shocks). However, in mildly magnetized outflows, a collisionless subshock can form, enhancing the efficiency of particle acceleration. We solve the hydrodynamic equations of a steady-state, radiation-mediated shock together with the radiative transfer equations accounting for electron and proton acceleration. Our goal is to explore the impact of the magnetic field and non-thermal radiation on the shock structure and the resulting spectral distribution of photons. To this purpose, we assume a relativistic upstream fluid velocity ($Γ_u = 10$) and investigate shock configurations with variable upstream magnetization ($σ_u = 0$, $10^{-8}$, $10^{-4}$, $0.1$, and $0.3$). We find that synchrotron self-absorption alters the shock profile for $σ_u \gtrsim 10^{-8}$, with resulting changes up to $100\%$ in the bulk Lorentz factor at the shock; for $σ_u \gtrsim 0.1$, a prominent subshock forms. The spectral energy distributions of upstream- and downstream-going photons are also altered. Radiative processes linked to accelerated protons are responsible for a high-energy ($\gtrsim 10$ GeV) tail in the photon spectrum; however, the radiation flux and pressure are negligibly affected with consequent minor impact on the shock structure. Our work highlights the importance of coupling the shock hydrodynamics to the transport of photons, electrons, protons, and intermediate particles to forecast the multi-messenger emission from astrophysical transients.

Figures (10)

• Figure 1: Sketch of the bulk Lorentz factor profile of a radiation-mediated magnetohydrodynamic shock along the $z$ direction. The vertical orange arrows represent the magnetic field lines, which are more intense in the downstream region, where the proton density is higher. The magnetic field component parallel to the shock normal does not directly affect the shock dynamics and it is not plotted here for simplicity. We distinguish four regions characterizing the shock structure: the far upstream, the deceleration region, the immediate downstream, and the thermal equilibrium region, from left to right, respectively. A subshock forms at $z=0$ allowing for efficient particle acceleration.
• Figure 2: Isocontours of $w_d/\sigma_d$ (dashed black lines) in the plane spanned by $\sigma_u$ and $\Gamma_u$. The color scale represents the contours of the energy budget converted from kinetic energy into other forms of energy ($L_{\rm TRP}/L_u$). The red stars mark the representative configurations adopted in this work. For fixed $\Gamma_u$, $w_d/\sigma_d$ and $\Delta L_{\rm ud}/L_u$ decrease as $\sigma_u$ increases.
• Figure 3: Flow chart summarizing the iterative approach adopted to solve the hydrodynamic and kinetic equations for a steady-state shock. We follow the evolution of the upstream (US) and downstream (DS) fluid and radiation properties, the related shock structure, as well as the photon spectral distribution accounting for leptonic and hadronic processes.
• Figure 4: Bulk Lorentz factor, plasma temperature, fraction of positrons, radiation pressure, and radiation flux as functions of $\hat{\tau}$, from top to bottom and for our five benchmark configurations (cf. Fig. \ref{['fig:sim_para']}): $\sigma_u = 0$ in blue, $\sigma_u = 10^{-8}$ in yellow, $\sigma_u = 10^{-4}$ in olive green, $\sigma_u = 0.1$ in red, and $\sigma_u = 0.3$ in black, respectively. The upstream (downstream) profiles are shown in the left (right) panels. As evident from the right panels, for $\sigma_u \neq 0$, a subshock forms and becomes more prominent as $\sigma_u$ increases; its position is marked with a vertical dotted line.
• Figure 5: Photon spectral intensity at the subshock for our five benchmark configurations with $\Gamma_u = 10$ and $\sigma_u = 0$, $10^{-8}$, $10^{-4}$, $0.1$, and $0.3$ from top left to bottom right, respectively. The radiation intensities for the upstream-going ($\mu_{\rm sh} = -1$) and downstream-going ($\mu_{\rm sh} = 1$) directions are plotted with dashed and solid lines, respectively. For $\sigma_u \lesssim 10^{-4}$, the peak frequency of the downstream photon spectrum is about two orders of magnitude larger than the one of the upstream spectrum because the upstream temperature and bulk Lorenz factor are larger than the downstream ones. For $\sigma_u \gtrsim 0.1$, the photon spectrum flattens due to non-negligible synchrotron losses.