Compression fronts from fast radio bursts

TL;DR

This work analyzes how ultrastrong FRB waves interact with magnetar winds, revealing a two-regime picture: stochastic heating and regular oscillations that drive a propagating compression front in the wind. By coupling microphysical particle heating in the fluid frame to macroscopic MHD evolution in a stationary wave packet, the authors derive a steady-front solution and show its relaxation dynamics, including radiative losses and memory effects. The study identifies critical radii, $r_{\rm damp}\sim10^{11}$ cm, $r_{\rm stoch}\sim10^{12}$ cm, and $r_{\star}\sim10^{13}$ cm, which demarcate damping, stochastic heating, and quasisteady compression zones, and demonstrates that FRBs must originate outside the damping zone to escape through magnetar winds. The results constrain FRB emission radii and link plasma heating, wave damping, and compression to observable FRB energetics, with implications for FRB progenitor models and wind parameters. Overall, the paper provides a self-consistent framework for predicting FRB propagation effects in magnetized, relativistic winds.

Abstract

When a fast radio burst (FRB) expands from its source through a surrounding tenuous plasma, it strongly heats and compresses the plasma at radii up to $\sim 10^{14}$cm. The likely central engines of FRBs are magnetars, and their ambient plasma at radii $r\gg 10^{10}$cm is a magnetized $e^\pm$ wind. We formulate basic equations of the FRB-plasma interaction, solve them numerically, and describe the physical picture of the interaction. We find the following: (1) FRBs emitted at $r<r_{\rm stoch}\sim 10^{12}$cm induce fast stochastic heating and strong compression of the wind, sweeping it like a broom. The outcome of this interaction is determined by the energy losses of the radio wave; we evaluate the parameter space where FRBs survive and escape. (2) At radii $r>r_{\rm stoch}$, FRB induces regular particle oscillations in the radio wave with the standard strength parameter $a$, and drives a compression wave in the wind. At $r>r_\star\sim 10^{13}$cm, the compression wave becomes locally quasisteady, with compression factor $1+a^2$. FRBs avoid damping if they are released into the wind medium outside $r_{\rm damp}\sim 10^{11}$cm.

Figures (10)

• Figure 1: Lorentz factor $\gamma$ of a test particle moving through the wave packet (averaged over the wave oscillation period). The upstream plasma is cold ($\tilde{\gamma}=1$) and static ($\kappa_{\rm u}=1$); it has gyro-frequency $\tilde{\omega}_B^{\rm u}=0.03\omega$ measured in the fluid frame. The test particle moves through the wave packet in the coordinate $\xi=t-z/c$ from right to left. The simulated packet consists of $10^3$ oscillations with an envelope described by Equation (\ref{['eq:packet']}) with $a_{\max}=4$, and the background field is described by Equations (\ref{['eq:EB_bg']}) and (\ref{['eq:bg']}). Different colors correspond to models with $\zeta=0$ (static background, $E_{\rm bg}=0$; black), $\zeta=0.4$ (blue), and $\zeta=1$ (green). For each model, dashed curve shows $\gamma$ measured in the fixed frame (where the upstream plasma is at rest), and solid curve shows $\tilde{\gamma}$ measured in the local fluid rest frame. All three solid curves overlap, demonstrating that $\tilde{\gamma}(\xi)$ is independent of the local fluid velocity $\beta_{\rm D}=E_{\rm bg}/B_{\rm bg}$ and follows the solution $\tilde{\gamma}^2=1+a^2(\xi)$ (red dotted curve, overlaping the solid curves).
• Figure 2: Average Lorentz factor $\tilde{\gamma}$ (measured in the local fluid rest frame) of particles interacting with the wave packet with amplitude $a_{\max}=30$. The upstream plasma is at rest ($\kappa_{\rm u}=1$) and has a small temperature $kT=10^{-2}m c^2$; its gyro-frequency is $\tilde{\omega}_B^{\rm u}=0.2\tilde{\omega}_{\rm u}$. The average $\tilde{\gamma}$ is calculated by tracking $4\times 10^3$ test particles. Background fields $B_{\rm bg}$ and $E_{\rm bg}$ are described by Equations (\ref{['eq:EB_bg']}) and (\ref{['eq:bg1']}). The model with $\zeta=0$ corresponds to no fluid acceleration in the wave packet and shows regular oscillations with $\tilde{\gamma}=\sqrt{1+a^2}$. The model with $\zeta=1$ demonstrates the transition to stochastic heating caused by the strong acceleration and compression of the fluid. Red dotted curves show the analytical predictions for regular oscillations ($\tilde{\gamma}=\sqrt{1+a^2}$) and stochastic heating (Equation (\ref{['eq:tg_stochastic']}) with $\chi=0.8$).
• Figure 3: Transition curve separating the regimes of regular oscillations and stochastic heating on the $a$-$b$ plane. Black circles show the results of 12 simulations: each circle shows $(a,b)$ at which the transition from regular oscillations to stochastic heating occurred as the particles moved through the wave packet. Dotted curve shows $b=(1/3)\sqrt{1+a^2}$. The region above the solid curve satisfies $b>2\sqrt{2}\,a$, which corresponds to wave amplitude $\tilde{E}_0<\tilde{B}_{\rm bg}/2$. In this region, the electromagnetic field satisfies $E^2<B^2$ throughout the radio wave oscillation, and stochastic heating is not expected. The radio wave cannot compress the background far above the solid line, as this would require energy exceeding the available energy of the wave.
• Figure 4: Top: relaxation of the non-radiative compression front $C(\xi)$ toward the steady-state $C_\star(\xi)$ (red curve, Equation (\ref{['eq:st']})) from an initial state with a uniform static plasma, $C=1$ and $\kappa=1$. Black curves show snapshots of the front at times $t$ indicated next to each curve in units of packet duration $T$. The wave packet (Equation \ref{['eq:packet']}) has $a_{\max}=\sqrt{24}$, which gives $w_{\max}=4$. The upstream magnetization is $\sigma_{\rm u}=10$. Bottom: evolution of $\kappa$ (black) from the initial $\kappa=1$ toward $\kappa_{\star}$ (red) in the same simulation.
• Figure 5: Relation between $\kappa=\gamma_{\rm D}(1+\beta_{\rm D})$ and $C=\rho/\rho_{\rm u}$ (here measured at the peak inside the compression front) during relaxation toward the final steady state. Black curve shows the simulation result (the model with $\sigma_{\rm u}=10$), and red dashed curve shows the relation $C=(\kappa^2+1)/2$ (equivalent to $\tilde{\rho}/\kappa=\rho_{\rm u}$ and uniform mass flux in $\xi$, $F_{\rm m}=\rho(c-v)$). Fluid density in the front closely tracks the steady-state solution $\tilde{\rho}=\kappa\rho_{\rm u}$ defined for an instantaneous profile of $\kappa(\xi)$, which slowly grows during relaxation. The correlated growth of $\kappa$ and $C$ stops when they reach $\kappa_{\max}^\star=5$ and $C_{\max}^\star=13$. Then, the fluxes of mass and $Q^-$ both become exactly uniform across the front, so a true steady state is achieved.