Global Kinetic Simulations of Monster Shocks and Their Emission

TL;DR

This work investigates how nonlinear steepening of fast magnetosonic waves in a magnetar's dipolar magnetosphere forms monster shocks and emits GHz precursor radiation. Using the first 2D global PIC simulations with realistic dipole geometry, the authors show shocks forming near the nonlinear radius with an upstream Lorentz factor γ_u that scales linearly with the background magnetization σ_{bg,nl} and the wave wavelength λ, and they quantify the angular range over which precursor waves arise. They derive FRB-relevant predictions for precursor spectra and energetics, e.g., ν_peak(r_{nl}) ≈ 0.22 B_{15}^{1/2} L_{42}^{-1/4} M_6 P_0^{-1} ω_4 GHz and L_R(r_{nl}) ≈ 5.4×10^{37} B_{15}^{-1/2} L_{42}^{3/4} ω_4^{-1} erg s^{-1}, with emission concentrated between r_{nl} and about 3 r_{nl} and Δt_obs ~ 0.5 ω_4^{-1} ms. The results support monster shocks as a plausible FRB mechanism under reasonable magnetar parameters, while also highlighting the importance of global geometry, obliquity, and cooling processes for precise spectral and polarization predictions. Future work should extend to 3D, include radiative cooling and pair production, and explore observer-angle dependencies.

Abstract

Fast magnetosonic waves are one of the two low-frequency plasma modes that can exist in a neutron star magnetosphere. It was recently realized that these waves may become nonlinear within the magnetosphere and steepen into some of the strongest shocks in the universe. These shocks, when in the appropriate parameter regime, may emit GHz radiation in the form of precursor waves. We present the first global Particle-in-Cell simulations of the nonlinear steepening of fast magnetosonic waves in a dipolar magnetosphere, and quantitatively demonstrate the strong plasma acceleration in the upstream of these shocks. In these simulations, we observe the production of precursor waves in a finite angular range. Using analytic scaling relations, we predict the expected frequency, power, and duration of this emission. Within a reasonable range of progenitor wave parameters, these precursor waves can reproduce many aspects of FRB observations.

Figures (6)

• Figure 1: Global structure of the monster shock from our fiducial simulation with fast wave wavelength $\lambda=0.6r_{\rm nl}$ and $\sigma_{\rm bg, nl}=250$. The snapshot is taken at time $t=1.6r_{\rm nl}/c$. The left panel shows $E_{\phi}r/B_{\rm bg, nl}r_{\rm nl}$, where $B_{\rm bg, nl}$ is the equatorial magnetic field at the nonlinear radius. The subsequent three panels show a zoomed-in view of the region within the red box in the left panel, with colors representing the scaled plasma density $n r^3/N_0$ (where $N_0=n_{\rm bg}r^3$ is a constant), the ratio of the electric field to the magnetic field, and the Lorentz factor of the bulk flow, respectively. In all panels the gray lines are the magnetic field lines. In the rightmost panel, the blue arrows indicate the direction of the bulk flow, and the arrow lengths are proportional to the bulk velocity. Click https://youtu.be/LyQCaSag0Zc for a YouTube video of these shocks.
• Figure 2: Structure of the shock on the equatorial plane in our fiducial simulation at the same time as in Figure \ref{['fig:Global']}. The top panel shows $B_{\theta}/B_{\rm bg,nl}$ and $E_{\phi}/B_{\rm bg,nl}$. The middle panel shows the radial component of the average plasma momentum $\langle p_r\rangle$. The third panel shows the scaled plasma density $n r^3/N_0$ and the horizontal dashed line indicates the value of $N_0$. The red dashed line marks the location of the shock.
• Figure 3: The top panel shows the scaling of the maximum upstream Lorentz factor $\gamma_{\rm max}$ on the equatorial plane with the background magnetization at the nonlinear radius $\sigma_{\rm bg,nl}$. We divide the measured $\gamma_{\rm max}$ by the fast wave wavelength $\lambda$. The resulting scaling relation is linear: $\gamma_{\rm max}/\lambda\propto \sigma_{\rm bg,nl}$. The bottom panel shows $\gamma_{u}$ as a function of position for simulations with different values of $\sigma_{\rm bg,nl}$, as well as the theoretically predicted curve, Equation \ref{['eq:full_monster']}. For better comparison purposes, the curves are normalized by their own maximum value $\gamma_{\rm max}$.
• Figure 4: The ratio of the total electric field to the total magnetic field for simulations with several different wavelengths. The fluctuating region with $E>B$ that occurs in the first full period of the fast wave is the precursor wave. The orange dashed lines mark the latitudes where the shock becomes parallel, namely, the magnetic field is parallel to the shock normal. From left to right, these latitudes are $\pm 23^{\circ}$, $\pm 18^{\circ}$, $\pm 14^{\circ}$, $\pm 9^{\circ}$, and $\pm 7^{\circ}$ respectively. Subsequent shocks become modified due to heating of the plasma from the first shock, and $E > B$ regions show up at higher latitudes due to plasma flowing towards the equator. The snapshots are all taken at the same time $t=2r_{\rm nl}/c$.
• Figure 5: Snapshots of the electric and magnetic fields from three simulations with different $\eta$ parameters, demonstrating different regimes of wave deformation. Each snapshot is taken at the timestep $t = 1.1r_{\rm nl}/c$. All three simulations have the same background magnetic field and wavelength. The only variable that changes is the plasma density. The top panel shows $\eta = 6$ to demonstrate the regime in which we do not expect $E>B$ to be successfully prevented. The center panel shows $\eta = 12.5$ which is close to the threshold necessary to prevent $E>B$. The bottom panel shows $\eta = 25$ in which $E>B$ is completely prevented with the exception of the precursor wave.