Superluminal Wave Activation at Relativistic Magnetized Shocks

Abstract

Fast radio bursts (FRBs) are extremely energetic radio transients, some are generated in magnetar magnetospheres and winds. Despite a growing number of observations, their emission mechanisms remain elusive. It has recently been proposed that Alfvénic perturbations can convert into superluminal O-modes at magnetized shocks and propagate in the downstream as a radio signal. We validate this superluminal wave activation mechanism using pair-plasma theory and particle-in-cell simulations. Theory predicts two different downstream modes: non-propagating Alfvénic perturbations and propagating superluminal O-modes. Superluminal wave activation occurs if the frequency of upstream perturbations in the shock frame exceeds the downstream plasma frequency. 1D particle-in-cell simulations confirm wavenumber and frequency jumps across the shock for upstream perturbations with frequencies well above the plasma frequency. Our simulations model both monochromatic upstream waves and broadband spectra with the downstream plasma frequency acting like a high-pass filter for superluminal O-modes. We discuss implications for FRB generation in relativistic magnetized winds.

Figures (6)

• Figure 1: Schematic visualization of mode conversion at relativistic magnetized shocks. A shock front propagates through a magnetized plasma. Non-propagating Alfvénic perturbations upstream of the shock ($\omega_A=0$, waves in white) convert into a superposition of non-propagating Alfvénic perturbations (white) and propagating superluminal O-modes (blue) in the downstream. Quantities measured in different frames are denoted as follows: downstream (d), upstream (u), shock (s).
• Figure 2: Shock and mode conversion dynamics of monochromatic seed waves. Left: Upstream scales $B_0=10$, $[\gamma_{\rm u}]^{\rm d}=4$, $[k_{\rm u}d_{\rm u}]^{\rm u}=0.63$. A superluminal O-mode (supO) propagates into the downstream, a small-amplitude non-propagating Alfvénic perturbation (AW) remains in the wake of the shock. The region of pure supO is shaded in blue, mixed supO/AW in red. The bottom panel shows EM fields associated with the propagating superluminal O-mode. Right: Upstream waves with $[k_{\rm u}d_{\rm u}]^{\rm u}=0.03$. No modes propagate into the downstream, only AW perturbations remain (red-shaded region of top panels).
• Figure 3: Wavenumber scaling (top) and frequency matching (bottom) across shocks with $[\gamma_{\rm u}]^{\rm d} = 4$ (left) and $[\gamma_{\rm u}]^{\rm d} = 8$ (right). Top panels show downstream wavenumbers as a function of upstream seed wavenumbers in the superposition region for AWs (red circles) and superluminal O-modes (blue circles). The scalings agree closely with Equations (\ref{['eq:AWUpMatch']}) and (\ref{['eq:DownUpMatch']}). Star markers denote cases with frequencies approximately below the plasma frequency cutoff (Equation \ref{['eq:omodematching']}, indicated by the vertical dashed line) when no propagating downstream modes can be measured. Bottom panels show the dispersion relation of propagating downstream modes. Downstream wavenumbers and corresponding wave frequencies trace the respective (hot) dispersion relation for the SupO-mode with temperatures $[T_{\rm d}]^{\rm d} = 0.96\, m_ec^2$ for $[\gamma_{\rm u}]^{\rm d} = 4$, and $[T_{\rm d}]^{\rm d}=2.1\, m_e c^2$ for $[\gamma_{\rm u}]^{\rm d} = 8$ (see also Equation \ref{['eq:HPD']}).
• Figure 4: Shock and mode conversion dynamics for a (discrete) spectrum of seed waves. Flow properties are as in Figure \ref{['fig:MSHOCK_G4_s25_HR_K0026']}. We initialize a spectrum of equal amplitude monochromatic waves sampled from $[k_{\rm u}d_{\rm u}]^{u}\in\left[0.03,6.28\right]$. We vary the number of modes; the left panel uses the minimum and maximum seed wavelength from Figure \ref{['fig:MSHOCK_G4_s25_HR_K0026']} ($N=2)$, the middle/right have randomly sampled seed wavenumbers ($N=5$ and $N=10$, in log-space). Low frequency seed waves produce non-propagating downstream AWs (red shaded region). Seed waves with scales above the critical frequency (Equation \ref{['eq:omodematching']}) induce propagating superluminal O-modes (blue shaded region). The bottom panel zooms in on the wave fields $[E_y]^{\rm d}$ (red color) and $[B_z]^{\rm d}$ (blue shaded regions).
• Figure 5: Schematic visualization of an observer frame's view of superluminal O-mode generation via Alfvén wave activation at magnetized shocks. Forward shock (panel a) and reverse shock (panel b) move through a propagating flow, like an expanding magnetar wind, as discussed in Appendix \ref{['app:ShockStructure']}. Depending on the wave propagation direction in the frame of the contact discontinuity (c), amplitude and frequency experience different boosts $\mathcal{C}$, see also Section \ref{['sec:discussion']}.