Fast Radio Bursts from non-resonant Alfvén waves and synchrotron maser emission in the magnetar wind

TL;DR

This paper proposes that fast radio bursts (FRBs) originate from synchrotron maser emission (SME) generated by non-resonant interactions between Alfvén waves and the relativistic magnetar wind, producing a crescent-shaped population inversion that drives SME. By calculating growth rates across a parameter space defined by temperature $\theta$, magnetisation $\sigma$, and wind Lorentz factor $\gamma_w$, the authors derive conditions under which SME can operate and emit at GHz frequencies, finding a minimum $\gamma_w \gtrsim 3\times 10^2$ and a low $\theta$ window ($\theta \lesssim 0.02$). They then impose FRB constraints on frequency, timescale, and emission-site size to bound the emission radius $R_{FRB}$ and assess whether the magnetosphere must be perturbed by flaring activity; applying the framework to FRB 20200428 shows that a perturbed magnetosphere greatly eases the required wind properties. The results connect FRB observables to the wind conditions near magnetars and offer a diagnostic for magnetar environments, while highlighting the roles of O-mode and X-mode SME and the need for relativistic winds beyond the light cylinder.

Abstract

Non-resonant interactions between Alfvén waves and a relativistic plasma result in the formation of the population inversions necessary for synchrotron maser emission (SME) across a wide range of magnetisations and temperatures. We calculate the peak frequencies of the SME resulting from this interaction and show that the characteristic frequencies and energetics of fast radio bursts (FRBs) can be produced in the relativistic wind of a magnetar using this mechanism. Wind Lorentz factors of $γ_w\gtrsim310$ are shown to be necessary to explain observed FRBs. Emission is possible at temperatures of $θ= k_bT/mc^2\lesssim 0.02$. We further examine the periods and magnetic fields of the central magnetar and demonstrate that the optimal values of these properties align with the observed magnetar population provided that the magnetosphere is disturbed by the flaring activity. These results allow the properties of the environment such as temperature and magnetisation to be probed from the observed FRB frequency and luminosity.

Figures (11)

• Figure 1: The dispersion relation for perpendicular propagation in a cold electron-positron plasma with $\sigma = 3$ is shown in blue, and $\sigma=300$ in orange. The solid lines show the ordinary mode dispersion relation, while the extraordinary modes are shown by dashed lines. The ordinary mode has a cutoff at $\omega = \omega_p$, which has a value of $\omega_p =0.58 \Omega$ for $\sigma = 3$ and $\omega_p = 5.8\times10^{-2}\Omega$ for $\sigma=300$. The extraordinary mode has a cutoff at $\omega = \left(\omega_p^2+\Omega^2\right)^{1/2}$ and a resonance at $\omega = \Omega$. The dispersion relation becomes more complicated for oblique propagation due to the introduction of further resonances.
• Figure 2: The growth rate $\omega_i$ normalised to the cyclotron frequency and density ratio for the first 10 harmonics of the O- and slow X-modes, with the majority of the contribution coming from the first 3 harmonics in both cases. The results are for a crescent shaped distribution with initial temperature $\theta=10^{-2}$, $\sigma = 10$ and turbulence level $\eta=1$. The individual ordinary mode harmonics are shown as faint blue lines, with the sum over all harmonics shown as the solid blue line. The same is the case for the extraordinary mode harmonics which are shown in orange. The fastest growing wavenumber for the O-mode occurs at $k\sim0.48\Omega/c$, while for the slow X-mode it is found at the higher wavenumber of $k\sim1.27\Omega/c$. The range of wavenumbers where the growth rate is positive is broadened due to the temperature of the distribution in comparison to a cold scenario. The overlap of harmonics due to this broadening acts to reduce the growth rate, especially for higher harmonics.
• Figure 3: An example distribution $F(q_\parallel,q_\perp,\eta)$ for $\theta = 10^{-2}$ and $\sigma = 300$. Panel (a) shows initial distribution at $\eta=0$ (where no non-resonant interaction has yet occurred) and panel (b) shows the distribution at a turbulence level of $\eta=1$. Both plots are normalized to the maximum value of $F(q_\parallel,q_\perp,0)$ for presentation purposes. In panel (b), the formation of a crescent shape is clear, with particles gaining energy in the region of positive parallel and perpendicular momentum. Note that the increase in the width of the distribution in the parallel direction is much lower than the increase in the perpendicular direction.
• Figure 4: Growth rate and emission frequency as a function of temperature: Panel (a) shows the growth rate $\Gamma_i$ normalised to the cyclotron frequency and density ratio for $\sigma=10$ and $\eta=1$, while panel (b) shows the peak emission frequency $\omega_m$, also normalised to the cyclotron frequency. The ordinary mode is shown by blue 'o's and the slow extraordinary mode (lower branch) by orange 'x's. The decrease in growth rate with increasing temperature is clearly visible. For temperatures of $\theta>0.02$ no maser emission occurs for the O-mode, while the emission in the X-mode continues to slightly higher temperatures of $\theta \sim 0.025$. Above these temperatures no growth was found. At this magnetisation the O-mode is dominant at temperatures of $\theta\gtrsim10^{-3}$, at which point the growth rates become comparable. In all cases the maximum growth rate is found at a propagation angle of $\pi/2$.
• Figure 5: Growth rate and emission frequency as a function of magnetisation: Panel (a) shows the growth rate $\Gamma_i$ normalised to the cyclotron frequency and density ratio for $\theta=10^{-2}$ and $\eta=1$, while panel (b) shows the peak emission frequency $\omega_m$, also normalised to the cyclotron frequency. The ordinary mode is shown by blue 'o's and the slow extraordinary mode (lower branch) by orange 'x's. The decrease in growth rate with increasing magnetisation due to the reduced number density is clearly visible. The O-mode is dominant at magnetisations of $\sigma\gtrsim5$ for this temperature, with no O-mode growth present for $\sigma<2$. The crossover value increases with decreasing initial temperatures. In all cases the maximum growth rate is found at a propagation angle of $\pi/2$.