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Nonlinear effects are crucial for the propagation of fast radio bursts (FRBs) near the source. We study the filamentation of FRBs in the relativistic winds of magnetars, which are commonly invoked as the most natural FRB progenitors. As a result of filamentation, the particle number density and radiation intensity develop strong gradients along the direction of the wind magnetic field. A steady state is reached when the plasma pressure balances the ponderomotive force. In such a steady state, particles are confined in periodically spaced thin sheets, and electromagnetic waves propagate between them as in a waveguide. We show the following. (i) The dispersion relation resembles that in the initial homogeneous plasma, but the effective plasma frequency is determined by the separation of the sheets, not directly by the mean particle density. (ii) The contribution of relativistic magnetar winds to the dispersion measure of FRBs could be several orders of magnitude larger than previously thought. The dispersion measure of the wind depends on the properties of individual bursts (e.g., the luminosity) and therefore can change significantly among different bursts from repeating FRBs. (iii) Induced Compton scattering is suppressed because most of the radiation propagates in near-vacuum regions.

 

Magnetars are the most promising progenitors of fast radio bursts (FRBs). Strong radio waves propagating through the magnetar wind are subject to non-linear effects, including modulation/filamentation instabilities. We derive the dispersion relation for modulations of strong waves propagating in magnetically dominated pair plasmas focusing on dimensionless strength parameters a0 ≲ 1, and discuss implications for FRBs. As an effect of the instability, the FRB-radiation intensity develops sheets perpendicular to the direction of the wind magnetic field. When the FRB front expands outside the radius where the instability ends, the radiation sheets are scattered due to diffraction. The FRB-scattering time-scale depends on the properties of the magnetar wind. In a cold wind, the typical scattering time-scale is τsc ∼  $\mu$s–ms at the frequency $\nu \sim 1\, {\rm GHz}$. The scattering time-scale increases at low frequencies, with the scaling τsc ∝ ν−2. The frequency-dependent broadening of the brightest pulse of FRB 181112 is consistent with this scaling. From the scattering time-scale of the pulse, one can estimate that the wind Lorentz factor is larger than a few tens. In a warm wind, the scattering time-scale can approach $\tau _{\rm sc}\sim \, {\rm ns}$. Then scattering produces a frequency modulation of the observed intensity with a large bandwidth, $\Delta \nu \sim 1/\tau _{\rm sc}\gtrsim 100\, {\rm MHz}$. Broad-band frequency modulations observed in FRBs could be due to scattering in a warm magnetar wind.

 

ABSTRACT Fast radio bursts (FRBs) are extreme astrophysical phenomena entering the realm of non-linear optics, a field developed in laser physics. A classical non-linear effect is self-modulation. We examine the propagation of FRBs through the circumburst environment using the idealized setup of a monochromatic linearly polarized GHz wave propagating through a uniform plasma slab of density N at distance R from the source. We find that self-modulation occurs if the slab is located within a critical radius Rcrit ∼ 1017(N/102 cm−3)(L/1042 erg s−1) cm, where L is the isotropic equivalent of the FRB luminosity. Self-modulation breaks the burst into pancakes transverse to the radial direction. When R ≲ Rcrit, the transverse size of the pancakes is smaller than the Fresnel scale. The pancakes are strongly diffracted as the burst exits the slab, and interference between the pancakes produces a frequency modulation of the observed intensity with a sub-GHz bandwidth. When R ∼ Rcrit, the transverse size of the pancakes becomes comparable with the Fresnel scale, and the effect of diffraction is weaker. The observed intensity is modulated on a time-scale of 10 µm, which corresponds to the radial width of the pancakes. Our results suggest that self-modulation may cause the temporal and frequency structure observed in FRBs.