Magnetic Field Line Wandering and Shock‐Front Acceleration: Application to the Radio Emission of SN 1987A

Abstract

The superposition of random fluctuations δ on a main, regular magnetic field 0 has been shown by Ragot to produce, on the scales of interest, a nondiffusive random walk of the magnetic field lines in the quasi-linear regime of turbulence. The spreading Δx2 of the field lines across the direction of 0 increases as zβ, z being the distance along 0 with a transport exponent β that is not necessarily equal to 1. This puts into question the diffusivity of magnetic field lines in a non-quasi-linear regime as well and could imply an anomalous transport of the cosmic rays accelerated at a shock front if their decorrelation time from the field lines is longer than their acceleration time. Under the assumption of such a long decorrelation time, the acceleration time of cosmic rays scattered along the wandering field lines is derived here as a function of the obliquity and speed of the shock for a general transport exponent of the field lines. It is shown that for high-speed shocks, the importance of magnetic field line wandering (MFLW) is not limited to quasi-perpendicular shocks as usually believed. Moreover, the turbulence ahead of the shock is in a non-quasi-linear regime on the length scale traveled by accelerated particles whenever MFLW is important. The inclusion of MFLW can make the acceleration time depart by orders of magnitude from its value estimated in the approximation of simple scattering. This discrepancy is actually most welcome to explain the acceleration time of GeV electrons at the reappearance of SN 1987A in the radio waveband, since the inferred diffusion coefficient along the shock normal is about 5 orders of magnitude greater than the limiting Bohm value of a cross-field scattering coefficient. From the requirement of a realistic turbulence spectrum and in the approximation of quasi-linear transport coefficients, it is found that the magnetic field lines ahead of the SN 1987A shock strongly supradiffuse (β ≈ 1.8) and that the compression ratio of the shock is larger than 3. Finally, this paper argues in favor of a radio silence of SN 1987A prior to 1990 due to a lack of scattering of the GeV electrons when the shock speed exceeds about one-tenth of the speed of light.