Fast reconnection in relativistic plasmas: the magnetohydrodynamics tearing instability revisited

TL;DR

This paper investigates the relativistic tearing instability in magnetically dominated plasmas using numerical simulations, revealing that the instability behaves similarly to classical MHD but with faster growth rates in the ideal tearing regime, relevant for high-energy astrophysics phenomena.

Contribution

It demonstrates that relativistic resistive MHD simulations reproduce classical tearing instability behavior and confirms the existence of the ideal tearing regime with rapid reconnection in relativistic plasmas.

Findings

Linear growth rate scales as S^-1/2, similar to classical MHD.

Ideal tearing mode occurs at S^-1/3 aspect ratio, leading to fast reconnection.

Nonlinear stage shows inverse cascade and Petschek-type jets.

Abstract

Fast reconnection operating in magnetically dominated plasmas is often invoked in models for magnetar giant flares, for magnetic dissipation in pulsar winds, or to explain the gamma-ray flares observed in the Crab nebula, hence its investigation is of paramount importance in high-energy astrophysics. Here we study, by means of two dimensional numerical simulations, the linear phase and the subsequent nonlinear evolution of the tearing instability within the framework of relativistic resistive magnetohydrodynamics, as appropriate in situations where the Alfven velocity approaches the speed of light. It is found that the linear phase of the instability closely matches the analysis in classical MHD, where the growth rate scales with the Lundquist number S as S^-1/2, with the only exception of an enhanced inertial term due to the thermal and magnetic energy contributions. In addition, when thin current sheets of inverse aspect ratio scaling as S^-1/3 are considered, the so-called "ideal" tearing regime is retrieved, with modes growing independently on S and extremely fast, on only a few light crossing times of the sheet length. The overall growth of fluctuations is seen to solely depend on the value of the background Alfven velocity. In the fully nonlinear stage we observe an inverse cascade towards the fundamental mode, with Petschek-type supersonic jets propagating at the external Alfven speed from the X-point, and a fast reconnection rate at the predicted value R~(ln S)^-1.