Fast reconnection in relativistic plasmas: the magnetohydrodynamics tearing instability revisited

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 non-linear evolution of the tearing instability within the framework of relativistic resistive magnetohydrodynamics (MHD), as appropriate in situations where the Alfve ́n 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 of 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 Alfve ́n velocity. In the fully non-linear stage, we observe an inverse cascade towards the fundamental mode, with Petschek-type supersonic jets propagating at the external Alfve ́n speed from the X-point, and a fast reconnection rate at the predicted value R ∼ (ln S)−1.