Relativistic Tearing Mode in Pair Plasmas and Application to Magnetic Giant Flares

Abstract

Relativistic magnetic reconnection is an important process in plasmas where relativity enters through large magnetization and relativistic temperature, and the tearing mode plays a significant role in the initial phase of spontaneous reconnection. Starting from general steady equilibrium, parallel as well as oblique tearing modes for relativistic pair plasmas are analyzed in this paper, including resistivity and thermal inertia (the generalization of the nonrelativistic electron inertia). A dispersion relation for arbitrary values of the tearing instability index Δ' is derived, containing both the large-Δ' regime and the small-Δ' regime, where the different limits are discussed with their implications for the tearing mode growth rate. It is found that in relativistic tearing mode, the parallel Lundquist number, electron skin-depth, and α that encodes the structure of the resonant surface all play roles in determining the tearing growth rate, where the parallel Lundquist number is defined with respect to the parallel magnetization σ∥ as well as the perpendicular magnetization σ⊥, and the electron skin-depth assumes the relativistic form for pair plasmas. These results hold for both pressure balance and force-free equilibrium. As an application, tearing instability is hypothesized as a possible mechanism for triggering fast gamma-ray burst. This work is important for understanding tearing modes in relativistic pair plasmas, and it serves as a basis for an analysis of relativistic plasmoid instability and relevant problems.