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Explosive reconnection in magnetars

X-ray activity of Anomalous X-ray Pulsars and Soft Gamma-Ray Repeaters may result from the heating of their magnetic corona by direct currents dissipated by magnetic reconnection. We investigate the possibility that X-ray flares and bursts observed from AXPs and SGRs result from magnetospheric reconnection events initiated by development of tearing mode in magnetically-dominated relativistic plasma. We formulate equations of resistive force-free electrodynamics, discuss its relation to ideal electrodynamics, and give examples of both ideal and resistive equilibria. Resistive force-free current layers are unstable toward the development of small-scale current sheets where resistive effects become important. Thin current sheets are found to be unstable due to the development of resistive force-free tearing mode. The growth rate of tearing mode is intermediate between the short \Alfven time scale $ τ_A$ and a long resistive time scale $τ_R$: $Γ\sim 1/(τ_R τ_A)^{1/2}$, similar to the case of non-relativistic non-force-free plasma. We propose that growth of tearing mode is related to the typical rise time of flares, $\sim 10$ msec. Finally, we discuss how reconnection may explain other magnetar phenomena and ways to test the model.