Explosive reconnection in magnetars

The X-ray activity of anomalous X-ray pulsars and soft γ-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 anomalous X-ray pulsars and soft γ-ray repeaters result from magnetospheric reconnection events initiated by development of the tearing mode in magnetically dominated relativistic plasma. We formulate equations of resistive force-free electrodynamics, discuss the relation of the latter to ideal electrodynamics, and give examples of both ideal and resistive equilibria. Resistive force-free current layers are unstable towards 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 the resistive force-free tearing mode. The growth rate of the tearing mode is intermediate between the short Alfvén time-scale  τ_A  and a long resistive time-scale  τ_R: Γ∼ 1/(τ_Rτ_A)^1/2  , similar to the case of non-relativistic non-force-free plasma. We propose that growth of the tearing mode is related to the typical rise time of flares, ∼10 ms. Finally, we discuss how reconnection may explain other magnetar phenomena and ways to test the model.