Relativistic resistive magnetohydrodynamic reconnection and plasmoid formation in merging flux tubes

We apply the general relativistic resistive magnetohydrodynamics code BHAC to perform a 2D study of the formation and evolution of a reconnection layer in between two merging magnetic flux tubes in Minkowski space-time. Small-scale effects in the regime of low resistivity most relevant for dilute astrophysical plasmas are resolved with very high accuracy due to the extreme resolutions obtained with adaptive mesh refinement. Numerical convergence in the highly non-linear plasmoid-dominated regime is confirmed for a sweep of resolutions. We employ both uniform resistivity and non-uniform resistivity based on the local, instantaneous current density. For uniform resistivity we find Sweet-Parker reconnection, from eta = 10(-2) down to eta = 10(-4), for a reference case of magnetization sigma = 3.33 and plasma-beta = 0.1. For uniform resistivity eta = 5 x 10(-5) the tearing mode is recovered, resulting in the formation of secondary plasmoids. The plasmoid instability enhances the reconnection rate to v(rec) similar to 0.03c compared to v(rec) similar to 0.01c for eta = 10(-4). For non-uniform resistivity with a base level eta(0) = 10(-4) and an enhanced current-dependent resistivity in the current sheet, we find an increased reconnection rate of v(rec) similar to 0.1c. The influence of the magnetization sigma and the plasma-beta is analysed for cases with uniform resistivity eta = 5 x 10(-5) and eta = 10(-4) in a range 0.5 <= sigma <= 10 and 0.01 <= beta <= 1 in regimes that are applicable for black hole accretion discs and jets. The plasmoid instability is triggered for Lundquist numbers larger than a critical value of S-c approximate to 8000.