Petschek-like Reconnection with Current-driven Anomalous Resistivity and its Application to Solar Flares

Recent numerical simulations of magnetic reconnection in two dimensions have shown that, when the resistivity is strongly localized, the reconnection region develops a Petschek-like structure, with the width of the inner diffusion region being of the order of the resistivity localization scale. In this paper, we combine this fact with a realistic model for locally-enhanced anomalous resistivity generated by current-driven microturbulence. The result is a qualitative model of the reconnection layer where the size of Petschek's diffusion region and, therefore, the final reconnection rate are determined self-consistently in terms of the main parameters of the functional dependence of anomalous resistivity on the electric current density. We then consider anomalous resistivity due to ion-acoustic turbulence as a particular case. This enables us to express the reconnection region's parameters directly in terms of the basic parameters of the plasma. Finally, we apply this reconnection model to solar flares and obtain specific predictions for typical reconnection times, which are very consistent with observations.