Effect of nonuniform resistivity in Petschek reconnection

Abstract

The controversial topic of the existence of a Petschek solution in steady-state magnetic reconnection for a uniform resistivity is investigated, by using two-dimensional time-dependent magnetohydrodynamic simulations. A classical localized nonuniform resistivity with a profile that is exponentially decreasing from the X point is helpful to set up the Petschek solution as a first step, using a procedure with overspecified boundary conditions. The response to changing the resistivity profile in various ways is then studied. It is found that a Petschek configuration is obtained when a quasiuniform resistivity is adopted. This is the case if the resistivity profile exhibits a weak negative gradient close to the X point, which dominates an inherent numerical contribution; otherwise an instability develops which disrupts the configuration. A truly uniform resistivity is probably only marginally stable. Finally, the validity of the arguments given by Kulsrud [Earth Planets Space 53, 417 (2001)] about the “incorrectness” of Petschek’s original model is discussed.