A generalized Petschek magnetic reconnection rate

Simple physical arguments show that a generalization of the basic Petschek reconnection rate allows it to be extended to the Hall magnetohydrodynamic (MHD) rate. This result is confirmed by direct numerical simulations of the compressible fluid equations. To ensure that Petschek reconnection is obtained we specify a localized resistivity. The new generalized reconnection rate therefore gives an accurate estimate of the unforced Petschek reconnection rate for both MHD and Hall MHD. Since the Hall Petschek rate does not vanish in the limit of zero resistivity this generalized rate may also give the collisionless Hall Petschek reconnection rate