Collisionless reconnection: Effects of Hall current and electron pressure gradient

An analytical treatment is given of two‐dimensional, quasi‐steady collisionless reconnection on the basis of the generalized Ohm's law, including the effects of the Hall current and scalar electron pressure gradient. The equilibrium magnetic field configuration is of the form , containing a neutral line at z = 0 and a constant guide field B T . The dispersion relations of the waves in the ideal region as well as the reconnection layer are discussed, including the effects of plasma beta. When B T = 0, the reconnection layer supports obliquely propagating Alfvén‐whistler waves, and the reconnection dynamics is controlled by the Hall current. When B T / B P 0 ≥ 1, the reconnection layer supports kinetic/inertial Alfvén waves, and the reconnection dynamics is controlled by the electron pressure gradient. Analytical estimates are obtained for the nonlinear reconnection rate with and without the guide field from the generalized Ohm's law. A recent claim by Shay et al. (1999) that the reconnection rate is a “universal constant” is questioned. Although the leading‐order reconnection rate is independent of the mechanism that breaks field lines (resistivity or electron inertia) and the system size as the system size becomes large, it does depend on global conditions such as the boundary conditions driving reconnection. The analytical predictions are tested by means of Hall magnetohydrodynamics simulations. While some of the geometric features of the reconnection layer and the weak dependence of the reconnection rate on resistivity are reminiscent of Petschek's classical model, the underlying wave and particle dynamics mediating reconnection in the presence of the Hall current and electron pressure gradient are qualitatively different.