Stationary Resistive MHD Solutions Near an Isolated Three-Dimensional Magnetic Null

Abstract

Magnetic null points define the magnetic field topology in stellar coronae, planetary magnetospheres, and astrospheres, and are commonly associated with magnetic reconnection. We investigate the local structure of stationary three-dimensional (3D) resistive, incompressible magnetohydrodynamic (MHD) flows in the vicinity of an isolated magnetic null and an isolated velocity stagnation point, assuming that the two nulls are colocated. The governing MHD equations are solved self-consistently using a first-order local expansion of the magnetic and velocity fields about the null. For any given magnetic-null configuration, the equations admit a two-parameter family of stationary solutions, comprising multiple solution branches with distinct velocity topologies. Along these families, the velocity-null polarity can change at bifurcation points where the flow becomes effectively 2.5D. A single magnetic null can therefore support positive-radial, negative-radial, and spiral stagnation flows, with qualitatively different inflow, outflow, and rotational properties. The associated pressure and resistivity distributions are likewise determined self-consistently and vary across the solution family, demonstrating that they are coupled to the flow topology rather than prescribed independently. The generic solutions do not require the velocity and magnetic separatrices to coincide, allowing plasma to cross the magnetic fan separatrix and providing a local reconnective flow. These results demonstrate that, in the presence of nonuniform resistivity, the magnetic topology alone does not uniquely determine the associated stationary flow, pressure, or resistivity structure around a 3D magnetic null, revealing the nonlinear feedback between all macroscopic variables and resistivity. The constant-resistivity field-aligned and spiral field-crossing solutions identified previously are recovered as special cases.