Generalised models for torsional spine and fan magnetic reconnection

Context. Three-dimensional (3D) null points are present in abundance in the solar corona, and the same is likely to be true in other astrophysical environments. Recent results from solar observations and from simulations suggest that reconnection at such 3D nulls may play an important role in the coronal dynamics. Aims. The properties of the torsional spine and torsional fan modes of magnetic reconnection at 3D nulls are investigated. New analytical models are developed, which for the first time include a current layer that is spatially localised around the null, extending along either the spine or the fan of the null. The principal aim is to investigate the effect of varying the degree of asymmetry of the null point magnetic field on the resulting reconnection process – where previous studies always considered a non-generic radially symmetric null. Methods. Analytical solutions are derived for the steady kinematic equations, and are compared with the results of numerical simulations in which the full set of resistive MHD equations is solved. Results. The geometry of the current layers within which torsional spine and torsional fan reconnection occur is strongly dependent on the symmetry of the magnetic field. Torsional spine reconnection occurs in a narrow tube around the spine, with elliptical cross-section when the fan eigenvalues are different. The eccentricity of the ellipse increases as the degree of asymmetry increases, with the short axis of the ellipse being along the strong field direction. The spatiotemporal peak current, and the peak reconnection rate attained, are found not to depend strongly on the degree of asymmetry. For torsional fan reconnection, the reconnection occurs in a planar disk in the fan surface, which is again elliptical when the symmetry of the magnetic field is broken. The short axis of the ellipse is along the weak field direction, with the current being peaked in these weak field regions. The peak current and peak reconnection rate in this case are clearly dependent on the asymmetry, with the peak current increasing but the reconnection rate decreasing as the degree of asymmetry is increased