Influence of the Hall effect on the reconnection rate at line-tied magnetic X-points

Context. The role of the Hall term in magnetic reconnection at line-tied planar magnetic X-points is explored. Aims. The goal is to determine the reconnection scaling laws and to investigate how the reconnection rate depends on the size of the system in Hall magnetohydrodynamics (MHD). Methods. The evolution of reconnective disturbances is determined numerically by solving the linearized compressible Hall MHD equations. Scaling laws are derived for the decay rate as a function of the dimensionless resistivity and ion inertial length. Results. Although the Hall effect leads to an increase in the decay rate, this increase is shown to be moderated in larger systems. A key finding is that the Hall term contribution to the decay rate, normalized by the resistive decay rate, scales inversely with the system size L, approximately as L-2. Conclusions. The evidence suggests that decay rate enhancements due to Hall effects in line-tied X-points are weakened for large-scale systems. The result may have important implications for modeling energy release in large-scale astrophysical plasma environments, such as solar flares