Magnetic Helicity of the Time-Dependent Separator Reconnection

Abstract

We present an analytical study of the time-dependent magnetic helicity creation in the separator magnetic reconnection model. The background field connects two 3D null points via a separator, and a localized flux ring perturbation with a linearly growing amplitude drives the reconnection. Using a gauge-invariant formulation, we derive a closed-form expression for the helicity creation rate. The rate scales linearly with the product of the background and perturbation field strengths, the geometric dimensions of the flux ring, and the square of its displacement from the separator axis. For typical coronal parameters, the model yields an analytical scaling law for the helicity source; a realistic reconnection diffusion region creates helicity at a negligible rate compared to the active-region helicity budget. The handedness of the created twist is determined by the sign of the perturbation amplitude, providing a clear observational signature. A comparison with a simple linear null point shows that the separator geometry is essential for a net helicity creation. These results provide the first analytical description of time-dependent helicity variation during separator reconnection and offer testable predictions for spectropolarimetric observations.