Self-similar solutions of oscillatory reconnection: parameter study of magnetic field strength and background temperature

Oscillatory reconnection is a specific type of time-dependent reconnection which involves periodic changes in the magnetic topology of a null point. The mechanism has been reported for a variety of magnetic field strengths and configurations, background temperatures and densities. All these studies report an oscillation in the current density at the null point, but also report a variety of periods, amplitudes and overall behaviors. We conduct a parametric study for equilibrium magnetic field strength and initial background temperature, solving 2D resistive MHD equations around a magnetic X-point. We introduce a parameter space for the ratio of internal-to-magnetic energy and find self-similar solutions for simulations where this ratio is below 0.1 (which represents a magnetically-dominated environment or, equivalently, a low-beta plasma). Self-similarity can be seen in oscillations in the current density at the null (including amplitude and period), Ohmic heating and the temperature generated via reconnection jets. The parameter space of energy ratios also allows us to contextualize previous studies of the oscillatory reconnection mechanism and bring those different studies together into a single unified understanding.