Scaling Law of Relativistic Sweet-Parker Type Magnetic Reconnection

TL;DR

This study uses relativistic resistive MHD simulations to analyze the scaling law of magnetic reconnection, revealing that the reconnection rate follows a non-relativistic scaling law and that outflows are heated but not ultra-relativistic.

Contribution

The paper demonstrates that relativistic Sweet-Parker reconnection obeys the same scaling law as non-relativistic cases, confirming theoretical predictions.

Findings

Reconnection rate scales as S^{-0.5}

Outflows are heated but not ultra-relativistic

Results align with Lyubarsky's theoretical model

Abstract

Relativistic Sweet-Parker type magnetic reconnection is investigated by relativistic resistive magnetohydrodynamic (RRMHD) simulations. As an initial setting, we assume anti-parallel magnetic fields and a spatially uniform resistivity. A perturbation imposed on the magnetic fields triggers magnetic reconnection around a current sheet, and the plasma inflows into the reconnection region. The inflows are then heated due to ohmic dissipation in the diffusion region, and finally become relativistically hot outflows. The outflows are not accelerated to ultra-relativistic speeds (i.e., Lorentz factor ~ 1), even when the magnetic energy dominates the thermal and rest mass energies in the inflow region. Most of the magnetic energy in the inflow region is converted into the thermal energy of the outflow during the reconnection process. The energy conversion from magnetic to thermal energy in the diffusion region results in an increase in the plasma inertia. This prevents the outflows from being accelerated to ultra-relativistic speeds. We find that the reconnection rate R obeys the scaling relation R S^{-0.5}, where S is the Lundquist number. This feature is the same as that of non-relativistic reconnection. Our results are consistent with the theoretical predictions of Lyubarsky (2005) for Sweet-Parker type magnetic reconnection.