Investigating Turbulence Effects on Magnetic Reconnection Rates Through Three-Dimensional Resistive Magnetohydrodynamical Simulations

We investigate the impact of turbulence on magnetic reconnection through high-resolution 3D magnetohydrodynamical (MHD) simulations, spanning Lundquist numbers from $S=10^3$ to $10^6$. Building on Lazarian and Vishniac's (1999) theory, which asserts reconnection rate independence from Ohmic resistivity, we introduce small-scale perturbations until $t=0.1\, t_A$. Even after the perturbations cease, turbulence persists, resulting in sustained high reconnection rates of $V_\text{rec}/V_A \sim 0.03-0.08$. These rates exceed those generated by resistive tearing modes (plasmoid chain) in 2D and 3D MHD simulations by factors of 5 to 6. Our findings match observations in solar phenomena and previous 3D MHD global simulations of solar flares, accretion flows, and relativistic jets. The simulations show a steady-state fast reconnection rate compatible with the full development of turbulence in the system, demonstrating the robustness of the process in turbulent environments. We confirm reconnection rate independence from the Lundquist number, supporting Lazarian and Vishniac's theory of fast turbulent reconnection. Additionally, we find a mild dependence of $V_\text{rec}$ on the plasma-$\beta$ parameter, decreasing from 0.036 to 0.028 (in Alfv\'en units) as $\beta$ increases from 2.0 to 64.0 for simulations with a Lundquist number of $10^5$. Lastly, we explore the magnetic Prandtl number's ($\text{Pr}_m=\nu/\eta$) influence on the reconnection rate and find it negligible during the turbulent regime across the range tested, from $\text{Pr}_m=1$ to $60$.