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

TL;DR

This study tests the Lazarian–Vishniac theory of fast turbulent magnetic reconnection in 3D MHD over Lundquist numbers $S$ from $10^3$ to $10^6$ by injecting a brief spectrum of small-scale perturbations to seed turbulence. It finds that turbulence, once self-sustained, drives reconnection at rates $V_{rec}/V_A \sim 0.03$–$0.08$ that are largely independent of $S$, with a mild decrease as $\beta$ increases and negligible dependence on the magnetic Prandtl number $\text{Pr}_m$; these rates exceed tearing-mode dominated values by factors of $5$–$6$ and are compatible with solar and astrophysical observations. The results show that in 3D, turbulence enables multiple reconnection sites and a Kolmogorov-like energy cascade, while plasmoid formation common in 2D is not observed; this underscores the importance of three-dimensional turbulence for fast reconnection in astrophysical plasmas. Overall, the work provides strong numerical support for turbulent reconnection as a robust mechanism in high-$S$ environments, with broad implications for plasma heating and particle acceleration in solar flares, accretion flows, and jets.

Abstract

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-$β$ parameter, decreasing from 0.036 to 0.028 (in Alfvén units) as $β$ increases from 2.0 to 64.0 for simulations with a Lundquist number of $10^5$. Lastly, we explore the magnetic Prandtl number's ($\text{Pr}_m=ν/η$) influence on the reconnection rate and find it negligible during the turbulent regime across the range tested, from $\text{Pr}_m=1$ to $60$.

Figures (22)

• Figure 1: Initial configuration of magnetic field and density. Black arrows represent the in-plane component of the magnetic field, and the colormap is the density profile. The out-of-plane component of the magnetic field $(B_z)$ is set to be constant.
• Figure 2: Dependence of the reconnection rate $V_{\text{rec}}$ on the Lundquist Number $S$ for simulations without forcing at early times, and for different values of plasma$-\beta$. The dashed black line represents the Sweet-Parker scaling of $V_{\text{rec}} \propto S^{-1/2}$. Some circles and squares are overlapped. This is the case for intermediate values of $\beta$, between 2 and 18, for both $S=10^3$ and $10^4$.
• Figure 3: 3D visualization of the current density magnitude, $|\mathbf{J}|$, at $t = 0$ (left) and $t=2.0$ (right) for the simulation with $S=10^5$, $\text{Pr}_m=1$, $B_z = 0.5$ and $\beta = 2.0$. Perturbation is injected up to $t=0.1 \, t_A$ with $k_\text{inj}=128$ and $P_{\text{inj}}=0.5$.
• Figure 4: Colormaps of 2D cuts ($xy-$ and $xz-$planes) of the current density magnitude at different times for the same simulation shown in Fig. \ref{['fig:3D_visu_t0_t2']}.
• Figure 5: Colormaps of 2D cuts ($xy-$ and $xz-$planes) of the vorticity magnitude $(|\omega| = |\nabla \times \mathbf{v}|)$ at different times for the same simulation shown in Fig. \ref{['fig:3D_visu_t0_t2']}.