Statistics of Reconnection-Driven Turbulence

Abstract

Magnetic reconnection is a process that changes magnetic field topology in highly conducting fluids. Within the standard Sweet-Parker model, this process would be too slow to explain observations (e.g. solar flares). In reality, the process must be ubiquitous as astrophysical fluids are magnetized and motions of fluid elements necessarily entail crossing of magnetic frozen-in field lines and magnetic reconnection. In the presence of turbulence, the reconnection is independent of microscopic plasma properties, and may be much faster than previously thought, as proposed in Lazarian & Vishniac (1999) and tested in Kowal et al. (2009, 2012). However, the considered turbulence in the Lazarian-Vishniac model was imposed externally. In this work we consider reconnection-driven magnetized turbulence in realistic three-dimensional geometry initiated by stochastic noise. We demonstrate through numerical simulations that the stochastic reconnection is able to self-generate turbulence through interactions between its outflows. We analyze the statistical properties of velocity fluctuations using power spectra and anisotropy scaling, which demonstrates that the reconnection produces Kolmogorov-like turbulence, compatible with Goldreich-Sridhar (1995) model. Anisotropy statistics are, however, strongly affected by the dynamics of reconnection outflows. Once the broad turbulent region is formed, the typical anisotropy scaling $l_\parallel \propto l_\perp^{2/3}$ is formed, especially for high resolution models, were the broader range of scales is available. The decay of reconnection outflows to turbulent-like fluctuations, characterized by different anisotropy scalings, strongly depends on $β$ plasma. Moreover, the estimated reconnection rates are weakly dependent on the resolution, suggesting that no external processes are required to make reconnection fast.