Weak Turbulence and B-field diffusion

Turbulence and magnetic fields are components of our Galaxy’s interstellar medium and are tightly interconnected through complex plasma processes. In special, the magnetic flux transport in the presence of magneto-hydrodynamic (MHD) turbulence in molecular clouds is an essential factor for understanding different processes involved in star formation. The theory of turbulent Reconnection Diffusion (RD), based on statistics of weak Alfvénic turbulence, predicts the dependence of the effective diffusion coefficient of the magnetic field with the Mach Alfvénic number M_A (which is the ratio between the turbulent velocity and the local Alfvén velocity). However, the current RD theory does not take into account the effects of compressibility, which should be important in the regime of supersonic MHD turbulence present in molecular clouds. In order to measure the diffusion coefficient D of magnetic fields in different regimes of compressible turbulence, characterized by different sonic Mach numbers M_S, we performed direct numerical simulations of forced turbulence in a periodic box with a strong uniform field B₀, for different values of M_A < 1. We employed a spectral code to investigate the limit of incompressible turbulence, and also a finite volume shock-capturing code for the compressible cases. We controlled the spectral properties of the turbulence injection and the domain size in order to reduce the 2D velocity modes which naturally grow, and we interpret the transport from these modes in our setup as artifacts due to the finite box size. Our simulations exhibit suppression in the energy cascade in the direction parallel to the global magnetic field, consistent with the weak turbulence theory. Our results confirm the RD hypothesis of the correspondence between the diffusion of the magnetic field lines with the diffusion of fluid Lagrangian particles. For incompressible turbulence, the measured diffusion is consistent with the strong suppression predicted by the RD theory: D ~ M_A³. Our compressible simulations show a trend to increase the diffusion efficiency when the turbulence is supersonic, with the suppression factor M_A^α decreasing with M_S, with α ≈ 0.5 for our most supersonic simulation with M_S ≈ 3. This quantitative characterization of this effective diffusion coefficient is critical for the modelling of the star formation process in turbulent molecular clouds, and for the evaluation of the efficiency of this transport process when compared to other mechanisms, for instance the Ambipolar Diffusion.