Andrey Beresnyak

Density fluctuations in mhd turbulence : Spectra, intermittency, and topology

We perform three-dimensional (3D) compressible MHD simulations over many dynamical times for an extended range of sonic and Alfven Mach numbers and analyze the statistics of 3D density and 2D column density, which include probability distribution functions, spectra, skewness, kurtosis, She-Leveque exponents, and genus. In order to establish the relation between the statistics of the observables, i.e., column densities, and the underlying 3D statistics of density, we analyze the effects of cloud boundaries. We define the parameter space for 3D measures to be recovered from column densities. In addition, we show that for subsonic turbulence the spectra of density fluctuations are consistent with k-7/3 in the case of a strong magnetic field and k-5/3 in the case of a weak magnetic field. For supersonic turbulence we confirm the earlier findings of the shallow spectra of density and Kolmogorov spectra of the logarithm of density. We find that the intermittencies of the density and velocity are very different.

Strong Imbalanced Turbulence

We consider stationary, forced, imbalanced, or cross helical MHD Alfvenic turbulence where the waves traveling in one direction have higher amplitudes than the opposite waves. This paper is dedicated to so-called strong turbulence, which cannot be treated perturbatively. Our main result is that the anisotropy of the weak waves is stronger than the anisotropy of strong waves. We propose that critical balance, which was originally conceived as a causality argument, has to be amended by what we call a propagation argument. This revised formulation of critical balance is able to handle the imbalanced case and reduces to the old formulation in the balanced case. We also provide a phenomenological model of energy cascading and discuss the possibility of self-similar solutions in a realistic setup of driven turbulence.

COMPARISON OF SPECTRAL SLOPES OF MAGNETOHYDRODYNAMIC AND HYDRODYNAMIC TURBULENCE AND MEASUREMENTS OF ALIGNMENT EFFECTS

We performed a series of high-resolution (up to 1024 3 ) direct numerical simulations of hydro and MHD turbulence. Our simulations correspond to the ”strong” MHD turbulence regime that cannot be treated perturbatively. We found that for simulations with normal viscosity the slopes for energy spectra of MHD are similar to ones in hydro, although slightly more shallower. However, for simulations with hyper viscosity the slopes were very different, for instance, the slopes for hydro simulations showed pronounced and well-defined bottleneck effect, while the MHD slopes were relatively much less affected. We believe that this is indicative of MHD strong turbulence being less local than Kolmogorov turbulence. This calls for revision of MHD strong turbulence models that assume local “as-in-hydro case” cascading. Non-locality of MHD turbulence casts doubt on numerical determination of the slopes with currently available (512 3 –1024 3 ) numerical resolutions, including simulations with normal viscosity. We also measure various so-called alignment effects and discuss their influence on the turbulent cascade. Subject headings: MHD – turbulence – ISM: kinematics and dynamics

Density Scaling and Anisotropy in Supersonic Magnetohydrodynamic Turbulence

We study the statistics of density for supersonic turbulence in a medium with magnetic pressure larger than the gaseous pressure. Our simulations exhibit clumpy density structures, with the contrast increasing with the Mach number. At Mach 10, the densities of some clumps are 3 orders of magnitude higher than the mean density. These clumps give rise to a flat and approximately isotropic density spectrum corresponding to the random distribution of clumps in space. We claim that the clumps originate from our random, isotropic turbulence driving. When the contribution from those clumps is suppressed by studying the logarithm of density, the density statistics exhibit scale-dependent anisotropy consistent with the models in which density structures arise from shearing by Alfven waves. It is noteworthy that originally such models were advocated for the case of low-Mach, nearly incompressible turbulence.

GROWTH OF MAGNETIC FIELDS INDUCED BY TURBULENT MOTIONS

We present numerical simulations of driven magnetohydrodynamic (MHD) turbulence with weak/moderate imposed magnetic fields. The main goal is to clarify dynamics of magnetic field growth. We also investigate the effects of the imposed magnetic fields on the MHD turbulence, including, as a limit, the case of zero external field. Our findings are as follows. First, when we start off simulations with weak mean magnetic field only (or with small scale random field with zero imposed field), we observe that there is a stage at which magnetic energy density grows linearly with time. Runs with different numerical resolutions and/or different simulation parameters show consistent results for the growth rate at the linear stage. Second, we find that, when the strength of the external field increases, the equilibrium kinetic energy density drops by roughly the product of the rms velocity and the strength of the external field. The equilibrium magnetic energy density rises by roughly the same amount. Third, when the external magnetic field is not very strong (say, less than ~0.2 times the rms velocity when measured in the units of Alfven speed), the turbulence at large scales remains statistically isotropic, i.e., there is no apparent global anisotropy of order B 0/v. We discuss implications of our results on astrophysical fluids.

TURBULENCE-INDUCED MAGNETIC FIELDS AND STRUCTURE OF COSMIC RAY MODIFIED SHOCKS

We propose a model for diffusive shock acceleration (DSA) in which stochastic magnetic fields in the shock precursor are generated through purely fluid mechanisms of a so-called small-scale dynamo. This contrasts with previous DSA models that considered magnetic fields amplified through cosmic ray (CR) streaming instabilities, i.e., either by way of individual particles resonant scattering in the magnetic fields, or by macroscopic electric currents associated with large-scale CR streaming. Instead, in our picture, the solenoidal velocity perturbations that are required for the dynamo to work are produced through the interactions of the pressure gradient of the CR precursor and density perturbations in the inflowing fluid. Our estimates show that this mechanism provides fast growth of magnetic field and is very generic. We argue that for supernovae shocks the mechanism is capable of generating upstream magnetic fields that are sufficiently strong for accelerating CRs up to around 1016 eV. No action of any other mechanism is necessary.

Cosmic ray scattering in compressible turbulence

We study the scattering of low-energy cosmic rays (CRs) in a turbulent, compressive magne- tohydrodynamic (MHD) fluid. We show that compressible MHD modes - fast or slow waves with wavelengths smaller than CR mean free paths induce cyclotron instability in CRs. The in- stability feeds the new small-scale Alfvenic wave component with wavevectors mostly along magnetic field, which is not a part of the MHD turbulence cascade. This new component gives feedback on the instability through decreasing the CR mean free path. We show that the ambient turbulence fully suppresses the instability at large scales, while wave steepening constrains the amplitude of the waves at small scales. We provide the energy spectrum of the plane-parallel Alfvenic component and calculate mean free paths of CRs as a function of their energy. We find that for the typical parameters of turbulence in the interstellar medium and in the intercluster medium the new Alfvenic component provides the scattering of the low-energy CRs that exceeds the direct resonance scattering by MHD modes. This solves the problem of insufficient scattering of low-energy CRs in the turbulent interstellar or intracluster medium that was reported in the literature.

STRUCTURE OF STATIONARY STRONG IMBALANCED TURBULENCE

In this paper we systematically study the spectrum and structure of incompressible MHD turbulence by means of high resolution direct numerical simulations. We considered both balanced and imbalanced (cross-helical) cases and simulated sub-Alfvenic as well as trans-Alfvenic turbulence. This paper extends numerics preliminarily reported in Beresnyak & Lazarian (2008). We confirm that driven imbalanced turbulence has a stationary state even for high degrees of imbalance. Our major finding is that the structure of the dominant and subdominant Alfvenic components are notably different. Using the most robust observed quantities, such as the energy ratio, we were able to reject several existing models of strong imbalanced turbulence.

Polarization Intermittency and Its Influence on MHD Turbulence

The Goldreich-Sridhar model of incompressible turbulence provides us with an elegant approach to describing strong MHD turbulence. It relies on the fact that interacting Alfvenic waves are independent and have random polarization. However, in case of strong interaction, a spontaneous local axial asymmetry can arise. We used direct numerical simulations to show that polarization alignment occurs and that it grows larger at smaller scales. Assuming critical balance, this effect could lead to a shallower spectrum and stronger anisotropy. Even small changes in these two properties will have important astrophysical consequences, e.g., for the cosmic-ray physics.

NUMERICAL STUDY OF COSMIC RAY DIFFUSION IN MAGNETOHYDRODYNAMIC TURBULENCE

We study the diffusion of cosmic rays (CRs) in turbulent magnetic fields using test particle simulations. Electromagnetic fields are produced in direct numerical MHD simulations of turbulence and used as an input for particle tracing, particle feedback on turbulence being ignored. Statistical transport coefficients from the test particle runs are compared with earlier analytical predictions. We find qualitative correspondence between them in various aspects of CR diffusion. In the incompressible case that we consider in this paper, the dominant scattering mechanism is the non-resonant mirror interactions with the slow-mode perturbations. Perpendicular transport roughly agrees with being produced by magnetic field wandering.