Magnetic flux transport via reconnection diffusion in different sonic regimes of interstellar MHD turbulence

The rate of magnetic field diffusion plays an essential role in several astrophysical plasma processes. It has been demonstrated that the omnipresent turbulence in astrophysical media induces fast magnetic reconnection, which consequently leads to large-scale magnetic flux diffusion at a rate independent of the plasma microphysics. This process is called 'reconnection diffusion' (RD) and allows for the diffusion of fields, which are dynamically important. The current theory describing RD is based on incompressible magnetohydrodynamic (MHD) turbulence. In this work, we have tested quantitatively the predictions of the RD theory when magnetic forces are dominant in the turbulence dynamics (Alfvénic Mach number MA < 1). We employed the Pencil Code to perform numerical simulations of forced MHD turbulence, extracting the values of the diffusion coefficient ηRD using the test-field method. Our results are consistent with the RD theory ($\eta _{\rm RD} \sim M_{\rm A}^{3}$ for MA < 1) when turbulence approaches the incompressible limit (sonic Mach number MS ≲ 0.02), while for larger MS the diffusion is faster ($\eta _{\rm RD} \sim M_{\rm A}^{2}$). This work shows for the first time simulations of compressible MHD turbulence with the suppression of the cascade in the direction parallel to the mean magnetic field, which is consistent with incompressible weak turbulence theory. We also verified that in our simulations the energy cascading time does not follow the scaling with MA predicted for the weak regime, in contradiction with the RD theory assumption. Our results generally support and expand the RD theory predictions.

Astrophysical fluids are turbulent a fact which changes the dynamics of many key processes, including magnetic reconnection. Fast reconnection of magnetic field in turbulent fluids allows the field to change its topology and connections. As a result, the traditional concept of magnetic fields being frozen into the plasma is no longer applicable. Plasma associated with a given magnetic field line at one instant is distributed along a different set of magnetic field lines at the next instant. This diffusion of plasmas and magnetic field is enabled by reconnection and therefore is termed “reconnection diffusion”. The astrophysical implications of this concept include heat transfer in plasmas, advection of heavy elements in interstellar medium, magnetic field generation etc. However, the most dramatic implications of the concept are related to the star formation process. The reason is that magnetic fields are dynamically important for most of the stages of star formation. The existing theory of star formation has been developed ignoring the possibility of reconnection diffusion. Instead, it appeals to the decoupling of mass and magnetic field arising from neutrals drifting in respect to ions entrained on magnetic field lines, i.e. through the process that is termed “ambipolar diffusion”. The predictions of ambipolar diffusion and reconnection diffusion are very different. For instance, if the ionization of media is high, ambipolar diffusion predicts that the coupling of mass and magnetic field is nearly perfect. At the same time, reconnection diffusion is independent of the ionization but depends on the scale of the turbulent eddies and on the turbulent velocities. In the paper we explain the physics of reconnection diffusion both from macroscopic and microscopic points of view, i.e. appealing to the reconnection of flux tubes and to the diffusion of magnetic field lines. We make use of the Lazarian and Vishniac (Astrophys. J. 517:700, 1999) theory of magnetic reconnection and show that this theory is applicable to the partially ionized gas. We quantify the reconnection diffusion rate both for weak and strong MHD turbulence and address the problem of reconnection diffusion acting together with ambipolar diffusion. In addition, we provide a criterion for correctly representing the magnetic diffusivity in simulations of star formation. We discuss the intimate relation between the processes of reconnection diffusion, field wandering and turbulent mixing of a magnetized media and show that the role of the plasma effects is limited to “breaking up lines” on small scales and does not affect the rate of reconnection diffusion. We address the existing observational results and demonstrate how reconnection diffusion can explain the puzzles presented by observations, in particular, the observed higher magnetization of cloud cores in comparison with the magnetization of envelopes. We also outline a possible set of observational tests of the reconnection diffusion concept and discuss how the application of the new concept changes our understanding of star formation and its numerical modeling. Finally, we outline the differences of the process of reconnection diffusion and the process of accumulation of matter along magnetic field lines that is frequently invoked to explain the results of numerical simulations.

Recent observational results for magnetic fields in molecular clouds reviewed by Crutcher (2012) seem to be inconsistent with the predictions of the ambipolar diffusion theory of star formation. These include the measured decrease in mass to flux ratio between envelopes and cores, the failure to detect any self-gravitating magnetically subcritical clouds, the determination of the flat PDF of the total magnetic field strengths implying that there are many clouds with very weak magnetic fields, and the observed scaling $B \propto \rho^{2/3}$ that implies gravitational contraction with weak magnetic fields. We consider the problem of magnetic field evolution in turbulent molecular clouds and discuss the process of magnetic field diffusion mediated by magnetic reconnection. For this process that we termed "reconnection diffusion" we provide a simple physical model and explain that this process is inevitable in view of the present day understanding of MHD turbulence. We address the issue of the expected magnetization of cores and envelopes in the process of star formation and show that reconnection diffusion provides an efficient removal of magnetic flux that depends only on the properties of MHD turbulence in the core and the envelope. As a result, the magnetic flux trapped during the collapse in the envelope is being released faster than the flux trapped in the core, resulting in much weaker fields in envelopes than in cores, as observed. We provide simple semi-analytical model calculations which support this conclusion and qualitatively agree with the observational results. We argue that magnetic reconnection provides a solution to the magnetic flux problem of star formation that agrees better with observations than the long-standing ambipolar diffusion paradigm.

In an effort to characterize the Mach numbers of ISM magnetohydrodynamic (MHD) turbulence, we study the probability distribution functions (PDFs) of patial increments of density, velocity, and magnetic field for fourteen ideal isothermal MHD simulations at resolution 512^3. In particular, we fit the PDFs using the Tsallis function and study the dependency of fit parameters on the compressibility and magnetization of the gas. We find that the Tsallis function fits PDFs of MHD turbulence well, with fit parameters showing sensitivities to the sonic and Alfven Mach numbers. For 3D density, column density, and position-position-velocity (PPV) data we find that the amplitude and width of the PDFs shows a dependency on the sonic Mach number. We also find the width of the PDF is sensitive to global Alfvenic Mach number especially in cases where the sonic number is high. These dependencies are also found for mock observational cases, where cloud-like boundary conditions, smoothing, and noise are introduced. The ability of Tsallis statistics to characterize sonic and Alfvenic Mach numbers of simulated ISM turbulence point to it being a useful tool in the analysis of the observed ISM, especially when used simultaneously with other statistical techniques.

Supersonic, magnetohydrodynamic (MHD) turbulence is thought to play an important role in many processes — especially in astrophysics, where detailed three-dimensional observations are scarce. Simulations can partially fill this gap and help to understand these processes. However, direct simulations with realistic parameters are often not feasible. Consequently, large eddy simulations (LES) have emerged as a viable alternative. In LES the overall complexity is reduced by simulating only large and intermediate scales directly. The smallest scales, usually referred to as subgrid-scales (SGS), are introduced to the simulation by means of an SGS model. Thus, the overall quality of an LES with respect to properly accounting for small-scale physics crucially depends on the quality of the SGS model. While there has been a lot of successful research on SGS models in the hydrodynamic regime for decades, SGS modeling in MHD is a rather recent topic, in particular, in the compressible regime. In this thesis, we derive and validate a new nonlinear MHD SGS model that explicitly takes compressibility effects into account. A filter is used to separate the large and intermediate scales, and it is thought to mimic finite resolution effects. In the derivation, we use a deconvolution approach on the filter kernel. With this approach, we are able to derive nonlinear closures for all SGS terms in MHD: the turbulent Reynolds and Maxwell stresses, and the turbulent electromotive force (EMF). We validate the new closures both a priori and a posteriori. In the a priori tests, we use high-resolution reference data of stationary, homogeneous, isotropic MHD turbulence to compare exact SGS quantities against predictions by the closures. The comparison includes, for example, correlations of turbulent fluxes, the average dissipative behavior, and alignment of SGS vectors such as the EMF. In order to quantify the performance of the new nonlinear closure, this comparison is conducted from the subsonic (sonic Mach number M s ≈ 0.2) to the highly supersonic (M s ≈ 20) regime, and against other SGS closures. The latter include established closures of eddy-viscosity and scale-similarity type. In all tests and over the entire parameter space, we find that the proposed closures are (significantly) closer to the reference data than the other closures. In the a posteriori tests, we perform large eddy simulations of decaying, supersonic MHD turbulence with initial M s ≈ 3. We implemented closures of all types, i.e. of eddy-viscosity, scale-similarity and nonlinear type, as an SGS model and evaluated their performance in comparison to simulations without a model (and at higher resolution). We find that the models need to be calculated on a scale larger than the grid scale, e.g. by an explicit filter, to have an influence on the dynamics at all. Furthermore, we show that only the proposed nonlinear closure improves higher-order statistics.

Turbulent magnetofluids appear in various geophysical and astrophysical contexts, in phenomena associated with planets, stars, galaxies and the universe itself. In many cases, large-scale magnetic fields are observed, though a better knowledge of magnetofluid turbulence is needed to more fully understand the dynamo processes that produce them. One approach is to develop the statistical mechanics of ideal (i.e. non-dissipative), incompressible, homogeneous magnetohydrodynamic (MHD) turbulence, known as “absolute equilibrium ensemble” theory, as far as possible by studying model systems with the goal of finding those aspects that survive the introduction of viscosity and resistivity. Here, we review the progress that has been made in this direction. We examine both three-dimensional (3-D) and two-dimensional (2-D) model systems based on discrete Fourier representations. The basic equations are those of incompressible MHD and may include the effects of rotation and/or a mean magnetic field B o. Statistical predictions are that Fourier coefficients of the velocity and magnetic field are zero-mean random variables. However, this is not the case, in general, for we observe non-ergodic behavior in very long time computer simulations of ideal turbulence: low wavenumber Fourier modes that have relatively large means and small standard deviations, i.e. coherent structure. In particular, ergodicity appears strongly broken when B o = 0 and weakly broken when B o ≠ 0. Broken ergodicity in MHD turbulence is explained by an eigenanalysis of modal covariance matrices. This produces a set of modal eigenvalues inversely proportional to the expected energy of their associated eigenvariables. A large disparity in eigenvalues within the same mode (identified by wavevector k ) can occur at low values of wavenumber k = | k |, especially when B o = 0. This disparity breaks the ergodicity of eigenvariables with smallest eigenvalues (largest energies). This leads to coherent structure in models of ideal homogeneous MHD turbulence, which can occur at lowest values of wavenumber k for 3-D cases, and at either lowest or highest k for ideal 2-D magnetofluids. These ideal results appear relevant for unforced, decaying MHD turbulence, so that broken ergodicity effects in MHD turbulence survive dissipation. In comparison, we will also examine ideal hydrodynamic (HD) turbulence, which, in the 3-D case, will be seen to differ fundamentally from ideal MHD turbulence in that coherent structure due to broken ergodicity can only occur at maximum k in numerical simulations. However, a nonzero viscosity eliminates this ideal 3-D HD structure, so that unforced, decaying 3-D HD turbulence is expected to be ergodic. In summary, broken ergodicity in MHD turbulence leads to energetic, large-scale, quasistationary magnetic fields (coherent structures) in numerical models of bounded, turbulent magnetofluids. Thus, broken ergodicity provides a large-scale dynamo mechanism within computer models of homogeneous MHD turbulence. These results may help us to better understand the origin of global magnetic fields in astrophysical and geophysical objects.

The role of magnetohydrodynamics (MHD) turbulence in astrophysical environments is still highly debated. An important question that permeates this debate is the transport of magnetic flux. This is particularly important, for instance, in the context of star formation. When clouds collapse gravitationally to form stars, there must be some magnetic flux transport. Otherwise, the newborn stars would have magnetic fields several orders of magnitude larger than the observed ones. Also, the magnetic flux that is dragged in the late stages of the formation of a star can remove all the rotational support from the accretion disc that grows around the protostar. The efficiency of the mechanism that is often invoked to allow transport of magnetic fields at different stages of star formation, namely ambipolar diffusion, has recently been put in check. We discuss here an alternative mechanism for magnetic flux transport which is based on turbulent fast magnetic reconnection. We review recent results from three-dimensional MHD numerical simulations that indicate that this mechanism is very efficient in decoupling and transporting magnetic flux from the inner denser regions to the outskirts of collapsing clouds at different stages of star formation. We discuss this mechanism also in the context of dynamo processes and speculate that it can play a role both in solar dynamo and in accretion disc dynamo processes.

This study is motivated by recent observations of ubiquitous interstellar density filaments and guided by modern theories of compressible magnetohydrodynamic (MHD) turbulence. The interstellar turbulence shapes the observed density structures. As the fundamental dynamics of compressible MHD turbulence, perpendicular turbulent mixing of density fluctuations entails elongated density structures aligned with the local magnetic field, accounting for low-density parallel filaments seen in diffuse atomic and molecular gas. The elongation of low-density parallel filaments depends on the turbulence anisotropy. When taking into account the partial ionization, we find that the minimum width of parallel filaments in the cold neutral medium and molecular clouds is determined by the neutral–ion decoupling scale perpendicular to magnetic field. In highly supersonic MHD turbulence in molecular clouds, both low-density parallel filaments due to anisotropic turbulent mixing and high-density filaments due to shock compression exist.

We present numerical simulations and explore scalings and anisotropy of compressible magnetohydrodynamic (MHD) turbulence. Our study covers both gas pressure dominated (high beta) and magnetically dominated (low beta) plasmas at different Mach numbers. In addition, we present results for superAlfvenic turbulence and discuss in what way it is similar to the subAlfvenic turbulence. We describe a technique of separating different magnetohydrodynamic (MHD) modes (slow, fast and Alfven) and apply it to our simulations. We show that, for both high and low beta cases, Alfven and slow modes reveal the Kolmogorov spectrum (index=-5/3) and scale-dependent Goldreich-Sridhar anisotropy, while fast modes exhibit spectrum with index=-3/2 and isotropy. We discuss the statistics of density fluctuations arising from MHD turbulence at different regimes. Our findings entail numerous astrophysical implications ranging from cosmic ray propagation to gamma ray bursts and star formation. In particular, we show that the rapid decay of turbulence reported by earlier researchers is not related to compressibility and mode coupling in MHD turbulence. In addition, we show that magnetic field enhancements and density enhancements are marginally correlated. Addressing the density structure of partially ionized interstellar gas on AU scales, we show that the new regime of MHD turbulence that we earlier reported for incompressible flows persists for compressible turbulence and therefore may provide an explanation for those mysterious structures.

We consider astrophysical maser radiation that is created in the presence of mildly supersonic, magnetohydrodynamic (MHD) turbulence. The focus is on the OH masers for which the magnetic field is strong enough that the separations of the Zeeman components are greater than the spectral line breadths. A long-standing puzzle has been the absence of the Zeeman π-components and the high circular polarization in the observed spectra of these masers. We first argue that the elongation of eddies along the field that has recently been recognized in MHD turbulence will enhance the optical depth parallel to the magnetic field in comparison with that perpendicular to the magnetic field. We then simulate maser emission with a numerical model of MHD turbulence to demonstrate quantitatively how the intensities of the linearly polarized π-components are suppressed and the intensities of the nearly circularly polarized σ-components are enhanced. This effect is also generic in the sense that most spectral lines in MHD turbulence with Mach number M ~ 1 should have larger optical depth parallel to the magnetic field than perpendicular. The effect is reduced considerably when M < 1. The simulations also demonstrate that the velocity and magnetic field variations due to the turbulence can (but do not necessarily) cause one of the σ-components to be much more intense than the other, as is often observed for mainline OH masers.

We present theoretical and computational results in magnetohydrodynamic turbulence that we feel are essential to understanding the geodynamo. These results are based on a mathematical model that focuses on magnetohydrodynamic (MHD) turbulence, but ignores compressibility and thermal effects, as well as imposing model-dependent boundary conditions. A principal finding is that when a turbulent magnetofluid is in quasi-equilibrium, the magnetic energy in the internal dipole component is equal to the magnetic helicity multiplied by the dipole wavenumber. In the case of the Earth, measurement of the exterior magnetic field gives us, through boundary conditions, the internal poloidal magnetic field. The connection between magnetic helicity and dipole field in the liquid core then gives us the toroidal part of the internal dipole field and a model value of 3 mT for the average core dipole magnetic field. Here, we present the theoretical analysis and numerical simulations that lead to these conclusions. We also test an earlier assertion that differential oblateness may be related to dipole alignment, and while there is an effect, rotation appears to be far more important. In addition, the relationship between dipole quasi-stationarity, broken ergodicity and broken symmetry is clarified. Lastly, we discuss how inertial waves in a rotating magnetofluid can affect dipole alignment.

&amp;lt;p&amp;gt;The induced magnetotails on Mars and Venus are considered to arise through the interplanetary magnetic field (IMF) draping around the planet and the solar wind deceleration due to the mass loading effect. They have very similar structures as that on Earth, two magnetic lobes of opposite radial magnetic fields and a plasma sheet in between. However, the orientation and geometry of the induced magnetotails are controlled by the IMF, not the planetary intrinsic magnetic field. In this study, we present another characteristic of the induced magnetotails on Mars and Venus with the observations of MAVEN and Venus Express. It is found that the magnetic flux in the induced magnetotails on Mars and Venus are inhomogeneous. There is more magnetic flux in the +E hemisphere than -E hemisphere. The magnetic flux is observed to transport gradually from the +E hemisphere to the -E hemisphere along the magnetotail. The magnetotail magnetic flux transport seems to be faster on Mars than that at Venus. Based on these observations, we suggest that the finite gyro-radius effect of the planetary ions that are picked up by the solar wind is responsible to the magnetic flux inhomogeneity and transport in the induced magnetotails. The role of the magnetic pressure gradient in the magnetotail will be discussed.&amp;lt;/p&amp;gt;

We have studied the effect of strong magnetic field on the viscous properties of hot QCD matter at finite chemical potential by calculating the shear viscosity (eta ) and the bulk viscosity (zeta ). The viscosities have been calculated using the relativistic Boltzmann transport equation within the relaxation time approximation. The interactions among partons are incorporated through their quasiparticle masses at finite temperature, strong magnetic field and finite chemical potential. From this study, one can understand the influence of strong magnetic field and the influence of chemical potential on the sound attenuation through the Prandtl number (Pl), on the nature of the flow by the Reynolds number (Rl), and on the relative behavior between the shear viscosity and the bulk viscosity through the ratio zeta /eta . We have observed that, both shear and bulk viscosities get increased in the presence of a strong magnetic field and the additional presence of chemical potential further enhances their magnitudes. With the increase of temperature, eta increases for the medium in the presence of a strong magnetic field as well as for the isotropic medium in the absence of magnetic field, whereas zeta is found to decrease with the temperature, contrary to its increase in the absence of magnetic field. We have observed that, the Prandtl number gets increased in the presence of strong magnetic field and finite chemical potential as compared to that in the isotropic medium, but it always remains larger than unity, thus instead of the thermal diffusion, the momentum diffusion largely affects the sound attenuation in the medium and this is more vigorous in the presence of both strong magnetic field and finite chemical potential. However, the Reynolds number becomes lowered than unity in an ambience of strong magnetic field and even gets further decreased in an additional presence of chemical potential, thus it implies the dominance of kinematic viscosity over the characteristic length scale of the system. Finally, the ratio zeta /eta is amplified to the value larger than unity, contrary to its value in the absence of magnetic field and chemical potential where it is less than unity, thus it is inferred that the bulk viscosity prevails over the shear viscosity for the hot and dense QCD matter in the presence of a strong magnetic field.

Session A : Large Interaction Parameter.- Liquid metal in a strong magnetic field (General Lecture).- Numerical solutions of three-dimensional MHD flows in strong non-uniform transverse magnetic fields.- MHD-flows at high Rm, N and Ha.- MHD pressure drop of liquid metal flow in circular and rectangular ducts under transverse magnetic field.- Linear approximation application limits in MHD-flow theory for strong magnetic fields. Experimental results.- Session B : Fusion Related Flows.- Application of the core flow approach to MHD fluid flow in geometric elements of a fusion reactor blanket.- Experimental and theoretical work on MHD at the kernforschungszentrum Karlsruhe. The MEKKA-program.- Liquid metal turbulent flow phenomena and their implications on fusion reactor blanket design.- Experimental investigation of 3-D MHD flows at high Hartmann number and interaction parameter.- Magnetohydrodynamics in nuclear energetics (General lecture).- Poster Session 1 : DC Fields.- Liquid metal flows with polydispersed solid and gaseous inclusions.- Dispersion of small particles in MHD flows.- Two-phase flows studies in mercury-air liquid metal MHD generators.- Liquid metal MHD generators in two-phase flow systems.- Modelling of magnetohydrodynamic two-phase flow in pipe.- Melt magnetohydrodynamics of single crystal growth.- The effect of electromagnetic field on semiconductor single crystal growth and characteristics.- Gas bubbles motion during vacuum treatment of liquid aluminium in MDV-type devices.- MHD turbulence decay behind spatial grids.- The effect of a uniform magnetic field on stability, transition and turbulence as a control means for liquid metal flow mixing.- Session C : Current Carrying Melts.- Electrically induced vortical flows (General lecture).- Liquid metal flow near magnetic neutral points.- Modelling of electrically induced flows for studying current carrying melts of electrometallurgical devices.- Session D : Aluminium Reduction Cells.- Amplitude evolution of interfacial waves in aluminium reduction cells.- Physical and mathematical modeling of MHD-processes in aluminium reduction cells.- On the analysis by perturbation methods of the anodic current fluctuations in an electrolytic cell for aluminium production.- Session E : AC Stirring.- Fluid flows induced by alternating magnetic (General lecture).- Fluid metal flow study in an induction furnace based on numerical simulation.- A high frequency induction furnace for oxide melting.- Directional melt-flow in channel induction furnaces.- Characteristic properties of MHD flow in magnetodynamic pumps.- Session F : Electromagnetic Shaping.- Deflection of a stream of liquid metal by means of an alternating magnetic field.- The shape of liquid metal jets under a uniform transverse magnetic field.- Electromagnetic control of liquid metal free surfaces.- Deformation of an electrically conducting drop in a magnetic field.- Controlled decomposition of liquid metal jets and films in technological and power devices.- Poster Session 2 : AC Fields.- More accurate skin-depth approximation.- Overall and local thickness measurement of layers with differing electrical properties.- Determination of MHD machine parameters using the 1D model of a non-uniform flow.- Experimental and theoretical studies on the stability of induction pumps at large Rm numbers.- 3500 m3/h MHD pump for fast breeder reactor.- Self-excitation of liquid metal MHD generators.- Comprehensive study on the MHD phenomena in the metal pool with the single-phase induction coil.- Grain refinement in continously cast ingots of light metals by electromagnetic casting.- Liquid metal flow control using AC fields.- Session G : Measurements.- Diagnostics of liquid metal flows using fibre-optic velocity sensor.- On local measurements of the up and downstream magnetic wake of a cylinder at low magnetic Reynolds number.- Metallurgical aspects of electromagnetic processing of materials (General lecture).- Session H : Dynamo Theory.- Liquid metal MHD and the geodynamo (General lecture).- The helical MHD dynamo.- The Ponomarenko dynamo.- MHD phenomena in fast neutron reactors with a liquid metal heat carrier.- Session I : Turbulence.- The effect of initial and boundary conditions upon the formation and development of MHD turbulence structure.- Two-dimensional MHD turbulence.- MHD instabilities and turbulence in liquid metal shear flows.- Session J : Stability with Uniform Field.- Dispersion and chaos in linear arrays of vortices.- Stability of magnetohydrodynamic flow over a stretching sheet.- Stability of closed azimuthal jet of liquid metal.

It is well known that magnetohydrodynamic (MHD) turbulence is ubiquitous in astrophysical environments. The correct understanding of the fundamental properties of MHD turbulence is a pre-requisite for revealing many key astrophysical processes. The development of observation-based measurement techniques has significantly promoted MHD turbulence theory and its implications in astrophysics. After describing the modern understanding of MHD turbulence based on theoretical analysis and direct numerical simulations, we review recent developments related to synchrotron fluctuation techniques. Specifically, we comment on the validation of synchrotron fluctuation techniques and the measurement performance of several properties of magnetic turbulence based on data cubes from MHD turbulence simulations and observations. Furthermore, we propose to strengthen the studies of the magnetization and 3D magnetic field structure’s measurements of interstellar turbulence. At the same time, we also discuss the prospects of new techniques for measuring magnetic field properties and understanding astrophysical processes, using a large number of data cubes from the Low-Frequency Array (LOFAR) and the Square Kilometre Array (SKA).