Compressible Magnetohydrodynamic Turbulence Research Articles

Small-amplitude Compressible Magnetohydrodynamic Turbulence Modulated by Collisionless Damping in Earth’s Magnetosheath: Observation Matches Theory

Plasma turbulence is a ubiquitous dynamical process that transfers energy across many spatial and temporal scales and affects energetic particle transport. Recent advances in the understanding of compressible magnetohydrodynamic (MHD) turbulence demonstrate the important role of damping in shaping energy distributions on small scales, yet its observational evidence is still lacking. This study provides the first observational evidence of substantial collisionless damping (CD) modulation on the small-amplitude compressible MHD turbulence cascade in Earth’s magnetosheath using four Cluster spacecraft. Based on an improved compressible MHD decomposition algorithm, turbulence is decomposed into three eigenmodes: incompressible Alfvén modes and compressible slow and fast (magnetosonic) modes. Our observations demonstrate that CD enhances the anisotropy of compressible MHD modes because CD has a strong dependence on wave propagation angle. The wavenumber distributions of slow modes are mainly stretched perpendicular to the background magnetic field ( B 0) and weakly modulated by CD. In contrast, fast modes are subjected to a more significant CD modulation. Fast modes exhibit a weak, scale-independent anisotropy above the CD truncation scale. Below the CD truncation scale, the anisotropy of fast modes enhances as wavenumbers increase. As a result, fast-mode fractions in the total energy of compressible modes decrease with the increase of perpendicular wavenumber (to B 0) or wave propagation angle. Our findings reveal how the turbulence cascade is shaped by CD and its consequences for anisotropies in the space environment.

The Diffusion and Scattering of Accelerating Particles in Compressible MHD Turbulence

We numerically study the diffusion and scattering of cosmic rays (CRs) together with their acceleration processes in the framework of the modern understanding of magnetohydrodynamic (MHD) turbulence. Based on the properties of compressible MHD turbulence obtained from observations and numerical experiments, we investigate the interaction of CRs with plasma modes. We find that (1) the gyroradius of particles exponentially increases with the acceleration timescale; (2) the momentum diffusion presents the power-law relationship with the gyroradius in the strong turbulence regime, and shows a plateau in the weak turbulence regime implying a stochastic acceleration process; (3) the spatial diffusion is dominated by the parallel diffusion in the sub-Alfvénic regime, while it is dominated by the perpendicular diffusion in the super-Alfvénic one; (4) as for the interaction of CRs with plasma modes, the particle acceleration is dominated by the fast mode in the high β case, while in the low β case, it is dominated by the fast and slow modes; and (5) in the presence of acceleration, magnetosonic modes still play a critical role in the diffusion and scattering processes of CRs, which is in good agreement with earlier theoretical predictions.

Energization of Charged Test Particles in Magnetohydrodynamic Fields: Waves versus Turbulence Picture

Direct numerical simulations of three-dimensional compressible magnetohydrodynamic (MHD) turbulence have been performed in order to study the relation between wave modes and coherent structures and the consequent energization of test particles. Moreover, the question of which is the main mechanism of this particle energization is rigorously discussed. In particular, using the same initial conditions, we analyzed the nonlinear and linear evolution of a turbulent state along with the case of randomized phases. Then, the behaviors of the linear and nonlinear simulations were compared through the study of the time evolution of particle kinetic energy and preferential concentration. Also, spatiotemporal spectra were used to identify the presence of wave modes and quantify the fraction of energy around the MHD modes in linear and nonlinear simulations. Finally, the variation of the correlation time of the external forcing is studied in detail along with the effect on the particle energization (and clustering) and the presence of wave modes. More specifically, particle energization tends to decrease when the fraction of linear energy increases, supporting the idea that energization by structures is the dominant mechanism for particle energization instead of resonance with wave modes as suggested by Fermi energization theory.

Measurement of the scaling slope of compressible magnetohydrodynamic turbulence by synchrotron radiation statistics

ABSTRACT Based on magnetohydrodynamic (MHD) turbulence simulations, we generate synthetic synchrotron observations to explore the scaling slope of the underlying MHD turbulence. We propose the new Q-U cross-intensity X and cross-correlation intensity Y to measure the spectral properties of magnetic turbulence, together with statistics of the traditional synchrotron I and polarization PI intensities. By exploring the statistical behaviour of these diagnostics, we find that the new statistics X and Y can extend the inertial range of turbulence to improve measurement reliability. When focusing on different Alfvénic and sonic turbulence regimes, our results show that the diagnostics proposed in this paper not only reveal the spectral properties of the magnetic turbulence but also gain insight into the individual plasma modes of compressible MHD turbulence. The synergy of multiple statistical methods can extract more reliable turbulence information from the huge amount of observation data from the Low-Frequency Array for radio astronomy and the Square Kilometer Array.

Probing 3D magnetic fields – I. Polarized dust emission

ABSTRACT Polarized dust emission is widely used to trace the plane-of-the-sky (POS) component of interstellar magnetic fields in two dimensions. Its potential to access 3D magnetic fields, including the inclination angle of the magnetic fields relative to the line of sight (LOS), is crucial for a variety of astrophysical problems. Based on the statistical features of observed polarization fraction and POS Alfvén Mach number $\overline{M_{\rm A}}_{,\bot }$ distribution, we present a new method for estimating the inclination angle. The magnetic field fluctuations raised by anisotropic magnetohydrodynamic (MHD) turbulence are taken into account in our method. By using synthetic dust emission generated from 3D compressible MHD turbulence simulations, we show that the fluctuations are preferentially perpendicular to the mean magnetic field. We find the inclination angle is the major agent for depolarization, while fluctuations of magnetic field strength and density have an insignificant contribution. We propose and demonstrate that the mean inclination angle over a region of interest can be calculated from the polarization fraction in a strongly magnetized reference position, where $\overline{M_{\rm A}}_{,\bot }^2\ll 1$. We test and show that the new method can trace the 3D magnetic fields in sub-Alfvénic, trans-Alfvénic, and moderately superAlfvénic conditions (0.4 ≲ MA ≲ 1.2). We numerically quantify that the difference of the estimated inclination angle and actual inclination angle ranges from 0° to 20° with a median value of ≤10°.

Studying the Properties of Compressible Magnetohydrodynamic Turbulence Using Synchrotron Fluctuation Statistics

We study the observable properties of compressible magnetohydrodynamic (MHD) turbulence covering different turbulence regimes, based on synthetic synchrotron observations arising from 3D MHD numerical simulations. Using the synchrotron emissivity and intensity, we first explore how the cosmic-ray spectral indices affect the measurements of the turbulence properties by employing normalized correlation functions. We then study how the anisotropy of the synchrotron total and polarization intensities arising from the three fundamental MHD modes varies with the viewing angle, i.e., the angle between the mean magnetic field and the line of sight. We employ the ratio of the quadrupole moment to the monopole moment (QM) for this purpose. Our numerical results demonstrate that: (1) the two-point correlation function of synchrotron statistics for the arbitrary cosmic-ray spectral index is related to the special case of the magnetic field index γ = 2, in agreement with the analytical formulae provided by Lazarian & Pogosyan; (2) the anisotropy of the synchrotron total and polarization intensities arising from the Alfvén and slow modes increases with the increase of the viewing angle, while that of fast mode remains almost unchanged with the viewing angle; and (3) the analytical formulae of the synchrotron intensities for studying turbulence can be applied to describe the statistics of the polarization intensities, and the QM can be successfully used to recover the turbulence anisotropy. This study validates the analytical approach of Lazarian & Pogosyan and opens up a way of studying turbulence from observations.

Nature and Scalings of Density Fluctuations of Compressible Magnetohydrodynamic Turbulence with Applications to the Solar Wind

The solar wind is a magnetized and turbulent plasma. Its turbulence is often dominated by Alfvénic fluctuations and often deemed as nearly incompressible far away from the Sun, as shown by in situ measurements near 1 au. However, for solar wind closer to the Sun, the plasma β decreases (often lower than unity) while the turbulent Mach number M t increases (can approach unity, e.g., transonic fluctuations). These conditions could produce significantly more compressible effects, characterized by enhanced density fluctuations, as seen by several space missions. In this paper, a series of 3D MHD simulations of turbulence are carried out to understand the properties of compressible turbulence, particularly the generation of density fluctuations. We find that, over a broad range of parameter space in plasma β, cross helicity, and polytropic index, the turbulent density fluctuations scale linearly as a function of M t , with the scaling coefficients showing weak dependence on parameters. Furthermore, through detailed spatiotemporal analysis, we show that the density fluctuations are dominated by low-frequency nonlinear structures, rather than compressible MHD eigenwaves. These results could be important for understanding how compressible turbulence contributes to solar wind heating near the Sun.

Energy balance and Alfvén Mach numbers in compressible magnetohydrodynamic turbulence with a large-scale magnetic field

ABSTRACT Energy equipartition is a powerful theoretical tool for understanding astrophysical plasmas. It is invoked, for example, to measure magnetic fields in the interstellar medium (ISM), as evidence for small-scale turbulent dynamo action, and, in general, to estimate the energy budget of star-forming molecular clouds. In this study, we motivate and explore the role of the volume-averaged root-mean-squared (rms) magnetic coupling term between the turbulent, $\delta {\boldsymbol{B}}$ , and large-scale, ${\boldsymbol{B}}_0$, fields, ${\left\langle (\delta \mathrm{{\boldsymbol {\mathit {B}}}}\cdot {\mathrm{{\boldsymbol {\mathit {B}}}}_0})^{2} \right\rangle ^{1/2}_{\mathcal {V}}}$. By considering the second moments of the energy balance equations we show that the rms coupling term is in energy equipartition with the volume-averaged turbulent kinetic energy for turbulence with a sub-Alfvénic large-scale field. Under the assumption of exact energy equipartition between these terms, we derive relations for the magnetic and coupling term fluctuations, which provide excellent, parameter-free agreement with time-averaged data from 280 numerical simulations of compressible magnetohydrodynamic (MHD) turbulence. Furthermore, we explore the relation between the turbulent mean field and total Alfvén Mach numbers, and demonstrate that sub-Alfvénic turbulence can only be developed through a strong, large-scale magnetic field, which supports an extremely super-Alfvénic turbulent magnetic field. This means that the magnetic field fluctuations are significantly subdominant to the velocity fluctuations in the sub-Alfvénic large-scale field regime. Throughout our study, we broadly discuss the implications for observations of magnetic fields and understanding the dynamics in the magnetized ISM.

Exact law for compressible pressure-anisotropic magnetohydrodynamic turbulence: Toward linking energy cascade and instabilities.

We derive an exact law for compressible pressure-anisotropic magnetohydrodynamic turbulence. For a gyrotropic pressure tensor, we study the double-adiabatic case and show the presence of new flux and source terms in the exact law, reminiscent of the plasma instability conditions due to pressure anisotropy. The Hall term is shown to bring ion-scale corrections to the exact law without affecting explicitly the pressure terms. In the pressure isotropy limit we recover all known results obtained for isothermal and polytropic closures. The incompressible limit of the gyrotropic system leads to a generalization of the Politano and Pouquet's law where a new incompressible source term is revealed and reflects exchanges of the magnetic and kinetic energies with the no-longer-conserved internal energy. We highlight the possibilities offered by the new laws to investigate potential links between turbulence cascade and instabilities widely observed in laboratory and astrophysical plasmas.

An In-depth Numerical Study of Exact Laws for Compressible Hall Magnetohydrodynamic Turbulence

Abstract Various exact laws governing compressible magnetohydrodynamic (MHD) and compressible Hall-MHD (CHMHD) turbulence have been derived in recent years. Other than their fundamental theoretical interest, these laws are generally used to estimate the energy dissipation rate from spacecraft observations in order to address diverse problems related, e.g., to heating of the solar wind and magnetospheric plasmas. Here we use various 10243 direct numerical simulation data of free-decay isothermal CHMHD turbulence obtained with the GHOST code (Geophysical High-Order Suite for Turbulence) to analyze two of the recently derived exact laws. The simulations reflect different intensities of the initial Mach number and the background magnetic field. The analysis demonstrates the equivalence of the two laws in the inertial range and relates the strength of the Hall effect to the amplitude of the cascade rate at sub-ion scales. When taken in their general form (i.e., not limited to the inertial range), some subtleties regarding the validity of the stationarity assumption or the absence of the forcing in the simulations are discussed. We show that the free-decay nature of the turbulence induces a shift from a large-scale forcing toward the presence of a scale-dependent reservoir of energy fueling the cascade or dissipation. The reduced form of the exact laws (valid in the inertial range) ultimately holds even if the stationarity assumption is not fully verified.

Energy budget in decaying compressible MHD turbulence

Abstract

Diffusion of large-scale magnetic fields by reconnection in MHD turbulence

ABSTRACT 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.

Shock identification and classification in 2D magnetohydrodynamiccompressible turbulence—Orszag–Tang vortex

Abstract Compressible magnetohydrodynamic (MHD) turbulence is a common feature of astrophysical systems such as the solar atmosphere and interstellar medium. Such systems are rife with shock waves that can redistribute and dissipate energy. For an MHD system, three broad categories of shocks exist (slow, fast, and intermediate); however, the occurrence rates of each shock type are not known for turbulent systems. Here, we present a method for detecting and classifying the full range of MHD shocks applied to the Orszag–Tang vortex. Our results show that the system is dominated by fast and slow shocks, with far less-frequent intermediate shocks appearing most readily near magnetic reconnection sites. We present a potential mechanism that could lead to the formation of intermediate shocks in MHD systems, and study the coherency and abundances of shocks in compressible MHD turbulence.

Trapping of Cosmic Rays in MHD Turbulence

Abstract Astrophysical plasmas are turbulent and magnetized. The interaction between cosmic rays (CRs) and magnetohydrodynamic (MHD) turbulence is a fundamental astrophysical process. Based on the current understanding of MHD turbulence, we revisit the trapping of CRs by magnetic mirrors in the context of MHD turbulence. In compressible MHD turbulence, isotropic fast modes dominate both trapping and gyroresonant scattering of CRs. The presence of trapping significantly suppresses the pitch-angle scattering and the spatial diffusion of CRs along the magnetic field. The resulting parallel diffusion coefficient has a weaker dependence on CR energy at higher energies. In incompressible MHD turbulence, the trapping by pseudo-Alfvén modes dominates over the gyroresonant scattering by anisotropic Alfvén and pseudo-Alfvén modes at all pitch angles and prevents CRs from diffusion.

Artificial neural network subgrid models of 2D compressible magnetohydrodynamic turbulence

We explore the suitability of deep learning to capture the physics of subgrid-scale ideal magnetohydrodynamics turbulence of 2-D simulations of the magnetized Kelvin-Helmholtz instability. We produce simulations at different resolutions to systematically quantify the performance of neural network models to reproduce the physics of these complex simulations. We compare the performance of our neural networks with gradient models, which are extensively used in the extensively in the magnetohydrodynamic literature. Our findings indicate that neural networks significantly outperform gradient models at reproducing the effects of magnetohydrodynamics turbulence. To the best of our knowledge, this is the first exploratory study on the use of deep learning to learn and reproduce the physics of magnetohydrodynamics turbulence.

Studying the Anisotropy of Compressible Magnetohydrodynamic Turbulence by Synchrotron Polarization Intensity

Abstract Based on statistical analysis of synchrotron polarization intensity, we study the anisotropic properties of compressible magnetohydrodynamic (MHD) turbulence. The second-order normalized structure function, quadrupole ratio modulus, and anisotropic coefficient are synergistically used to characterize the anisotropy of the polarization intensity. On the basis of predecomposition data cubes, we first explore the anisotropy of the polarization intensity in different turbulence regimes and find that the most significant anisotropy occurs in the sub-Alfvénic regime. Using postdecomposition data cubes in this regime, we then study the anisotropy of the polarization intensity from Alfvén, slow, and fast modes. The statistics of the polarization intensity from Alfvén and slow modes demonstrate the significant anisotropy, while the statistics of the polarization intensity from fast modes show isotropic structures. This is consistent with earlier results provided in Cho & Lazarian. As a result, both quadrupole ratio modulus and anisotropic coefficient for polarization intensities can quantitatively recover the anisotropy of underlying compressible magnetohydrodynamic turbulence. The synergistic use of the two methods helps enhance the reliability of the magnetic field measurement.

Three-dimensional Simulation of the Fast Solar Wind Driven by Compressible Magnetohydrodynamic Turbulence

Abstract Using a three-dimensional compressible magnetohydrodynamic (MHD) simulation, we have reproduced the fast solar wind in a direct and self-consistent manner, based on the wave/turbulence-driven scenario. As a natural consequence of Alfvénic perturbations at the coronal base, highly compressional and turbulent fluctuations are generated, leading to heating and acceleration of the solar wind. The analysis of power spectra and structure functions reveals that the turbulence is characterized by its imbalanced (in the sense of outward Alfvénic fluctuations) and anisotropic nature. The density fluctuation originates from the parametric decay instability (PDI) of outwardly propagating Alfvén waves and plays a significant role in the Alfvén-wave reflection that triggers turbulence. Our conclusion is that the fast solar wind is heated and accelerated by compressible MHD turbulence driven by PDI and resultant Alfvén-wave reflection.

Magnetohydrodynamic simulation code CANS+: Assessments and applications

Abstract We present a new magnetohydrodynamic (MHD) simulation package with the aim of providing accurate numerical solutions to astrophysical phenomena where discontinuities, shock waves, and turbulence are inherently important. The code implements the Harten–Lax–van Leer–discontinuitues (HLLD) approximate Riemann solver, the fifth-order-monotonicity-preserving interpolation (MP5) scheme, and the hyperbolic divergence cleaning method for a magnetic field. This choice of schemes has significantly improved numerical accuracy and stability, and saved computational costs in multidimensional problems. Numerical tests of one- and two-dimensional problems show the advantages of using the high-order scheme by comparing with results from a standard second-order total variation diminishing monotonic upwind scheme for conservation laws (MUSCL) scheme. The present code enables us to explore the long-term evolution of a three-dimensional accretion disk around a black hole, in which compressible MHD turbulence causes continuous mass accretion via nonlinear growth of the magneto-rotational instability (MRI). Numerical tests with various computational cell sizes exhibits a convergent picture of the early nonlinear growth of the MRI in a global model, and indicates that the MP5 scheme has more than twice the resolution of the MUSCL scheme in practical applications.

On the Formation of Density Filaments in the Turbulent Interstellar Medium

Abstract 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.

Dissipation Scale Lengths of Solar Wind Turbulence

Abstract Knowing the lengthscales at which turbulent fluctuations dissipate is key to understanding the nature of weakly compressible magnetohydrodynamic turbulence. We use radio wavelength interferometric imaging observations that measure the extent to which distant cosmic sources observed against the inner solar wind are scatter-broadened. We interpret these observations to determine that the dissipation scales of solar wind density turbulence at heliocentric distances of 2.5–20.27 R ⊙ range from ≈13500 to 520 m. Our estimates from ≈10 to 20 R ⊙ suggest that the dissipation scale corresponds to the proton gyroradius. They are relevant to in situ observations to be made by the Parker Solar Probe and are expected to enhance our understanding of solar wind acceleration.