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, $\delta \mathbf{B}$ and large-scale, ${\mathbf{B}}_0$ fields, ${⟨(\delta \mathbf{B}\cdot {\mathbf{B}}_0{)}^2⟩}_{\mathcal{V}}^{1/2}$. 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 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 magnetised ISM.

arXiv commentAccepted in MNRAS. 20 pages. 16 figures. 1 table

References in corpus (89)

• SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python
• Array Programming with NumPy
• scikit-image: Image processing in Python
• From filamentary clouds to prestellar cores to the stellar IMF: Initial highlights from the Herschel Gould Belt survey
• A General Theory of Turbulence-Regulated Star Formation, From Spirals to ULIRGs
• Comparing the statistics of interstellar turbulence in simulations and observations: Solenoidal versus compressive turbulence forcing
• The Star Formation Rate of Turbulent Magnetized Clouds: Comparing Theory, Simulations, and Observations
• Spectrum of magnetohydrodynamic turbulence
• The Density Probability Distribution in Compressible Isothermal Turbulence: Solenoidal versus Compressive Forcing
• Simulations of small-scale turbulent dynamo
• Thermal and Fragmentation Properties of Star-forming Clouds in Low-metallicity Environments
• The origin, evolution and signatures of primordial magnetic fields
• The Star Formation Rate of Supersonic MHD Turbulence
• A new Jeans resolution criterion for (M)HD simulations of self-gravitating gas: Application to magnetic field amplification by gravity-driven turbulence
• On the universality of supersonic turbulence
• What determines the density structure of molecular clouds ? A case study of Orion B with Herschel
• An Imprint of Molecular Cloud Magnetization in the Morphology of the Dust Polarized Emission
• Inefficient star formation through turbulence, magnetic fields and feedback
• Mach Number Dependence of Turbulent Magnetic Field Amplification: Solenoidal versus Compressive Flows
• The link between turbulence, magnetic fields, filaments, and star formation in the Central Molecular Zone cloud G0.253+0.016
• Supernova Driving. I. The Origin of Molecular Cloud Turbulence
• Collapse, outflows and fragmentation of massive, turbulent and magnetized prestellar barotropic cores
• Dynamo theories
• The generation of strong magnetic fields during the formation of the first stars
• The Stellar IMF, Core Mass Function, & The Last-Crossing Distribution
• Analytical theory for the initial mass function: II. Properties of the flow
• Pre-galactic metal enrichment - The chemical signatures of the first stars
• A robust numerical scheme for highly compressible magnetohydrodynamics: Nonlinear stability, implementation and tests
• Is Turbulence in the Interstellar Medium Driven by Feedback or Gravity? An Observational Test
• Low-Mach-number turbulence in interstellar gas revealed by radio polarization gradients
• A General Theory of Turbulent Fragmentation
• Turbulent Driving Scales in Molecular Clouds
• Magnetic field amplification in turbulent astrophysical plasmas
• The sonic scale revealed by the world's largest supersonic turbulence simulation
• A model of nonlinear evolution and saturation of the turbulent MHD dynamo
• The Link between Magnetic Fields and Filamentary Clouds: Bimodal Cloud Orientations in the Gould Belt
• The Star Formation Rate in the Gravoturbulent Interstellar Medium
• The Turbulent Dynamo in Highly Compressible Supersonic Plasmas
• Magnetic Field Amplification by Small-Scale Dynamo Action: Dependence on Turbulence Models and Reynolds and Prandtl Numbers
• Turbulence and star formation efficiency in molecular clouds: solenoidal versus compressive motions in Orion B
• Testing Physical Models for Cosmic Ray Transport Coefficients on Galactic Scales: Self-Confinement and Extrinsic Turbulence at GeV Energies
• Algorithmic comparisons of decaying, isothermal, supersonic turbulence
• A method for reconstructing the variance of a 3D physical field from 2D observations: Application to turbulence in the ISM
• The initial conditions for planet formation: Turbulence driven by hydrodynamical instabilities in disks around young stars
• How Galactic Environment affects the Dynamical State of Molecular Clouds and their Star Formation Efficiency
• Cosmic ray transport in starburst galaxies
• Metallicity Fluctuation Statistics in the Interstellar Medium and Young Stars. I. Variance and Correlation
• Cosmic Ray Scattering in Compressible Turbulence
• Turbulent dynamo in a conducting fluid and partially ionized gas
• Saturation of the Turbulent Dynamo
• Magnetic Field Morphology in Interstellar Clouds with the Velocity Gradient Technique
• The structure and statistics of interstellar turbulence
• Turbulence in the Interstellar Medium
• The impact of stellar feedback on the density and velocity structure of the interstellar medium
• Distribution of velocity gradient orientations: Mapping magnetization with the Velocity Gradient Technique
• A method for reconstructing the PDF of a 3D turbulent density field from 2D observations
• The magnetic field and dust filaments in the Polaris Flare
• The RWST, a comprehensive statistical description of the non-Gaussian structures in the ISM
• First experimental search for production of magnetic monopoles via the Schwinger mechanism
• From primordial seed magnetic fields to the galactic dynamo
• Magnetic Fields in the Formation of the First Stars. I. Theory vs. Simulation
• Magnetic fields in star formation: a complete compilation of all the DCF estimations
• Seed magnetic fields in turbulent small-scale dynamos
• Impact of galactic shear and stellar feedback on star formation
• Star formation from dense shocked regions in supersonic isothermal magneto-turbulence
• Magnetic fields in the Milky Way from pulsar observations: effect of the correlation between thermal electrons and magnetic fields
• Classification of Magnetohydrodynamic Simulations using Wavelet Scattering Transforms
• Mapping the magnetic field in the Taurus/B211 filamentary cloud with SOFIA HAWC+ and comparing with simulation
• On the effective turbulence driving mode of molecular clouds formed in disc galaxies
• The JCMT BISTRO Survey: The Distribution of Magnetic Field Strengths towards the OMC-1 Region
• Magnetic field fluctuations in anisotropic, supersonic turbulence
• On the compressive nature of turbulence driven by ionising feedback in the pillars of the Carina Nebula
• A multi-shock model for the density variance of anisotropic, highly-magnetised, supersonic turbulence
• Filaments and striations: anisotropies in observed, supersonic, highly-magnetised turbulent clouds
• Curvature of magnetic field lines in compressible magnetized turbulence: Statistics, magnetization predictions, gradient curvature, modes and self-gravitating media
• An Observational Method to Measure the Relative Fractions of Solenoidal and Compressible Modes in Interstellar Clouds
• Fundamental scales in the kinematic phase of the turbulent dynamo
• Efficient highly-subsonic turbulent dynamo and growth of primordial magnetic fields
• The driving of turbulence in simulations of molecular cloud formation and evolution
• Do Androids Dream of Magnetic Fields? Using Neural Networks to Interpret the Turbulent Interstellar Medium
• The relation between the turbulent Mach number and observed fractal dimensions of turbulent clouds
• The relative orientation between the magnetic field and gradients of surface brightness within thin velocity slices of 12CO and 13CO emission from the Taurus molecular cloud
• First extragalactic measurement of the turbulence driving parameter: ALMA observations of the star-forming region N159E in the Large Magellanic Cloud
• Testing the Turbulent Origin of the Stellar Initial Mass Function
• The Effect of Supernovae on the Turbulence and Dispersal of Molecular Clouds
• Kinematics of the molecular interstellar medium probed by Gaia: steep velocity dispersion-size relation, isotropic turbulence, and location-dependent energy dissipation
• The relative orientation between the magnetic field and gas density structures in non-gravitating turbulent media
• High resolution simulations of nonhelical MHD turbulence
• Diagnosing Turbulence in the Neutral and Molecular Interstellar Medium of Galaxies

Cited by in corpus (10)

• Magnetic field properties in star formation: a review of their analysis methods and interpretation
• The Strength of the Sheared Magnetic Field in the Galactic's Circum-Nuclear Disk
• The density distribution and physical origins of intermittency in supersonic, highly magnetised turbulence with diverse modes of driving
• The spectrum of magnetized turbulence in the interstellar medium
• Mapping the Galactic Magnetic Field Orientation and Strength in Three Dimensions
• Growth or Decay -- I: universality of the turbulent dynamo saturation
• Aspect ratios of far-infrared and H i filaments in the diffuse interstellar medium at high Galactic latitudes
• CONGRuENTS (COsmic-ray, Neutrino, Gamma-ray and Radio Non-Thermal Spectra). I. A predictive model for galactic non-thermal emission
• Analytic characterization of sub-Alfvénic turbulence energetics
• Taking control of compressible modes: bulk viscosity and the turbulent dynamo