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.

Accepted in MNRAS. 20 pages. 16 figures. 1 table

References in corpus (39)

• Array Programming with NumPy
• scikit-image: Image processing in Python
• The Density Probability Distribution in Compressible Isothermal Turbulence: Solenoidal versus Compressive Forcing
• A new Jeans resolution criterion for (M)HD simulations of self-gravitating gas: Application to magnetic field amplification by gravity-driven turbulence
• What determines the density structure of molecular clouds ? A case study of Orion B with Herschel
• Inefficient star formation through turbulence, magnetic fields and feedback
• The link between turbulence, magnetic fields, filaments, and star formation in the Central Molecular Zone cloud G0.253+0.016
• A robust numerical scheme for highly compressible magnetohydrodynamics: Nonlinear stability, implementation and tests
• Magnetic field amplification in turbulent astrophysical plasmas
• The sonic scale revealed by the world's largest supersonic turbulence simulation
• The Turbulent Dynamo in Highly Compressible Supersonic Plasmas
• Turbulence and star formation efficiency in molecular clouds: solenoidal versus compressive motions in Orion B
• Cosmic ray transport in starburst galaxies
• Cosmic Ray Scattering in Compressible Turbulence
• Turbulent dynamo in a conducting fluid and partially ionized gas
• The structure and statistics of interstellar turbulence
• Magnetic Field Morphology in Interstellar Clouds with the Velocity Gradient Technique
• Turbulence in the Interstellar Medium
• The impact of stellar feedback on the density and velocity structure of the interstellar medium
• The magnetic field and dust filaments in the Polaris Flare
• First experimental search for production of magnetic monopoles via the Schwinger mechanism
• 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
• Magnetic fields in the Milky Way from pulsar observations: effect of the correlation between thermal electrons and magnetic fields
• Mapping the magnetic field in the Taurus/B211 filamentary cloud with SOFIA HAWC+ and comparing with simulation
• The JCMT BISTRO Survey: The Distribution of Magnetic Field Strengths towards the OMC-1 Region
• Magnetic field fluctuations in anisotropic, supersonic turbulence
• Filaments and striations: anisotropies in observed, supersonic, highly-magnetised turbulent clouds
• A multi-shock model for the density variance of anisotropic, highly-magnetised, supersonic turbulence
• Fundamental scales in the kinematic phase of the turbulent dynamo
• Efficient highly-subsonic turbulent dynamo and growth of primordial magnetic fields
• An Observational Method to Measure the Relative Fractions of Solenoidal and Compressible Modes in Interstellar Clouds
• The relation between the turbulent Mach number and observed fractal dimensions of turbulent clouds
• First extragalactic measurement of the turbulence driving parameter: ALMA observations of the star-forming region N159E in the Large Magellanic Cloud
• 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
• Kinematics of the molecular interstellar medium probed by Gaia: steep velocity dispersion-size relation, isotropic turbulence, and location-dependent energy dissipation
• Testing the Turbulent Origin of the Stellar Initial Mass Function
• Diagnosing Turbulence in the Neutral and Molecular Interstellar Medium of Galaxies

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