Energy balance and Alfvén Mach numbers in compressible magnetohydrodynamic turbulence with a large-scale magnetic field. Issue 4 (28th July 2022)

• Record Type: Journal Article
• Authors: Beattie, James R; Krumholz, Mark R; Skalidis, Raphael; Federrath, Christoph; Seta, Amit; Crocker, Roland M; Mocz, Philip; Kriel, Neco
• Is Part Of: Monthly notices of the Royal Astronomical Society. Volume 515:Issue 4(2022)
• Page Start: 5267
• Page End: 5284
• Publication Date: 2022-07-28
• Subjects: dynamo -- MHD -- turbulence -- ISM: kinematics and dynamics -- ISM: magnetic fields; Astronomy -- Periodicals; Periodicals; 520.5
• DOI: 10.1093/mnras/stac2099
• Languages: English
• ISSNs: 0035-8711

Abstract

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.