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, $\delta \mathrm{{\boldsymbol {\mathit {B}}}}$ and large-scale, $\operatorname{\mathrm{{\boldsymbol {\mathit {B}}}}_0}$ fields, $\operatorname{\left\langle (\delta \mathrm{{\boldsymbol {\mathit {B}}}}\cdot \operatorname{\mathrm{{\boldsymbol {\mathit {B}}}}_0})^{2} \right\rangle ^{1/2}_{\mathcal {V}}}$. 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 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.

Aspect ratios of far-infrared and H i filaments in the diffuse interstellar medium at high Galactic latitudes

“…For turbulent as well as for mean magnetic field strengths, we find an average scaling relation of B ∝ n 0.58 H . We confirm the models by Federrath (2016), Beattie et al (2020), and Beattie et al (2022) with the prediction of a critical transition for the magnetic-field evolution that imposes upper limits on the strengths of mean-field normalized magnetic field fluctuations. 2022).…”

“…( 11) to (13). Furthermore, only B POS = B ST from the ST solution shows an upper limit to |δB|/|B POS | for the expected equilibrium between turbulent and mean magnetic fields as predicted by Federrath (2016), Beattie et al (2020), andBeattie et al (2022). Our results strongly support compressible quasi-static fluctuation models (Fig.…”

“…This is the regime of MHD turbulence where anisotropic structures are expected in the case of an incompressible medium (Goldreich & Sridhar 1995). It is also the critical transition region where Federrath (2016), Beattie et al (2020), andBeattie et al (2022) found energy equipartition be-tween the turbulent and large-scale magnetic field in the case of compressible turbulence.…”

“…According to relation (29) of Beattie et al (2020), the critical transition occurs in MHD simulations at an Alfvénic Mach number of M Acrit = 1.44; see also Fig. 7 of Beattie et al (2022). In the following, we intend to also compare this model prediction with observational data.…”

Magnetic field properties in star formation: A review of their analysis methods and interpretation

“…In this case, the volume-averaged coupling-term magnetic energy is 0 by definition (Zweibel and McKee, 1995;Liu et al, 2022), which should not be used in analyses. Several numerical studies (Federrath, 2016;Beattie et al, 2020;Beattie et al, 2022) have suggested that the volume-averaged RMS coupling-term magnetic energy fluctuation should be studied instead of the volume-averaged coupling-term magnetic energy. With non-self-gravitating sub-Alfvénic simulations, they found that the coupling-term field energy fluctuation is in equipartition with the turbulent kinetic energy within the whole simulation box.…”