Energy balance and Alfvén Mach numbers in compressible magnetohydrodynamic turbulence with a large-scale magnetic field. Issue 4 (28th July 2022) - Beattie, James R; Krumholz, Mark R; Skalidis, Raphael; Federrath, Christoph; Seta, Amit; Crocker, Roland M; Mocz, Philip; Kriel, Neco
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, $δ {\boldsymbol{B}}$, and large-scale, ${\boldsymbol{B}}_0$, fields, ${\left\langle (δ \mathrm{{\boldsymbol {B}}}· {\mathrm{{\boldsymbol {B}}}_0})^{2} \right\rangle ^{1/2}_{\mathcal {V}}}$ . 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.