Energy balance and Alfvén Mach numbers in compressible magnetohydrodynamic turbulence with a largescale 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 smallscale turbulent dynamo action, and, in general, to estimate the energy budget of starforming molecular clouds. In this study, we motivate and explore the role of the volumeaveraged rootmeansquared (rms) magnetic coupling term between the turbulent, $\delta {\boldsymbol{B}}$ , and largescale, ${\boldsymbol{B}}_0$, 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 volumeaveraged turbulent kinetic energy for turbulence with a subAlfvénic largescale field. Under the assumption of exact energy equipartition between these terms, we derive relations for the magnetic and coupling term fluctuations, which provide excellent, parameterfree agreement with timeaveraged 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 subAlfvénic turbulence can only be developed through a strong, largescale magnetic field, which supports an extremely superAlfvénic turbulent magnetic field. This means that the magnetic field fluctuations are significantly subdominant to the velocity fluctuations in the subAlfvénic largescale field regime. Throughout our study, we broadly discuss the implications for observations of magnetic fields and understanding the dynamics in the magnetized ISM.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 October 2022
 DOI:
 10.1093/mnras/stac2099
 arXiv:
 arXiv:2202.13020
 Bibcode:
 2022MNRAS.515.5267B
 Keywords:

 dynamo;
 MHD;
 turbulence;
 ISM: kinematics and dynamics;
 ISM: magnetic fields;
 Astrophysics  Astrophysics of Galaxies;
 Physics  Fluid Dynamics;
 Physics  Plasma Physics
 EPrint:
 Accepted in MNRAS. 20 pages. 16 figures. 1 table