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 invoked, example, to measure magnetic fields in the interstellar medium (ISM), as evidence small-scale turbulent dynamo action, and, general, estimate energy budget of star-forming molecular clouds. In this study, we motivate and explore role volume-averaged root-mean-squared (rms) coupling term between turbulent, $\delta {\boldsymbol{B}}$ , large-scale, ${\boldsymbol{B}}_0$, fields, ${\left\langle (\delta \mathrm{{\boldsymbol {\mathit {B}}}}\cdot {\mathrm{{\boldsymbol {B}}}}_0})^{2} \right\rangle ^{1/2}_{\mathcal {V}}}$. By considering second moments balance equations show that rms with kinetic turbulence sub-Alfvénic large-scale field. Under assumption exact these terms, derive relations fluctuations, which provide excellent, parameter-free agreement time-averaged data from 280 numerical simulations compressible magnetohydrodynamic (MHD) turbulence. Furthermore, relation mean field total Alfvén Mach numbers, demonstrate can only be developed through strong, field, supports an extremely super-Alfvénic This means fluctuations are significantly subdominant velocity regime. Throughout our broadly discuss implications observations dynamics magnetized ISM.