Energy balance and Alfv\'en Mach numbers in compressible
  magnetohydrodynamic turbulence with a large-scale magnetic field
  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, $\delta\mathbf{B}$ and large-scale, $\mathbf{B}_0$ fields, $\left<
(\delta\mathbf{B}\cdot\mathbf{B}_0)^{2} \right>^{1/2}_{\mathcal{V}}$. 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-Alfv\'enic 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 Alfv\'en Mach numbers, and
demonstrate that sub-Alfv\'enic turbulence can only be developed through a
strong, large-scale magnetic field, which supports an extremely
super-Alfv\'enic turbulent magnetic field. This means that the magnetic field
fluctuations are significantly subdominant to the velocity fluctuations in the
sub-Alfv\'enic 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.
