Sub-Alfvenic Turbulence: Magnetic to Kinetic Energy Ratio, Modification of Weak Cascade and Implications for Magnetic Field Strength Measurement

We study the properties of sub-Alfvenic magnetohydrodynamic (MHD) turbulence, i.e., turbulence with Alfven Mach number $M_A=V_L/V_A<1$, where $V_L$ is the velocity at the injection scale and $V_A$ is the Alfven velocity. We demonstrate that weak turbulence can have different regimes depending on whether it is driven by velocity or magnetic fluctuations. If the turbulence is driven by isotropic bulk forces, i.e. velocity-driven, in an incompressible conducting fluid, we predict that the kinetic energy is $M_A^{-2}$ times larger than the energy of magnetic fluctuations. This effect arises from the long parallel wavelength tail of the forcing, which excites modes with $k_\|/k_\perp < M_A$. We also predict that as the turbulent cascade reaches the strong regime the energy of slow modes exceeds the energy of Alfven modes by a factor $M_A^{-1}$. These effects are absent if the turbulence is magnetically driven at the injection scale. We confirm these predictions with numerical simulations. As the assumption of magnetic and kinetic energy equipartition is at the core of the Davis-Chandrasekhar-Fermi (DCF) approach to measuring magnetic field strength in sub-Alfvenic turbulence, we conclude that the DCF technique is not universally applicable. In particular, we suggest that the dynamical excitation of long azimuthal wavelength modes in the galactic disk may compromise the use of the DCF technique. We discuss alternative expressions that can be used to obtain magnetic field strength from observations.