Sub-Alfvénic Turbulence: Magnetic-to-kinetic Energy Ratio, Modification of Weak Cascade, and Implications for Magnetic Field Strength Measurements

Abstract We study the properties of sub-Alfvénic magnetohydrodynamic (MHD) turbulence, i.e., turbulence with Alfvén mach number M A = V L / V A &lt; 1, where V L is the velocity at the injection scale and V A is the Alfvén velocity. We demonstrate that MHD turbulence can have different properties, depending on whether it is driven by velocity or magnetic fluctuations. If the turbulence is driven by isotropic bulk forces acting upon the fluid, i.e., is velocity driven, in an incompressible conducting fluid we predict that the kinetic energy is <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mi>M</mml:mi> <mml:mi mathvariant="normal">A</mml:mi> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> 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 ⊥ &lt; M A . We also predict that as the MHD turbulent cascade reaches the strong regime, the energy of slow modes exceeds the energy of Alfvén modes by a factor <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mi>M</mml:mi> <mml:mi mathvariant="normal">A</mml:mi> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> . These effects are absent if the turbulence is driven through magnetic fluctuations at the injection scale. We confirm our predictions with numerical simulations. Since 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-Alfvénic 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 and consider ways of distinguishing the cases of velocity and magnetically driven turbulence using observational data.