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Abstract We study the properties of sub-Alfvénic magnetohydrodynamic (MHD) turbulence, i.e., turbulence with Alfvén mach numberMA=VL/VA< 1, whereVLis the velocity at the injection scale andVAis 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 times larger than the energy of magnetic fluctuations. This effect arises from the long parallel wavelength tail of the forcing, which excites modes withk∥/k⊥<MA. 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 . 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.
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Gradient Technique Theory: Tracing Magnetic Field and Obtaining Magnetic Field Strength
Abstract The gradient technique is a promising tool with theoretical foundations based on the fundamental properties of MHD turbulence and turbulent reconnection. Its various incarnations use spectroscopic, synchrotron, and intensity data to trace the magnetic field and measure the media magnetization in terms of Alfvén Mach number. We provide an analytical theory of gradient measurements and quantify the effects of averaging gradients along the line of sight and over the plane of the sky. We derive analytical expressions that relate the properties of gradient distribution with the Alfvén Mach numberMA. We show that these measurements can be combined with measures of sonic Mach number or line broadening to obtain the magnetic field strength. The corresponding technique has advantages to the Davis–Chandrasekhar–Fermi way of obtaining the magnetic field strength.
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- Award ID(s):
- 2307840
- PAR ID:
- 10548972
- Publisher / Repository:
- DOI PREFIX: 10.3847
- Date Published:
- Journal Name:
- The Astrophysical Journal
- Volume:
- 974
- Issue:
- 2
- ISSN:
- 0004-637X
- Format(s):
- Medium: X Size: Article No. 237
- Size(s):
- Article No. 237
- Sponsoring Org:
- National Science Foundation
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