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The mean plane-of-sky magnetic field strength is traditionally obtained fromthe combination of polarization and spectroscopic data using theDavis-Chandrasekhar-Fermi (DCF) technique. However, we identify the majorproblem of the DCF to be its disregard of the anisotropic character of MHDturbulence. On the basis of the modern MHD turbulence theory we introduce a newway of obtaining magnetic field strength from observations. Unlike the DCF, thenew technique uses not the dispersion of the polarization angle and line ofsight velocities, but increments of these quantities given by the structurefunctions. To address the variety of the astrophysical conditions for which ourtechnique can be applied, we consider the turbulence in both media withmagnetic pressure larger than the gas pressure corresponding e.g. to molecularand the gas pressure larger than the magnetic pressure corresponding to thewarm neutral medium. We provide general expressions for arbitrary admixture ofAlfv\'en, slow and fast modes in these media and consider in detail theparticular cases relevant to diffuse media and molecular clouds. Wesuccessfully test our results using synthetic observations obtained from MHDturbulence simulations. We demonstrate that our Differential Measure Approach(DMA), unlike the DCF, can be used to measure the distribution of magneticfield strengths, can provide magnetic field measurements with limited data andis much more stable in the presence of large scale variations induces ofnon-turbulent nature. In parallel, our study uncover the deficiencies of theearlier DCF research.

Magnetic field strength from turbulence theory (I): Using differential measure approach (DMA)