Obtaining Magnetization of Super-Alfv\'enic Turbulence with the Structure Functions of Gradient Directions

Abstract

Super-Alfv\'enic turbulence is widespread in astrophysical environments, including molecular clouds and the diffuse plasma of galaxy clusters. At large scales, magnetic fields play only a minor dynamical role; however, for sufficiently extended turbulent cascades, the motions transition into the MHD regime at a characteristic scale $l_A$. We introduce a new diagnostic based on the structure functions of the gradient directions, which can be obtained directly from spectroscopic and synchrotron intensity observations. We demonstrate that the new measure robustly recovers the transition scale $l_A$. Building on this result, we propose a generalized expression that replaces the traditional Davis-Chandrasekhar-Fermi (DCF) method for estimating magnetic field strength in the super-Alfv\'enic regime, where the DCF approach fails. We further show how the magnetization and magnetic field strength of diffuse media, such as the intracluster medium, can be inferred using synchrotron intensity maps. Our theoretical predictions are validated through numerical simulations.