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Probing magnetic fields in the interstellar medium (ISM) is notoriouslychallenging. Motivated by the modern theories of magnetohydrodynamic (MHD)turbulence and turbulence anisotropy, we introduce the Structure-FunctionAnalysis (SFA) as a new approach to measure the magnetic field orientation andestimate the magnetization. We analyze the statistics of turbulent velocitiesin three-dimensional compressible MHD simulations through the second-orderstructure functions in both local and global reference frames. In thesub-Alfvenic turbulence with the magnetic energy larger than the turbulentenergy, the SFA of turbulent velocities measured in the directionsperpendicular and parallel to the magnetic field can be significantlydifferent. Their ratio has a power-law dependence on the Alfven Mach number$M_A$, which is inversely proportional to the magnetic field strength. Wedemonstrate that the anisotropic structure functions of turbulent velocitiescan be used to estimate both the orientation and strength of magnetic fields.With turbulent velocities measured using different tracers, our approach can begenerally applied to probing the magnetic fields in the multi-phaseinterstellar medium.

Anisotropies in Compressible MHD Turbulence: Probing Magnetic Fields and Measuring Magnetization