Distribution of velocity gradient orientations: Mapping magnetization with the Velocity Gradient Technique

Recent developments of the Velocity Gradient Technique (VGT) show that the velocity gradients provide a reliable tracing of magnetic field direction in turbulent plasmas. In this paper, we explore the ability of velocity gradients to measure the magnetization of interstellar medium. We demonstrate that the distribution of velocity gradient orientations provides a reliable estimation of the magnetization of the media. In particular, we determine the relation between Alfvenic Mach number $M_A$ in the range of $M_A \in [0.2,1.7]$ and properties of the velocity gradient distribution, namely, with the dispersion of velocity gradient orientation as well as with the peak to base ratio of the amplitudes. We apply our technique for a selected GALFA-HI region and find the results consistent with the expected behavior of $M_A$. Using 3D MHD simulations we successfully compare the results with our new measure of magnetization that is based on the dispersion of starlight polarization. We demonstrate that, combined with the velocity dispersion along the line of sight direction, our technique is capable to delivering the magnetic field strength. The new technique opens a way to measure magnetization using other gradient measures such as synchrotron intensity gradients (SIGs) and synchrotron polarization gradients (SPGs).