Dispersion of velocity gradients: Mapping magnetization with the Velocity Gradient Technique.

Recent developments of the Velocity Gradient Technique (VGT) show that the velocity provides a robust measure of magnetic field direction. In this paper, we use velocity centroids as the measures of velocity and propose a new way of studying media magnetization. We use the block averaging technique in Yuen & Lazarian (2017a) and demonstrate that the properties of the distribution of the directions of velocity gradients provide a reliable estimate the magnetization of the interstellar media. Guided by the theory of MHD turbulence, we find a robust correlation between Alfvenic Mach number and both the dispersion of velocity gradient orientation within the block as well as with the peak to base ratio of the amplitudes within the distribution. We apply our techniques for a selected GALFA-HI region and find that the distribution of magnetization obtained is in good agreement. We show that, combined with the velocity dispersion along the line of sight direction, our new techniques are capable to measure the local magnetic field strength. We argue that this technique is also applicable to another measure of velocity gradients, namely, Velocity Channel Gradients (VChGs), and that using the VChGs together with the Galactic rotation curve, one can obtain the 3D map of magnetic field strength. The new techniques open a way to measure magnetization using other gradient measures such as synchrotron intensity gradients (SIGs) and synchrotron polarization gradients (SPGs).