Magnetic fields, while ubiquitous in many astrophysical environments, are challenging to measure observationally. Based on the properties of anisotropy of eddies in magnetized turbulence, the Velocity Gradient Technique is a method synergistic to dust polarimetry that is capable of tracing plane-of-the-sky magnetic field, measuring the magnetization of interstellar media and estimating the fraction of gravitational collapsing gas in molecular clouds using spectral line observations. In this paper, we apply this technique to five low-mass star-forming molecular clouds in the Gould Belt and compare the results to the magnetic-field orientation obtained from polarized dust emission. We find the estimates of magnetic field orientations and magnetization for both methods are statistically similar. We estimate the fraction of collapsing gas in the selected clouds. By means of the Velocity Gradient Technique, we also present the plane-of-the-sky magnetic field orientation and magnetization of the Smith cloud, for which dust polarimetry data are unavailable.

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 ∈ [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).

Magnetohydrodynamic(MHD) turbulence displays velocity anisotropies which reflect the direction of the magnetic field. This anisotropy has led to the development of a number of statistical techniques for studying magnetic fields in the interstellar medium. In this paper, we review and compare three techniques that use radio position-position-velocity data for determining magnetic field strength and morphology : the correlation function anisotropy (CFA), Principal Component Analysis of Anisotropies (PCAA), and the more recent Velocity Gradient Technique (VGT). We compare these three techniques and suggest improvements to the CFA and PCAA techniques to increase their accuracy and versatility. In particular, we suggest and successfully implement a much faster way of calculating non-periodic correlation functions for the CFA. We discuss possible improvements to the current implementation of the PCAA. We show the advantages of the VGT in terms of magnetic field tracing and stress the complementary nature with the other two techniques.