Velocity Gradients as a Tracer for Magnetic Fields

Strong Alfv\'enic turbulence develops eddy-like motions perpendicular to the local direction of magnetic fields. This local alignment induces velocity gradients perpendicular to the local direction of the magnetic field. We use this fact to propose a new technique of studying the direction of magnetic fields from observations, the Velocity Gradient Technique. We test our idea by employing the synthetic observations obtained via 3D MHD numerical simulations for different sonic and Alfv\'en Mach numbers. We calculate the velocity gradient, $\mathbf{\Omega}$, using the velocity centroids. We find that $\mathbf{\Omega}$ traces the projected magnetic field best for the synthetic maps obtained with sub-Alfv\'enic simulations providing good point-wise correspondence between the magnetic field direction and that of $\mathbf{\Omega}$. The reported alignment is much better than the alignment between the density gradients and the magnetic field and we demonstrated that it can be used to find the magnetic field strength using the Chandrasekhar-Fermi method. Our study opens a new way of studying magnetic fields using spectroscopic data.