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.
