Advancing the Velocity Gradient Technique: Using Gradient Amplitudes and
  handling thermal broadening
  The recent development of the Velocity Gradient Technique allows observers to
map magnetic field orientations and magnetization using the direction of
velocity gradients. Aside from the directions, amplitudes of velocity gradients
also contain valuable information about the underlying properties of
magneto-hydrodynamic (MHD) turbulence. In this paper, we explore what physical
information is contained in the amplitudes of velocity gradients and discuss
how this information can be used to diagnose properties of turbulence in both
diffuse and self-gravitating interstellar media. We identify the relations
between amplitudes of both intensity and velocity centroid gradients and the
sonic Mach number $M_s$ and they are consistent with the theory's predictions.
We test the robustness of the method and discuss how to utilize the amplitudes
of gradients into self-gravitating media. To extend the velocity gradient
technique we also discuss the usage of amplitude method to Position-Position
Velocity (PPV) space as a possible way to retrieve the velocity channel maps
before the contamination of thermal broadening. We discuss that the Velocity
Gradient Technique with these advancements could potentially give a
significantly more accurate statistical insight into the properties magnetized
turbulence.
