Obtaining magnetic field strength using differential measure approach
  and velocity channel maps
  We introduce two new ways of obtaining the strength of plane-of-sky (POS)
magnetic field by simultaneous use of spectroscopic Doppler-shifted lines and
the information on magnetic field direction. The latter can be obtained either
through polarization measurements or using the velocity gradient technique. We
show the advantages that our techniques have compared to the traditional
Davis-Chandrasekhar-Fermi (DCF) technique of estimating magnetic field strength
from observations. The first technique that we describe in detail employs
structure functions of velocity centroids and structure functions of Stokes
parameters. We provide analytical expressions for obtaining magnetic field
strength from observational data. We successfully test our results using
synthetic observations obtained with results of MHD turbulence simulations. We
measure velocity and magnetic field fluctuations at small scales using two,
three and four point structure functions and compare the performance of these
tools. We show that, unlike the DCF, our technique is capable of providing the
detailed distribution of POS magnetic field and it can measure magnetic field
strength in the presence of both velocity and magnetic field distortions
arising from external shear and self-gravity. The second technique applies the
velocity gradient technique to velocity channel maps in order to obtain the
Alfven Mach number and uses the amplitudes of the gradients to obtain the sonic
Mach number. The ratio of these two Mach numbers provides the intensity of
magnetic field in the region contributing to the emission in the channel map.
We test the technique and discuss obtaining the 3D distribution of POS galactic
Magnetic field with it. We discuss the application of the second technique to
synchrotron data.
