Velocity Gradients: Magnetic Field Tomography towards the Supernova
  Remnant W44
  As a novel approach for tracing interstellar magnetic fields, the Velocity
Gradient Technique (VGT) has been proven to be effective for probing magnetic
fields in the diffuse interstellar medium (ISM). In this work, we verify the
VGT in a broader context by applying the technique to a molecular cloud
interacting with the supernovae remnant (SNR) W44. We probe the magnetic fields
with the VGT using CO, $\rm HCO^+$, and H I emission lines and make a
comparison with the Planck 353 GHZ dust polarization. We show that the VGT
gives an accurate measurement that coheres with the Planck polarization
especially in intense molecular gas emission regions. We further study the
foreground's contribution to the polarization that results in a misalignment
between the VGT and the Planck measurements in low-intensity molecular gas
areas. We advance the VGT to achieve magnetic field tomography by decomposing
the W44 into various velocity components. We show that W44's velocity component
at $v\sim45$ km s$^{-1}$ exhibits the largest coverage and gives the best
agreement with Planck polarization in terms of magnetic field orientation.
