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.