Improving the accuracy of magnetic field tracing by velocity gradients: principal component analysis

Tracing of the magnetic field with Velocity Gradient Technique (VGT) allows observers to probe magnetic field directions with spectroscopic data. In this paper, we employ the method of principal component analysis (PCA) to extract the spectroscopic information most valuable for VGT. By using synthetic observation data from numerical simulations, we show that PCA acts in a way similar to spatial filtering along the velocity axis. We study both subsonic and supersonic simulations and show that with the PCA filtering the tracing of magnetic fields by the VGT is significantly improved. Using 21 cm Galactic ALFA data, we demonstrate that the PCA filtering improves the alignment of the velocity gradients and the Planck dust polarization.