Mapping the Galactic Magnetic Field Orientation and Strength in Three Dimensions

The mapping of the Galactic Magnetic Field (GMF) in three dimensions is essential to comprehend various astrophysical processes that occur within the Milky Way. This study endeavors to map the GMF by utilizing the latest MM2 technique, the Velocity Gradient Technique (VGT), the Column Density Variance Approach, and the GALFA-H I survey of Neutral Hydrogen (H I) emission. The MM2 and VGT methods rely on an advanced understanding of magnetohydrodynamics turbulence to determine the magnetic field strength and orientation respectively. The H I emission data, combined with the Galactic rotational curve, gives us the distribution of H I gas throughout the Milky Way. By combining these two techniques, we map the GMF orientation and strength, as well as the Alfv\'en Mach number $M_{\rm A}$ in 3D for a low galactic latitude ($b<30^{\rm o}$) region close to the Perseus Arm. The analysis of column density variance gives the sonic Mach number $M_{\rm s}$ distribution, The results of this study reveal the sub-Alfv\'enic and subsonic (or trans-sonic) nature of the H I gas. The variation of mean $M_{\rm A}$ along the line-of-sight approximately ranges from 0.6 to 0.9, while that of mean $M_{\rm s}$ is from 0.2 to 1.5. The mean magnetic field strength varies from ~0.5 $\mu$G to ~2.5 $\mu$G exhibiting a decreasing trend towards the Galaxy's outskirt. This work provides a new avenue for mapping the GMF, especially the magnetic field strength, in 3D. We discuss potential synergetic applications with other approaches.