Decomposing Magnetic Fields in Three Dimensions over the Central
  Molecular Zone
  Measuring magnetic fields in the interstellar medium and obtaining their
distribution along line-of-sight is very challenging with the traditional
techniques. The Velocity Gradient Technique (VGT), which utilizes anisotropy of
magnetohydrodynamic (MHD) turbulence, provides an attractive solution.
Targeting the central molecular zone (CMZ), we test this approach by applying
the VGT to $\rm ^{12}CO$ and $\rm ^{13}CO$ (J = 1-0) data cubes. We first used
the SCOUSEPY algorithm to decompose the CO line emissions into separate
velocity components, and then we constructed pseudo-Stokes parameters via the
VGT to map the plane-of-the-sky magnetic fields in three-dimension. We present
the decomposed magnetic field maps and investigate their significance. While
the line-of-sight integrated magnetic field orientation is shown to be
consistent with the polarized dust emission from the Planck survey at 353 GHz,
individual velocity components may exhibit different magnetic fields. We
present a scheme of magnetic field configuration in the CMZ based on the
decomposed magnetic fields. In particular, we observe a nearly vertical
magnetic field orientation in the dense clump near the Sgr B2 and a change in
the outflow regions around the Sgr A*. Two high-velocity structures associated
with an expanding ring in the CMZ show distinct swirling magnetic field
structures. These results demonstrate the potential power of the VGT to
decompose velocity or density-dependent magnetic structures.
