Anisotropic Turbulence in Position-Position-Velocity Space: Probing
  Three-Dimensional Magnetic Fields
  Direct measurements of three-dimensional magnetic fields in the interstellar
medium (ISM) are not achievable. However, the anisotropic nature of
magnetohydrodynamic (MHD) turbulence provides a novel way of tracing the
magnetic fields. Guided by the advanced understanding of turbulence's
anisotropy in the Position-Position-Velocity (PPV) space, we extend the
Structure-Function Analysis (SFA) to measure both the three-dimensional
magnetic field orientation and Alfven Mach number $M_A$, which provides the
information on magnetic field strength. Following the theoretical framework
developed in Kandel et al. (2016), we find that the anisotropy in a given
velocity channel is affected by the inclination angle between the 3D magnetic
field direction and the line-of-sight as well as media magnetization. We
analyze the synthetic PPV cubes generated by incompressible and compressible
MHD simulations. We confirm that the PPV channel's intensity fluctuations
measured in various position angles reveal plane-of-the-sky magnetic field
orientation. We show that by varying the channel width, the anisotropies of the
intensity fluctuations in PPV space can be used to simultaneously estimate both
magnetic field inclination angle and strength of total magnetic fields.
