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.