Disentangling 3D Magnetic Field Geometry from Turbulence: A Polarization-Based Classification Method

We develop a decision tree classifier that recovers 3D magnetic field geometry from synthetic polarization and position angle maps of a magnetized, turbulent field. We test the classifier for a series of geometries: Uniform, Wavy, Helical, and Hourglass. The classifier is calibrated across a range of Alfvénic Mach numbers and injected Stokes Q,U noise levels for each geometry. Our models show the median and skewness of the polarization fraction, as well as the position angle circular variance, vary systematically with both geometry and the Alfvénic Mach number. We find that the 3D geometry can be isolated by using a variety of polarization and position angle metrics to break degeneracies. The classifier recovers most geometries well for sub-Alfvénic cases (Alfvénic Mach Number < 1). For Alfvénic Mach Number > 1, polarization and position angle statistics converge across all geometries and the classifier fails to recover the magnetic field structure.