Magnetic Field Properties in High Mass Star Formation from Large to Small Scales - A Statistical Analysis from Polarization Data

Polarization data from high mass star formation regions (W51 e2/e8, Orion BN/KL) are used to derive statistical properties of the plane of sky projected magnetic field. Structure function and auto-correlation function are calculated for observations with various resolutions from the BIMA and SMA interferometers, covering a range in physical scales from $\sim 70$~mpc to $\sim 2.1$~mpc. Results for the magnetic field turbulent dispersion, its turbulent to mean field strength ratio and the large-scale polarization angle correlation length are presented as a function of the physical scale at the star formation sites. Power law scaling relations emerge for some of these physical quantities. The turbulent to mean field strength ratio is found to be close to constant over the sampled observing range, with a hint of a decrease toward smaller scales, indicating that the role of magnetic field and turbulence is evolving with physical scale. A statistical method is proposed to separate large and small scale correlations from an initial ensemble of polarization segments. This also leads to a definition of a turbulent polarization angle correlation length.