Systematic Underestimation of Polarization Angle Dispersion and Its Consequences for Magnetic Field Strength Estimates in Star-forming Regions

Abstract Polarised dust emission observations are a valuable tool to infer the structure of the magnetic field, and the dispersion of polarization position angles may be used to estimate magnetic field strengths. A natural consequence of magnetodynamic turbulence is for the angular dispersion to have a length scale dependence, making the measurement of angular dispersion nontrivial. In this paper we present a study of parameterized, scale-dependent maps, focusing on the effect of pixel size and beam convolution on the measured angular dispersion when using the commonly employed unsharp-masking and structure function methods. We find that in all cases the measured angular dispersion is underestimated compared to the true value. The degree to which the measured angular dispersion is underestimated varies by factors of 1–10 when measured on scales of 1–3× the beam size and depends on the underlying structure of the polarization angle field. This suggests that currently derived magnetic field strengths using angular dispersions are chronically overestimated, potentially leading to an overly magnetically dominated view of star formation. We present a method to estimate a correction factor to account for this and apply it to JCMT Orion A OMC-1 observations. We find that the magnetic field in OMC-1 is predominately found to vary on scales much larger than the JCMT’s 14″ beam and has a rather low degree of unresolved dispersion, leading to a correction factor of only ∼1.6 for angular dispersion measured at a scale of 14″/0.028 pc.