B-field Orion Protostellar Survey (BOPS). IV: The Relative Orientation Between Magnetic Fields and Density Structures in Young Protostellar Envelopes

Abstract: We investigate the relative alignment between density structures and magnetic fields in eight young protostars from the ALMA B-field Orion Protostellar Survey. Column density maps are derived from 870 $μ$m dust continuum emission, and the Histogram of Relative Orientations (HRO) method is applied to quantify the correlation between magnetic field orientations and density structures on envelope scales ($\sim$10$^{3}$~au). We find that the relative alignment shows overall weak evidence of systematic evolution with column density, suggesting that column density alone does not fully determine the alignment. The magnetization level also plays a crucial role, with weakly magnetized envelopes exhibiting predominantly parallel or random alignment, whereas strongly magnetized ones show perpendicular configurations even at moderate densities. These results reveal that density and magnetization jointly shape the morphology of protostellar envelopes and the coupling between gravity and magnetic fields during early stages of star formation.