Synthetic polarization observations of magnetized pillars in HII regions: Assessing the reliability of the Davis-Chandrasekhar-Fermi method
We investigated the morphology and strength of magnetic fields in pillar-shaped structures at the boundaries of HII regions by combining three-dimensional radiation-magnetohydrodynamic (R-MHD) simulations with synthetic polarimetric and molecular-line observations. Our analysis focuses on a self-consistently formed pillar as a proof of concept to test the Davis-Chandrasekhar-Fermi (DCF) method under externally driven conditions. The pillar arises as an ionization front compresses a dense clump, producing a magnetically aligned, elongated structure whose morphology and field configuration resemble systems such as the pillars in M16. Synthetic 850 μm dust-polarization maps reproduce the pillar's large-scale magnetic-field morphology, confirming polarimetry as a reliable tracer of magnetic-field geometry. To evaluate DCF-based methods, we extract local density and velocity dispersion self-consistently from synthetic 13CO observations and measure polarization-angle dispersion using single-Gaussian fits to the synthetic polarization-angle distributions. We find that DCF-based methods systematically overestimate the intrinsic plane-of-sky magnetic-field strength by average factors of ~7 for the classical DCF method and ~5 for the modified Skalidis & Tassis formulation. This overestimation is already present in the full-pillar measurement and is not removed by applying polarimetric S/N cuts or by excluding the dynamically complex head. We attribute the discrepancy to external compression by the expanding H II region, which organizes the magnetic field on pillar scales while driving non-thermal gas motions. Consequently, the measured velocity and polarization-angle dispersions no longer trace the same turbulence-driven perturbation field assumed by DCF. Our results highlight the need for caution when applying DCF-based analyses to pillars or other externally compressed structures.