Filamentary Dust Polarization and the Morphology of Neutral Hydrogen Structures

Filamentary structures in neutral hydrogen (HI) emission are well aligned with the interstellar magnetic field, so HI emission morphology can be used to construct templates that strongly correlate with measurements of polarized thermal dust emission. We explore how the quantification of filament morphology affects this correlation. We introduce a new implementation of the Rolling Hough Transform (RHT) using spherical harmonic convolutions, which enables efficient quantification of filamentary structure on the sphere. We use this Spherical RHT algorithm along with a Hessian-based method to construct HI-based polarization templates. We discuss improvements to each algorithm relative to similar implementations in the literature and compare their outputs. By exploring the parameter space of filament morphologies with the Spherical RHT, we find that the most informative HI structures for modeling the magnetic field structure are the thinnest resolved filaments. For this reason, we find a $\sim10\%$ enhancement in the $B$-mode correlation with polarized dust emission with higher-resolution HI observations. We demonstrate that certain interstellar morphologies can produce parity-violating signatures, i.e., nonzero $TB$ and $EB$, even under the assumption that filaments are locally aligned with the magnetic field. Finally, we demonstrate that $B$ modes from interstellar dust filaments are mostly affected by the topology of the filaments with respect to one another and their relative polarized intensities, whereas $E$ modes are mostly sensitive to the shapes of individual filaments.