Mapping the Magnetic Interstellar Medium in Three Dimensions Over the Full Sky with Neutral Hydrogen

Recent analyses of 21-cm neutral hydrogen (HI) emission have demonstrated that HI gas is organized into linear filamentary structures that are preferentially aligned with the local magnetic field, and that the coherence of these structures in velocity space traces line-of-sight magnetic field tangling. On this basis, we introduce a paradigm for modeling the properties of magnetized, dusty regions of the interstellar medium, using the orientation of HI structure at different velocities to map "magnetically coherent" regions of space. We construct three-dimensional (position-position-velocity) Stokes parameter maps using HI4PI full-sky spectroscopic HI data. We compare these maps, integrated over the velocity dimension, to Planck maps of the polarized dust emission at 353 GHz. Without any free parameters governing the relation between HI intensity and dust emission, we find that our $Q$ and $U$ maps are highly correlated ($r > 0.75$) with the 353 GHz $Q$ and $U$ maps of polarized dust emission observed by Planck and reproduce many of its large-scale features. The $E/B$ ratio of the dust emission maps agrees well with the HI-derived maps at large angular scales ($\ell \lesssim 120$), supporting the interpretation that this asymmetry arises from the coupling of linear density structures to the Galactic magnetic field. We demonstrate that our 3D Stokes parameter maps constrain the 3D structure of the Galactic interstellar medium and the orientation of the interstellar magnetic field.