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.
