The Power Spectra of Polarized, Dusty Filaments
  We develop an analytic model for the power spectra of polarized filamentary
structures as a way to study the Galactic polarization foreground to the Cosmic
Microwave Background. Our approach is akin to the cosmological halo-model
framework, and reproduces the main features of the Planck 353 GHz power
spectra. We model the foreground as randomly-oriented, three-dimensional,
spheroidal filaments, accounting for their projection onto the sky. The main
tunable parameters are the distribution of filament sizes, the filament
physical aspect ratio, and the dispersion of the filament axis around the local
magnetic field direction. The abundance and properties of filaments as a
function of size determine the slopes of the foreground power spectra, as we
show via scaling arguments. The filament aspect ratio determines the ratio of
$B$-mode power to $E$-mode power, and specifically reproduces the
Planck-observed dust ratio of one-half when the short axis is roughly
one-fourth the length of the long axis. Filament misalignment to the local
magnetic field determines the $TE$ cross-correlation, and to reproduce Planck
measurements, we need a (three-dimensional) misalignment angle with a root mean
squared dispersion of about 50 degrees. These parameters are not sensitive to
the particular filament density profile. By artificially skewing the
distribution of the misalignment angle, this model can reproduce the
Planck-observed (and parity-violating) $TB$ correlation. The skewing of the
misalignment angle necessary to explain $TB$ will cause a yet-unobserved,
positive $EB$ dust correlation, a possible target for future experiments.
