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We develop an analytic model for the power spectra of polarized filamentarystructures as a way to study the Galactic polarization foreground to the CosmicMicrowave Background. Our approach is akin to the cosmological halo-modelframework, and reproduces the main features of the Planck 353 GHz powerspectra. We model the foreground as randomly-oriented, three-dimensional,spheroidal filaments, accounting for their projection onto the sky. The maintunable parameters are the distribution of filament sizes, the filamentphysical aspect ratio, and the dispersion of the filament axis around the localmagnetic field direction. The abundance and properties of filaments as afunction of size determine the slopes of the foreground power spectra, as weshow via scaling arguments. The filament aspect ratio determines the ratio of$B$-mode power to $E$-mode power, and specifically reproduces thePlanck-observed dust ratio of one-half when the short axis is roughlyone-fourth the length of the long axis. Filament misalignment to the localmagnetic field determines the $TE$ cross-correlation, and to reproduce Planckmeasurements, we need a (three-dimensional) misalignment angle with a root meansquared dispersion of about 50 degrees. These parameters are not sensitive tothe particular filament density profile. By artificially skewing thedistribution of the misalignment angle, this model can reproduce thePlanck-observed (and parity-violating) $TB$ correlation. The skewing of themisalignment angle necessary to explain $TB$ will cause a yet-unobserved,positive $EB$ dust correlation, a possible target for future experiments.

The Power Spectra of Polarized, Dusty Filaments