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 physical aspect ratio of filaments, 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 ofB-mode power toE-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 theTEcross-correlation, and to reproduce Planck measurements we need a (three-dimensional) misalignment angle with an rms 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)TBcorrelation. The skewing of the misalignment angle necessary to explainTBwill cause a yet-unobserved, positiveEBdust correlation, a possible target for future experiments.