Characterizing line-of-sight variability of polarized dust emission with future CMB experiments

While Galactic dust emission is often accounted for in cosmic microwave background (CMB) analyses by fitting a two-parameter modified blackbody (MBB) model in each pixel, typically a number of such clouds are found along each line of sight and within each angular pixel, resulting in a superposition of their spectra. We study the effects of this superposition on pixel-based foreground fitting strategies by modeling the spectral energy distribution (SED) in each pixel as the integral of individual MBB spectra over various physically motivated statistical distributions of dust cloud properties. We show that fitting these SEDs with the two-parameter MBB model generally results in unbiased estimates of the CMB Stokes Q and U amplitudes per pixel, unless there are significant changes in both the dust SED and polarization angle along the line of sight, in which case significant (>10σ) biases are observed in an illustrative model. We find that the best-fitting values of the dust temperature, Td, and spectral index, βd, are significantly biased from the mean/median of the corresponding statistical distributions when the distributions are broad, suggesting that MBB model fits can give an unrepresentative picture of the physical properties of dust at microwave wavelengths if not interpreted carefully. Using Fisher matrix analysis, we determine the experimental sensitivity required to recover the parameters of the Td and βd distributions by fitting a probabilistic MBB model, finding that only the parameters of broad distributions can be measured by SED fitting on a single line of sight.