Limits on Polarized Dust Spectral Index Variations for CMB Foreground Analysis

Using Planck polarization data, we search for and constrain spatial variations of the polarized dust foreground for cosmic microwave background (CMB) observations, specifically in its spectral index, beta(d) . Failure to account for such variations will cause errors in the foreground cleaning that propagate into errors on cosmological parameter recovery from the cleaned CMB map. It is unclear how robust prior studies of the Planck data that constrained beta(d) variations are due to challenges with noise modeling, residual systematics, and priors. To clarify constraints on beta(d) and its variation, we employ two pixel space analyses of the polarized dust foreground at >3.degrees 7 scales on approximate to 60% of the sky at high Galactic latitudes. A template fitting method, which measures beta (d) over three regions of approximate to 20% of the sky, does not find significant deviations from a uniform beta(d) = 1.55, consistent with prior Planck determinations. An additional analysis in these regions, based on multifrequency fits to a dust and CMB model per pixel, puts limits on sigma beta d, the Gaussian spatial variation in beta(d) . The data support sigma beta d up to 0.45 at the highest latitudes, 0.30 at midlatitudes, and 0.15 at low latitudes. We also demonstrate that care must be taken when interpreting the current Planck constraints, beta(d) maps, and noise simulations. Due to residual systematics and low dust signal-to-noise ratios at high latitudes, forecasts for ongoing and future missions should include the possibility of large values of sigma beta d as estimated in this paper, based on current polarization data.