Limits on Polarized Dust Spectral Index Variations for CMB Foreground Analysis

TL;DR

This study uses Planck polarization data to constrain spatial variations in the polarized dust spectral index, finding that such variations could be larger than previously thought, which impacts CMB foreground cleaning.

Contribution

The paper provides new constraints on the spatial variation of the dust spectral index using pixel space analyses, highlighting the importance of accounting for potential large variations in future CMB studies.

Findings

No significant deviation from uniform $eta_d$ at high latitudes.

Limits on $\sigma_{eta_d}$ up to 0.45 at high latitudes.

Residual systematics and noise affect current constraints.

Abstract

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 which 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 $>3.7^{\circ}$ scales on $\approx 60\%$ of the sky at high Galactic latitudes. A template fitting method, which measures $\beta_d$ over three regions of $\approx 20\%$ of the sky, does not find significant deviations from an 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 $\beta_d$. At the highest latitudes, the data support $\sigma_{\beta_d}$ up to $0.45$, $0.30$ at mid-latitudes, 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 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.