The Simons Observatory: Assessing the Impact of Dust Complexity on the Recovery of Primordial $B$-modes

TL;DR

This study examines how complex dust foreground variations can bias measurements of primordial gravitational waves in CMB polarization data, emphasizing the need for advanced foreground modeling in upcoming experiments.

Contribution

It demonstrates that spatial variations in dust spectral index can bias tensor-to-scalar ratio estimates and shows that extended parametric models can mitigate this bias.

Findings

Bias in r can reach ~0.03 with extreme dust complexity

Low-order moment expansions may fail under high dust variation

Flexible foreground models are necessary for unbiased r estimates

Abstract

We investigate how dust foreground complexity can affect measurements of the tensor-to-scalar ratio, $r$, in the context of the Simons Observatory, using a cross-spectrum component separation analysis. Employing a suite of simulations with realistic Galactic dust emission, we find that spatial variation in the dust frequency spectrum, parametrized by $\beta_d$, can bias the estimate for $r$ when modeled using a low-order moment expansion to capture this spatial variation. While this approach performs well across a broad range of dust complexity, the bias increases with more extreme spatial variation in dust frequency spectrum, reaching as high as $r\sim0.03$ for simulations with no primordial tensors and a spatial dispersion of $\sigma(\beta_d)\simeq0.3$ -- the most extreme case considered, yet still consistent with current observational constraints. This bias is driven by changes in the $\ell$-dependence of the dust power spectrum as a function of frequency that can mimic a primordial $B$-mode tensor signal. Although low-order moment expansions fail to capture the full effect when the spatial variations of $\beta_d$ become large and highly non-Gaussian, our results show that extended parametric methods can still recover unbiased estimates of $r$ under a wide range of dust complexities. We further find that the bias in $r$, at the highest degrees of dust complexity, is largely insensitive to the spatial structure of the dust amplitude and is instead dominated by spatial correlations between $\beta_d$ and dust amplitude, particularly at higher orders. If $\beta_d$ does spatially vary at the highest levels investigated here, we would expect to use more flexible foreground models to achieve an unbiased constraint on $r$ for the noise levels anticipated from the Simons Observatory.