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

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 $r\sim 0.03$ for simulations with no primordial tensors and a spatial dispersion of $\sigma ({\beta }_d)\simeq 0.3$ -- 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.

arXiv comment27 pages, 14 figures, submitted to JCAP

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