The Simons Observatory: assessing the impact of dust complexity on the recovery of primordial <i>B</i> -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 β 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 ∼ 0.03 for simulations with no primordial tensors and a spatial dispersion of σ ( β d ) ≃ 0.3 — the most extreme case considered, yet still consistent with current observational constraints. This bias is driven by changes in the ℓ-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 β 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 β d and dust amplitude, particularly at higher orders. If β 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.