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

TL;DR

The paper investigates how dust foreground complexity, particularly spatial variation in the dust spectral index $β_d$ and LOS decorrelation, biases the recovery of the primordial tensor-to-scalar ratio $r$ with the Simons Observatory using a cross-spectrum framework. It uses a suite of realistic foreground simulations (including the d10 dust model) and a minimal moment-expansion for $β_d$ variation, augmented by decorrelation-aware covariance, to assess biases and robustness of $r$ estimates. The key finding is that low-order moment models can bias $r$ by up to $ oughly 0.03$ under extreme decorrelation, but extended parametric models plus covariance updates largely remove the bias across many scenarios; residual biases at the highest complexity levels point to higher-order statistics and non-Gaussian correlations between $β_d$ and dust amplitude as the main culprits. The work suggests that, for SO-level data, more flexible foreground models or higher-order moment terms (or hybrid approaches) will be needed to ensure unbiased $r$ constraints in the presence of strong dust complexity.

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 $r\sim0.03$ for simulations with no primordial tensors and a spatial dispersion of $σ(β_d)\simeq0.3$ -- 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 $β_d$ 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.

Figures (14)

• Figure 1: The distribution of dust emissivity indices, $\beta_d$, for the d10 simulation in the SO region without scaling (blue, $x_{{\beta}}^{{d10}} = 1.$), at the maximum scaling considered (orange, $x_{{\beta}}^{{d10}} = 2.$), and at the scaling that matches the degree of decorrelation in the d12 simulation (black, $x_{{\beta}}^{{d10}} = 1.6$). These are compared to 30 Gaussian realizations (gray), scaled to $x_{\beta_d}^G=10$, with resulting frequency decorrelation that matches that of the $x_{{\beta}}^{{d10}} = 1.6$ case.
• Figure 2: The angular power spectra of the d10 dust simulation at 280 GHz (left), and the s5 synchrotron simulation at 27 GHz (right), calculated in the SO-SAT region used in this study. In each panel, the orange points shows the binned power spectrum of the simulated foreground maps with noise, and the blue show spectra for noiseless maps. The spectra are computed as the mean of cross-split spectra, described in Section \ref{['sec:cross_cl']}. The errors shown, and their associated covariance matrix, are estimated using the 'Cov1' method described in Section \ref{['sec:cross_cl-covar']}. The black dashed line shows the best-fitting power law to the noisy spectra, with the $\chi^2$, degrees of freedom ($\nu$), and probability-to-exceed (PtE) for the fits indicated. The power law is an acceptable fit to the 280 GHz dust spectrum, but a poor fit to the 27 GHz simulated synchrotron spectrum at the larger scales.
• Figure 3: The 217 GHz $\times$ 353 GHz BB cross-spectrum for the d10 dust simulation, compared to the Planck PR4 data, estimated over the SO-SAT region used in our analysis. At these frequencies the dust signal dominates the Planck spectrum. We note features departing from a pure power-law in both cases.
• Figure 4: The degree of dust decorrelation ($1 - \mathcal{R}_{BB}^{217\times353}$) between the $217$ GHz and $353$ GHz simulated maps, calculated over the Planck LR71 mask and for scales $30 < \ell < 300$, as a function of dust parameter scaling, $x$. The three panels correspond to scaling the $\beta_d$ field (left), the $T_d$ field (middle) and the $\beta_d$ field of just the Q Stokes maps to approximate line-of-sight decorrelation (right). The orange points in each panel show the decorrelation of the d10 Nominal dust simulation before our modifications. The x-axis scalings are specified in Section \ref{['sec:sim-fg']}. The data points show the decorrelation values averaged over the bandpowers, using the same binning as in Figure \ref{['fig:dust_sync_chi2']}, and the errors reflect the dispersion over the bandpowers. The gray dashed line indicates the mean and dispersion for d12.
• Figure 5: Frequency decorrelation over the Planck LR71 mask in the Gaussian simulations as a function of dispersion in $\beta_d$ ($\sigma_{\beta_d}$, blue). The top x-axis label indicates the corresponding scaling factor, $x_{\beta_d}^{\rm G}$. This is compared to the $\beta_d$-Spatial scenario (orange) from Figure \ref{['fig:beta_d_scaling']}. As in Figure \ref{['fig:beta_d_scaling']}, the d12 level is indicated.