Foreground Mitigation for CMB Lensing with the Global Minimum Variance Quadratic Estimator

TL;DR

This work tackles foreground biases in CMB lensing reconstruction by integrating $tSZ$-deproj and cross-ILC into the global minimum variance (GMV) quadratic estimator. By employing asymmetric inputs (e.g., a $tSZ$-nulled temperature map and a MV or CIB-nulled map) and symmetrization, the method suppresses foreground-induced trispectrum and bispectrum biases, enabling more robust lensing measurements. Across simulations mimicking SPT-3G and SO, the bias reductions are substantial: from roughly $4\%$ with standard GMV/SQE to about $2\%$ with $tSZ$-deproj and to $<1\%$ with cross-ILC for $L<1000$, while reconstruction noise increases by about 5–15\% due to nulled inputs; leveraging higher $\ell_{\max}^T$ can recover much of the sensitivity. The results demonstrate that foreground-mitigated GMV pipelines produce foreground-cleaned lensing maps suitable for cross-correlation analyses, offering a practical path to percent-level lensing constraints in upcoming CMB surveys. Key implications include enabling higher-resolution temperature-based lensing reconstructions with controlled foreground systematics, improving cross-correlation capabilities, and informing design choices for next-generation CMB experiments.

Abstract

Weak gravitational lensing of the cosmic microwave background (CMB) is a powerful probe of cosmology, providing insight into structure formation and the evolution of the universe. Current and upcoming CMB experiments such as SPT-3G and the Simons Observatory (SO) provide high-resolution, low-noise temperature and polarization maps that are ideal for lensing reconstruction. The global minimum variance (GMV) quadratic estimator for CMB lensing reduces reconstruction noise over the standard quadratic estimator (SQE). In this work, we extend the GMV framework to incorporate the tSZ-deproj and cross-ILC foreground mitigation techniques, which enhance robustness against contamination from astrophysical sources. For SPT-3G Ext-10k and SO Extended at $\ell_{\mathrm{max}}^T = 3500$, the lensing bias at $L < 1000$ is reduced from $\sim4\%$ with standard GMV and SQE to $2\%$ with tSZ-deproj, and to $< 1\%$ with cross-ILC. These methods enable the construction of foreground-cleaned lensing maps suitable for cross-correlation analyses, with direct relevance for current and future surveys.

Figures (7)

• Figure 1: The lensing bias for the $TT$-only SQE reconstruction with no foreground treatment, on input maps containing only CMB and tSZ, assuming experimental noise levels matching the SPT-3G D1 analysis. Here, the lensing bias is defined as $\Delta C_L^{\kappa\kappa} = C_L^{\kappa\kappa,\mathrm{recon}} - C_L^{\kappa\kappa,\mathrm{in}}$ and it is normalized by the input $\kappa$ spectrum. The bias is split up into the trispectrum contribution and the bispectrum contribution. The total bias is negative for $L \lesssim 300$, after which it becomes positive as the trispectrum contribution starts to dominate.
• Figure 2: MV, tSZ-nulled, and CIB-nulled ILC weights for SPT-3G D1 noise levels.
• Figure 3: Reconstruction noise spectra comparison, with $\ell_{\mathrm{max}}^T = 3500$. Left panel: Noise spectra plotted against the CAMB theory $\kappa$ auto-spectrum. The standard GMV case with no foreground treatment has the lowest reconstruction noise, as expected. Right panel: Noise spectra normalized to the standard GMV case. Here we see clearly the increase in noise of the standard SQE MV, tSZ-deproj GMV, and cross-ILC GMV, with respect to standard GMV. For $L \lesssim 200$, the noise performance of foreground-mitigated GMV is better than standard SQE, leading to both gain in sensitivity and robustness against foreground biases.
• Figure 4: Lensing bias comparison for $\ell_{\mathrm{max}}^T = 3500$. Here, the lensing bias is defined as $\Delta C_L^{\kappa\kappa} = C_L^{\kappa\kappa,\mathrm{recon}} - C_L^{\kappa\kappa,\mathrm{in}}$ and it is normalized by the input $\kappa$ spectrum. The error bars are measurement error for full sky. The standard SQE and GMV with no foreground treatment have comparable bias, at around 4%. tSZ-deproj GMV removes tSZ bias, reducing the bias to around 2%. Cross-ILC further cleans CIB as well as tSZ, reducing the bias to be consistent with zero for $L \lesssim 1000$.
• Figure 5: Lensing bias comparison for $\ell_{\mathrm{max}}^T = 3000, 3500, 4000$ cases. The error bars correspond to measurement errors for a full sky reconstruction. The data points for the different $\ell_{\mathrm{max}}^T$ values are shifted horizontally for clarity. We see that going up in $\ell_{\mathrm{max}}^T$ leads to a significant increase in lensing bias in the standard case with no foreground mitigation, but the penalty is significantly reduced with foreground mitigation applied.