A halo model of extragalactic contamination to CMB lensing, delensing, and cross-correlations

Abstract

CMB lensing reconstructions are a sensitive probe of the growth of structure across cosmic time and a key tool to sharpen investigations of the very early Universe via delensing. At present, a large fraction of this information is drawn from the temperature anisotropies, which are ultimately also the most informative when reconstructing lenses on arcminute scales and smaller. But extragalactic foreground emission from galaxies and clusters can contaminate these reconstructions, limiting our ability to use information from small-scale temperature anisotropies. We develop analytic predictions of the biases from the thermal Sunyaev-Zeldovich and cosmic infrared background to CMB lensing auto- and cross-correlations with low-redshift matter tracers, as well as B-mode delensing, based on a halo model for the dominant one- and two-halo contributions to the relevant foreground bi- and tri-spectra. The method is flexible enough to allow variations in cosmology, astrophysical modeling, experimental configurations and analysis choices, thus enabling an improved understanding of the uncertainties involved in current mitigation strategies. We find that the shape of the bias relative to the CMB lensing auto-spectrum signal is remarkably insensitive to changes in cosmological and astrophysical parameter values. On the other hand, the shape appears to depend on $Ω_m$ for cross-correlations with low-redshift galaxies. We also clarify the ranges of redshifts and masses that simulations need to resolve in order to capture these effects accurately. Our code, CosmoBLENDER, is made publicly available.

Figures (23)

• Figure 1: Fractional bias to the CMB lensing auto-spectrum associated with tSZ (left panel), CIB (middle) and their combination (right, including cross-terms) for an experiment similar to ACT DR6 with $\ell_{\rm max}=3000$. Different line styles correspond to different couplings of the four-point function, with the total shown as solid lines. Different colors correspond to different maximum halo mass cuts. While the trispectrum bias is always positive, the primary bispectrum bias is negative for $L<2000$, and the secondary bispectrum term is always negative. When stringent mass cuts are imposed (or in the case of the CIB, which is insensitive to the high masses varied here), the bispectrum terms dominate and the total bias is negative on the scales of interest. On the other hand, as higher mass halos are included, the bias becomes positive starting at high $L$ and with the zero-crossing moving to larger scales as the mass cut is raised.
• Figure 2: Fractional contribution of one-halo (solid) and two-halo terms (dashed) to each of the CMB lensing auto-spectrum bias couplings (different columns, with the total bias being shown in the rightmost column). Top and bottom rows correspond to the tSZ and CIB biases, respectively. Different colors show different cuts in the maximum halo mass allowed to feature in the calculation. At any given scale, higher-mass cuts shift the emphasis towards one-halo terms. Notably, for the ACT-like setup and masking scheme described here, two-halo terms dominate the total tSZ bias below $L<400$, with one-halo terms becoming more relevant at higher multipoles. The CIB bias is always dominated by two-halo terms.
• Figure 3: Minimum-variance ILC weights for our SO configuration (left) and power spectrum residuals from different sky components after using these weights to produce multi-freuency cleaned maps. The contribution from the correlation between tSZ and CIB is negative, so we plot it as dashed line.
• Figure 4: Fractional bias on the CMB lensing auto-spectrum for an SO-like experiment as a function of the maximum multipole used in the reconstructions ($\ell_{\rm max}$; different colors), multi-frequency cleaning prescription (different columns) and extragalactic foreground contribution (different rows). In all cases, halos with $M_{\rm vir}>2\times 10^{14}\,M_{\rm \odot}$ have been removed, which increases the importance of bispectrum terms over trispectrum ones (particularly for higher $\ell_{\rm max}$). Raising $\ell_{\rm max}$ increases the significance of the bias and induces a sign change that shifts to smaller scales with higher $\ell_{\rm max}$ (driven by the primary bispectrum bias; cf. figure \ref{['fig:zero_crossing_prim_bispec']}). When cluster-masking is this extensive, tSZ biases are greatly reduced and there is no clear advantage in further deprojecting tSZ, as this would significantly boost CIB contributions.
• Figure 5: Fractional bias to the cross-correlation of DESI-like LRGs with ACT-DR6-like CMB lensing reconstructions, broken up into contributions from one-halo (dotted), two-halo (dot-dashed) terms as well as the their sum (solid). Different panels show the impact of different foreground contaminants, with the rightmost one showing the combination of tSZ and CIB, including contributions arising from the fact that they are correlated. This analysis assumes an $\ell_{\rm max}=3000$ and that no foreground cleaning is applied to the CMB maps besides a removal of structures more massive than the thresholds listed in the legend (identified, presumably, via their tSZ signature).