Weak Lensing of the CMB by Large-Scale Structure

TL;DR

The paper investigates reconstructing the CMB weak lensing convergence κ from high-resolution CMB temperature maps using the Hu01a optimal quadratic estimator, and tests its performance against simulations that include non-Gaussian κ fields and kinetic SZ contamination. It demonstrates that while the estimator can recover large-scale convergence, realistic non-Gaussianity and foregrounds introduce substantial additive and multiplicative biases in the reconstructed κ power spectrum, necessitating higher-order corrections or model-based approaches. Masking the kSZ using thermal SZ information can mitigate some contamination but leaves residual biases, and the bias–signal trade-off depends strongly on instrument resolution and sky coverage. The results indicate that detecting lensing with upcoming surveys is feasible, but achieving high-fidelity reconstructions of the matter power spectrum will require careful treatment of non-Gaussianities and foregrounds, with polarization and more advanced estimators offering potential improvements.

Abstract

Several recent papers have studied lensing of the CMB by large-scale structures, which probes the projected matter distribution from $z=10^3$ to $z\simeq 0$. This interest is motivated in part by upcoming high resolution, high sensitivity CMB experiments, such as APEX/SZ, ACT, SPT or Planck, which should be sensitive to lensing. In this paper we examine the reconstruction of the large-scale dark matter distribution from lensed CMB temperature anisotropies. We go beyond previous work in using numerical simulations to include higher order, non-Gaussian effects and study how well the quadratic estimator of \cite{Hu01a} is able to recover the input field. We also study contamination by kinetic Sunyaev-Zel'dovich signals, which is spectrally indistinguishable from lensed CMB anisotropies. We finish by estimating the sensitivity of the previously cited experiments.

Figures (13)

• Figure 1: Maps of (left) input and (right) reconstructed projected mass, in units of dimensionless convergence $\kappa$, for two smoothing scales and $2 \mu \rm K$-arcmin uncorrelated Gaussian instrument noise. While the (top) input and reconstructed $\kappa$ maps smoothed by a $10^\prime$ FWHM Gaussian beam do contain many of the same structures, the agreement between the two (bottom) visibly improves when they are smoothed on a $20^\prime$ scale. The input $\kappa$ maps shown here are Gaussian random fields, and all the maps are $7.5^\circ\times 7.5^\circ$.
• Figure 2: Reconstruction of the power spectrum for a Gaussian convergence map. The input $C_{\ell}^{\kappa\kappa}$ convergence spectrum (black) is poorly reconstructed, as is clear in the auto-spectrum (green) if noise terms are not subtracted. The situation improves markedly as the noise is subtracted to first order (orange), and still more when second order terms are subtracted (red), while the cross-spectrum (blue) fit is quite good.
• Figure 3: The ratio of the reconstructed power spectra to the input spectrum for a Gaussian $\kappa$ map (the spectra themselves are given in Fig. \ref{['fig:Gspec']}). The ratio for the cross-spectrum case (blue) is consistent with a no multiplicative bias; however, as is evident from the plot of $C_{\ell}^{\rm est}$ (red), there is still a substantial ($\sim 25\%$) additive bias even when second order noise terms are included. If only the first order correction is included in the noise estimate (Eq. \ref{['eq:noise']}), the bias is close to $\sim 70\%$.
• Figure 4: Reconstructions of a (top left) input non-Gaussian $\kappa$ map. The (top right) map has been reconstructed in the absence of foregrounds, and while it clearly contains much of the same structure as the input map, the correspondence is far from perfect, as we discuss in Section \ref{['sec:nongauss']}. When the kSZ is included, the (bottom left) reconstruction still retains some visual similarity to the original, although additional spurious features are added to the map, such as the hot spot near $(-2^\circ,-2^\circ)$. In the last panel we show the (bottom right) reconstruction when the kSZ is masked using the technique described in Section \ref{['sec:ksz']}. The worst of the spurious structures caused by the kSZ have disappeared, and the map bears a strong resemblance to the reconstruction made in the absence of kSZ. The maps are $7.5^\circ\times 7.5^\circ$ fields sampled at $0.^{\prime}8$ resolution, include $2 \mu$K-arcmin of instrument noise, and have been smoothed by a $20^\prime$ FWHM Gaussian window for presentation.
• Figure 5: As Fig. \ref{['fig:Gspec2']}, but now including the non-Gaussian contribution to the $\kappa$ map. The cross-spectrum (blue) is now biased high by roughly $10\%$, and the total bias in the estimated convergence spectrum (red) is about $50\%$.