Mitigating foreground biases in CMB lensing reconstruction using cleaned gradients

Reconstructed maps of the lensing convergence of the cosmic microwave background (CMB) will play a major role in precision cosmology in coming years. CMB lensing maps will enable calibration of the masses of high-redshift galaxy clusters and will yield precise measurements of the growth of cosmic structure through cross correlations with galaxy surveys. During the next decade, CMB lensing reconstruction will rely heavily on temperature data, rather than polarization, thus necessitating a detailed understanding of biases due to extragalactic foregrounds. In the near term, the most significant bias among these is that due to the thermal Sunyaev-Zel’dovich (tSZ) effect. Moreover, high-resolution observations will be available at only a few frequencies, making full foreground cleaning challenging. In this paper, we demonstrate a solution to the foreground bias problem that involves cleaning only the large-scale gradients of the CMB temperature map. We show that the data necessary for tSZ-bias-free CMB lensing maps already exist in the form of large-scale measurements of the CMB across multiple frequencies by the Planck and WMAP satellite experiments. Specifically, we show that the bias to halo masses inferred from CMB lensing is eliminated by the utilization of clean gradients obtained from multifrequency component separation involving Planck and WMAP data, and that special lensing maps for galaxy cross correlations can be prepared with only a small penalty in signal-to-noise while requiring no masking, in-painting, modeling, or simulation effort for the tSZ bias. While we focus on cross correlations, we also show that gradient cleaning can mitigate biases to the CMB lensing autospectrum that arise from the presence of foregrounds in temperature and polarization with minimal loss of signal-to-noise.

Figure 1

Stacks on different CMB temperature maps at the locations of SDSS DR8 redMaPPer clusters. Top: The Planck 143 GHz map. The expected tSZ decrement at this frequency is clearly seen. Center: The Planck foreground-cleaned SMICA map. A large tSZ residual is visible, because the tSZ contamination is not explicitly deprojected in SMICA. Bottom: The LGMCA $\text{Planck}+\mathrm{WMAP}$ foreground-cleaned map. There is no visible evidence of any foreground residual in this stack. In particular, LGMCA explicitly deprojects the tSZ foreground using its known frequency dependence.

Figure 2

Beam-deconvolved noise in CMB temperature maps. The orange solid curve shows the measured noise power spectrum in the LGMCA $\text{Planck}+\mathrm{WMAP}$ foreground-cleaned maps. The blue solid curves shows the same for the Planck SMICA map. The dashed curves show the noise power spectra for various representative high-resolution, ground-based experiments with white noise levels of 6, 10, and $20\mu \mathrm{K}\text{−}\mathrm{arcmin}$, a beam of $\mathrm{FWHM}=1.5\mathrm{arcmin}$, and atmospheric noise with ${\ell }_{\mathrm{knee}}=3000$ and $\alpha =-4$. The black solid curve shows the fiducial CMB temperature power spectrum.

Figure 3

Mass estimation bias for four different halo mass bins as determined from map-based simulations. The red circles show the relative mass bias when both the gradient and the high-resolution map are contaminated with tSZ signal (at levels expected at 150 GHz). For medium- and high-mass clusters, the bias is very large. The purple diamonds show the case when the gradient is free from tSZ contamination, but the high-resolution map contains tSZ. The bias is no longer detectable. The horizontal axis is on neither a linear nor a logarithmic scale; the mass bin ranges on the horizontal axis are listed in Table 1.

Figure 4

The tSZ bias to the CMB lensing-galaxy density cross correlation as measured from simulations, with and without clean gradients. Both curves here are relative differences with respect to the case where no tSZ was added to the CMB maps. We show the case where tSZ contamination is present in both the gradient and high-resolution CMB maps (orange) and the case where the tSZ contamination is only in the high-resolution map and the gradient does not contain tSZ (blue). The error bars show the uncertainty on our estimate of these biases when averaged across 42 patches of $100{\mathrm{deg}}^2$ each.

Figure 5

Lensing noise curves for asymmetric lensing reconstruction compared to symmetric reconstruction. The solid curves show the lensing noise power spectrum when the high-resolution CMB experiment is used in both legs of the quadratic estimator for TT. This case is expected to have a very significant tSZ bias. The dashed curves show the case when the temperature gradient leg of the TT estimator is replaced with the LGMCA (tSZ-free) map. This case has slightly lower S/N at large scales, but is expected to be free of tSZ bias. All curves are minimum-variance combinations of TT, ET, EB, EE and TB.