Bias to CMB lensing reconstruction from temperature anisotropies due to large-scale galaxy motions

Gravitational lensing of the cosmic microwave background (CMB) is expected to be amongst the most powerful cosmological tools for ongoing and upcoming CMB experiments. In this work, we investigate a bias to CMB lensing reconstruction from temperature anisotropies due to the kinematic Sunyaev-Zel’dovich (kSZ) effect, that is, the Doppler shift of CMB photons induced by Compton scattering off moving electrons. The kSZ signal yields biases due to both its own intrinsic non-Gaussianity and its nonzero cross-correlation with the CMB lensing field (and other fields that trace the large-scale structure). This kSZ-induced bias affects both the CMB lensing autopower spectrum and its cross-correlation with low-redshift tracers. Furthermore, it cannot be removed by multifrequency foreground separation techniques because the kSZ effect preserves the blackbody spectrum of the CMB. While statistically negligible for current data sets, we show that it will be important for upcoming surveys, and failure to account for it can lead to large biases in constraints on neutrino masses or the properties of dark energy. For a stage 4 CMB experiment, the bias can be as large as $\approx 15\%$ or 12% in cross-correlation with LSST galaxy lensing convergence or galaxy overdensity maps, respectively, when the maximum temperature multipole used in the reconstruction is ${\ell }_{\max }=4000$, and about half of that when ${\ell }_{\max }=3000$. Similarly, we find that the CMB lensing autopower spectrum can be biased by up to several percent. These biases are many times larger than the expected statistical errors. We validate our analytical predictions with cosmological simulations and present the first complete estimate of secondary-induced CMB lensing biases. The predicted bias is sensitive to the small-scale gas distribution, which is affected by pressure and feedback mechanisms, thus making removal via “bias-hardened” estimators challenging. Reducing ${\ell }_{\max }$ can significantly mitigate the bias at the cost of a decrease in the overall lensing reconstruction signal-to-noise. A bias $\lesssim 1\%$ on large scales requires ${\ell }_{\max }\lesssim 2000$, which leads to a reduction in signal-to-noise by a factor of $\approx 3–5$ for a stage 4 CMB experiment. Polarization-only reconstruction may be the most robust mitigation strategy.

Figure 1

Window functions for LSST galaxy lensing (left peak), LSST galaxies (middle peak), and CMB lensing (right peak). They are related to the window functions defined in the text by $W(z)=W(\eta )d\eta /dz$.

Figure 2

Fractional bias to the cross-correlation of CMB lensing and galaxy density (denoted $Y=g$) or galaxy lensing ($Y={\kappa }_{\mathrm{gal}}$) maps from LSST. From top to bottom, the panels show results for CMB lensing reconstructions from Planck SMICA, CMB-S3, and CMB-S4, respectively. The lensing reconstruction is performed on CMB temperature only, with ${\ell }_{\min }=30$ and ${\ell }_{\max }=3000$ (left panels) or ${\ell }_{\max }=4000$ (right panels). The kSZ-induced bias is computed via Eq. (13). The solid curves assume the gas perfectly traces the dark matter, while the dashed curves consider the effect of baryonic physics via the Jeans scale given in Eq. (21). The bias is considerably larger than the forecasted error bars on such cross-correlation measurements for CMB-S3 and CMB-S4, shown here assuming $f_{\mathrm{sky}}=0.44$ for the overlap between LSST and these surveys.

Figure 3

Fractional bias to the CMB lensing autopower spectrum arising from the term discussed in Sec. 5 (see Fig. 6 for an estimate of the full bias derived from simulations). The panel ordering is identical to Fig. 2. The lensing reconstruction is performed on temperature only, with ${\ell }_{\min }=30$ and ${\ell }_{\max }=3000$ (left panels) or ${\ell }_{\max }=4000$ (right panels) and the kSZ-induced bias is computed via Eq. (18). The solid curves assume the gas perfectly traces the dark matter, while the dashed curves consider the effect of baryonic physics via the Jeans scale given in Eq. (21). For comparison, the dot-dashed curve shows the effect of massive neutrinos with a summed mass of 0.06 eV (the minimum mass in the normal hierarchy), which causes a $\approx 3\%$ reduction in power compared to the fiducial case with massless neutrinos. The error bars show the statistical significance expected in 6 equally spaced multipole bins and assuming $f_{\mathrm{sky}}=0.5$ for all experiments.

Figure 4

Comparison of simulation-derived (dashed curves with error bars) and analytic predictions (solid curves) for the fractional kSZ-induced bias on the cross-correlation of CMB lensing and tracers, for various experimental configurations. All reconstructions here use ${\ell }_{\max }=4000$. The agreement between the theory and simulations is generally good. The small discrepancies seen on large scales for the CMB-S4 case may be related to filtering applied to the kSZ field in the simulation or differing treatments of baryonic effects between the analytic calculation and the simulation. Note that the cosmological parameters and $f_{\mathrm{free}}$ here differ from the fiducial ones in the rest of the paper and are chosen to match those in the simulations.

Figure 5

Comparison of simulation-derived (dashed curves with error bars) and analytic predictions (solid curves) for the fractional kSZ-induced bias on the CMB lensing autopower spectrum, for various experimental configurations, including only the term discussed in Sec. 5 (see Fig. 6 for an estimate of the full bias including all terms). All reconstructions here use ${\ell }_{\max }=4000$. The agreement between the theory and simulations is generally good, though somewhat less precise than in Fig. 4. The discrepancies seen on large scales for the CMB-S3 and CMB-S4 cases may be due to filtering applied to the kSZ field in the simulation or differing treatments of baryonic effects (particularly He reionization) between the analytic calculation and the simulation. Note that the cosmological parameters and $f_{\mathrm{free}}$ here differ from the fiducial ones in the rest of the paper and are chosen to match those in the simulations.

Figure 6

Fractional bias to the reconstructed CMB lensing autopower spectrum arising from the sum of all terms discussed in Appendix pp2 (terms $\mathrm{B}+\mathrm{C}+\mathrm{E}$), as estimated via the procedure described in Sec. 7b. The panel ordering is identical to Figs. 2 and 3. The lensing reconstruction is performed on temperature only, with ${\ell }_{\min }=30$ and ${\ell }_{\max }=3000$ (left panels) or ${\ell }_{\max }=4000$ (right panels) and the kSZ-induced bias is computed by comparing reconstructions involving Gaussian kSZ maps to those using the true non-Gaussian kSZ map (see Sec. 7b). The solid curves show our estimate of the full kSZ-induced bias (modulo reionization contributions), while the dashed curves show the contribution of term B [i.e., Eq. (18) only, as plotted in Fig. 5. This term is indeed the dominant contribution to the total bias on large scales. The error bars on the solid curves are computed from the scatter amongst the ten Gaussian kSZ realizations.