Joint analysis of Dark Energy Survey Year 3 data and CMB lensing from SPT and Planck. I. Construction of CMB lensing maps and modeling choices

Joint analyses of cross-correlations between measurements of galaxy positions, galaxy lensing, and lensing of the cosmic microwave background (CMB) offer powerful constraints on the large-scale structure of the Universe. In a forthcoming analysis, we will present cosmological constraints from the analysis of such cross-correlations measured using Year 3 data from the Dark Energy Survey (DES), and CMB data from the South Pole Telescope (SPT) and Planck. Here we present two key ingredients of this analysis: (1) an improved CMB lensing map in the SPT-SZ survey footprint and (2) the analysis methodology that will be used to extract cosmological information from the cross-correlation measurements. Relative to previous lensing maps made from the same CMB observations, we have implemented techniques to remove contamination from the thermal Sunyaev Zel’dovich effect, enabling the extraction of cosmological information from smaller angular scales of the cross-correlation measurements than in previous analyses with DES Year 1 data. We describe our model for the cross-correlations between these maps and DES data, and validate our modeling choices to demonstrate the robustness of our analysis. We then forecast the expected cosmological constraints from the galaxy survey-CMB lensing auto and cross-correlations. We find that the galaxy-CMB lensing and galaxy shear-CMB lensing correlations will on their own provide a constraint on $S_8={\sigma }_8\sqrt{{\mathrm{\Omega }}_{\mathrm{m}}/0.3}$ at the few percent level, providing a powerful consistency check for the DES-only constraints. We explore scenarios where external priors on shear calibration are removed, finding that the joint analysis of CMB lensing cross-correlations can provide constraints on the shear calibration amplitude at the 5% to 10% level.

Figure 1

Upper: diagram illustrating the input temperature maps used to construct the two different lensing maps utilized in this analysis. The operation “QE” (quadratic estimator) is the lensing reconstruction step described in Sec. 2d2. Lower: illustration of the sky coverage and lensing maps for the North (Planck) and South ($\mathrm{SPT}+$Planck) patches. The red line indicates the cut in declination ($\mathrm{dec}=-40°$) that divides the two regions. The union of the DES mask used in the DES Y3 analysis and the Planck lensing map mask is applied.

Figure 2

CMB convergence map generated using the tSZ nulling method described in the text. The map has been smoothed with a Gaussian beam with $\mathrm{FWHM}=60^{\prime }$ for visualization purposes.

Figure 3

Noise levels estimated from simulations for $\mathrm{SPT}+$Planck/SMICAnoSZ (teal) and Planck (orange) over the patch of sky that will be used to measure the cross-correlations. Also shown are the noise levels from [20] (light gray) and an analytical prediction for the convergence signal (black). The procedures described in Sec. 2d eliminate tSZ contamination from the lensing maps at the cost of a small increase in the map noise (teal vs. light gray).

Figure 4

Stacks of CMB lensing maps at the locations of clusters from [22] with signal-to-noise in the range $5<S/N<10$. Without tSZ nulling (left panel), the stacked CMB lensing map shows a strong feature at the cluster center due to tSZ contamination of the lensing estimator. With tSZ nulling (right panel), the stacked map shows no strong features at the cluster center, as expected since the cluster lensing signal is weak.

Figure 5

The power spectrum of the convergence map constructed from the combination of SPT and Planck (blue points). Shown for reference are the points from [16] (gray squares) and points from [20] (gray open circles), and the analytical convergence power spectrum calculated using the fiducial cosmology assumed in our analysis (black solid line). The inset shows the power spectrum in the high-$L$ range, where possible contamination from the tSZ would show most strongly.

Figure 6

Cross-correlation between various CMB lensing maps and the 545 GHz map from [42], which is dominated by CIB. The correlation with the $\mathrm{SPT}+$Planck/SMICAnoSZ lensing map (blue) produced in this analysis is consistent with other measurements and with an external simulation (gray curve), demonstrating that this lensing map is not significantly contaminated by CIB.

Figure 7

Redshift distribution for the MagLim lens galaxy sample (upper) and Metacalibration source galaxy sample (lower). The highest two redshift bins of the lens sample (in dashed lines) are not be used for the forecasting in this work.

Figure 8

Decomposition of the diagonal of the covariance matrix into the various terms in Eq. (28). Results are shown for an arbitrary bin (bin four for both lens and source), but appear similar in other bins. We also overlay the total covariance measured from the FLASK simulations, described in Sec. 4b.

Figure 9

Plot of the $⟨{\delta }_{\mathrm{g}}{\kappa }_{\mathrm{CMB}}⟩+⟨{\gamma }_{\mathrm{t}}{\kappa }_{\mathrm{CMB}}⟩$ correlation matrix. The off-diagonal cross ($\mathrm{SPT}+$Planck)-(Planck) blocks are set to zero as discussed in Sec. 4b2. Each $⟨{\delta }_{\mathrm{g}}{\kappa }_{\mathrm{CMB}}⟩$ and $⟨{\gamma }_{\mathrm{t}}{\kappa }_{\mathrm{CMB}}⟩$ block has 80 elements (4 redshift bins with 20 angular bins each).

Figure 10

Left: distribution of ${\chi }^2$ derived from FLASK simulations and our covariance model for $⟨{\delta }_{\mathrm{g}}{\kappa }_{\mathrm{CMB}}⟩$ and $⟨{\gamma }_{\mathrm{t}}{\kappa }_{\mathrm{CMB}}⟩$ data vectors in the $\mathrm{SPT}+$Planck and Planck patches separately. The histograms are overlaid with a ${\chi }_{\nu }^2$ distribution (smooth black curve), and we only include data points after the scale cuts (see Sec. 5). Right: same as the left panel but for the combined data vector of $⟨{\delta }_{\mathrm{g}}{\kappa }_{\mathrm{CMB}}⟩$ and $⟨{\gamma }_{\mathrm{t}}{\kappa }_{\mathrm{CMB}}⟩$ in both patches (filled histogram). The open gray histogram represents the ${\chi }^2$ distribution prior to applying the 4% correction and the dashed histogram corresponds to the ${\chi }^2$ distribution when combining different realizations for the $\mathrm{SPT}+$Planck and Planck patches, effectively nulling the off-diagonal block of the covariance in the FLASK realizations, as described in Sec. 4b2.

Figure 11

Fractional biases computed from the contaminated/uncontaminated data vectors with the effects of baryonic effects on the matter power spectrum (orange), nonlinear galaxy bias (teal), and the sum of the two (dark gray). Also shown are the standard deviations of the $\mathrm{SPT}+$Planck data vectors scaled down by a factor of 10. The arrows indicate the angular scales used in the analysis.

Figure 12

Forecasted constraints on ${\mathrm{\Omega }}_{\mathrm{m}}$ and $S_8$ using the fiducial data vector (blue) and a data vector contaminated with our model of nonlinear galaxy bias and baryonic effects on the small-scale matter power spectrum (red). The four panels show (from left to right) results for the combinations of $⟨{\delta }_{\mathrm{g}}{\delta }_{\mathrm{g}}⟩+⟨{\delta }_{\mathrm{g}}{\kappa }_{\mathrm{CMB}}⟩$, $⟨{\gamma }_{\mathrm{t}}{\kappa }_{\mathrm{CMB}}⟩$, $⟨{\delta }_{\mathrm{g}}{\kappa }_{\mathrm{CMB}}⟩+⟨{\gamma }_{\mathrm{t}}{\kappa }_{\mathrm{CMB}}⟩$ and $5\times 2\mathrm{pt}$. The shift in the two contours are shown in the bottom right of each panel.

Figure 13

Comparison of the forecasted constraints on cosmological parameters ${\mathrm{\Omega }}_{\mathrm{m}}$, ${\sigma }_8$, $S_8$ and intrinsic alignment parameters $a_1$, $a_2$, ${\eta }_1$, ${\eta }_2$, and $b_{\mathrm{TA}}$ using the combination of galaxy clustering and galaxy-CMB lensing correlation, with and without the addition of shear-ratio information, compared with the constraints from $3\times 2\mathrm{pt}$. The dashed lines represent the input values for the individual parameters.

Figure 14

Comparison of the forecast constraints on ${\mathrm{\Omega }}_{\mathrm{m}},{\sigma }_8$ and $S_8$ from the $3\times 2\mathrm{pt}$ and $5\times 2\mathrm{pt}$ probes using linear galaxy bias modeling (open orange and dashed blue contours) and nonlinear galaxy modeling (filled blue contours).

Figure 15

Simulated constraints from $3\times 2\mathrm{pt}$ (red) and $5\times 2\mathrm{pt}$ (blue) probes when the fiducial priors on the shear calibration parameters are replaced by very wide priors (free $m$). The results show the ability of the data to constrain these nuisance parameters with the $3\times 2\mathrm{pt}$ and $5\times 2\mathrm{pt}$ probes respectively. Also overlaid are the fiducial $5\times 2\mathrm{pt}$ constraints, where the $m_i$ parameters are informed by external priors.

Figure 16

tSZ power spectra at $100/143/217/353/545/857\mathrm{GHz}$ (various blue lines), as well as the tSZ residual power spectrum after passing the individual frequency maps through the SMICAnoSZ weights (orange).

Figure 17

Comparison of the density—CMB lensing correlation for two types of CMB lensing map reconstruction: one quadratic estimator leg contaminated with the tSZ effect and the other tSZ nulled (blue) and both temperature legs contaminated with the tSZ effect (orange).

Figure 18

Residuals of best-fit 3D galaxy-matter correlation function in the MICE simulation (with the MagLim galaxy sample) assuming a nonlinear galaxy bias model. The shaded region indicates bias exceeding 3%, which we exclude in our analysis when we assume nonlinear galaxy bias.

Figure 19

Same as Fig. 12 but for the redMaGiC sample.

Figure 20

Comparison of the forecasted constraints on ${\mathrm{\Omega }}_{\mathrm{m}}-{\sigma }_8-S_8$ plane when using the fiducial model of assuming a shift in $n(z)$ and when drawing from possible realizations using HYPERRANK.