Also, due to the nonlocality of the tangential shear estimator, we adopted the scheme proposed in MacCrann et al. Tangential shear measurements of the redMaGiC(top) and MagLim(bottom) sample along with the theory line of best fit from the DES Y33×2pt results. 61], Blake et al [62], which became part of the standard estimator for galaxy-galaxy lensing analyses.
We show the effect of the magnification factor correction on the data vector in Figure 1.
MODELING THE TANGENTIAL SHEAR The tangential shear is the main measurement used in
In the DES Y33×2pt cosmological analysis, we model the tangential displacement using the curved-sky transformation (vs. the flat-sky approximation, used in the DES Y13×2pt analysis, for example), and we correctly average within the range of scales that in each angle bin (vs. just picking a value in the middle of the bin, also used in the Y1 modeling). MacCrann et al.[29] propose to analytically marginalize over a point mass (PM) scaling as R−2 with physical separation Rbetween the lens and the source galaxy, including some additional terms in the tangential displacement covariance that come from the uncertainty in the model prediction of the galaxy–matter correlation function under a given scale. The SNR for the tangential displacement measurements is changed from 55to-28for the red MaGiCsample when the point-mass marginalization is applied to the inverse covariance.7For.
75]for further details on the implementation of mass marginalization in the DES Y33× 2pt analysis. In this section we describe how lensing affects galaxy measurements of galaxies, how important the effect is for the tangential shear probe, and how we model it. These are two competing effects, and the dominant one depends on the specifics of the galaxy sample.
Difference in the tangential displacement inverse covariance matrix between the cases assuming the point-mass correlation is included or not,C−1;þPM−C−1. In our tangential displacement estimator from Eq.(18), we average the ellipticity components to extract the displacement. Our tangential shear fiducial model includes the lens magnification term, intrinsic adjustments, and cross terms between lens magnification and IAs and can be written as.
MODEL VALIDATION
We now consider the influence of reduced shear approximation and the effects of source magnification and source grouping, all of which are related to each other, as well as to the lensing magnification and IA terms that we described in Sect. We also extend the connection of source magnification and source clustering effects to the tangential shear estimator presented in this work. We have not calculated the rest of the terms, but since we find the reduced shear and source magnification terms to be negligible with the current uncertainties, we expect them to be negligible as well, being even smaller than the terms we have calculated.
We also estimated the impact of the reduced shear approach using the BUZZARDN body simulations, directly comparing the tangential shear measurements obtained with real shear to the shear contaminated by the factor ð1−κÞ−1. In Figure 9 we compare the different estimates of the reduced shear effect with the tangential shear estimator, including two theoretical estimates using a tree-level bispectrum based on the nonlinear power spectrum Pnl or on the linear power spectrum Plin. In this work, we did not calculate the term arising from the coupling between lens magnification and reduced shear, as it would be smaller than the term for reduced shear alone, and therefore negligible for our analysis.
Vertical gray shading corresponds to 6Mpc=h scale cuts and blue shading to tangential cut uncertainties. Alternatively, if there is any correlation between the large-scale structure at source galaxy redshift δs and that at lensing redshift δl , this could bias our tangential shear estimator. The influence depends on the characteristics of the source sample, in particular on whether the magnification factor Cs [analogous to that defined in Eq. (51) for the lens sample] is positive or negative.
MEASUREMENT ROBUSTNESS TESTS In the previous section we have explored the impact of
Therefore, the error that will propagate into the estimate of the angular separation between a given lens-source pair comes from the difference between the deviation angles of the source and the lensing galaxies between the lensing redshift and us. Since the relative position of a given lens source plane will be affected by the variation in the angles of deviation, this causes an error in the projection of the components of the Cartesian ellipticity onto the tangential, as illustrated in Fig. 3 of Chang and Jain[91] . Therefore, our cross-section measurements are consistent with zero at all scales, not just those used for the galaxy–galaxy lensing probe in the DES Y33×2pt cosmological analysis.
On the one hand, we look at PSF shape residuals which are the differences between the measured shape of the (reserved) stars and the point spread functions in the full field of view model shape [50] at the same locations. On the other hand, the PSF size residual is calculated by rescaling the size of the measured PSF to match the difference in PSF size between the measurement and the model of the PSF, but keeping the PSF shape to its measured value . In Fig.12 we show the measurement average of the tangential component of the two PSF residuals we just described around redMaGiC galaxies, including the subtraction of the same amount around random points, in the same way as for the tangential shift signal.
The dependence of galaxy density on observation conditions introduces a spurious cluster signal that can have a strong impact on some of the observables used in the DES Y3 cosmological analysis, especially on galaxy clustering. However, because the lensing between galaxies is a cross-correlation between lensing and source galaxies, we expect that the impact of varying observing conditions, and thus of the weighting scheme, will be less important[10]. In Figure 4 we show the impact of the weighting on the galaxy-to-galaxy lens measurements, reporting a Δχ2¼4.2 for all scales (corresponding to 400 data points) and a Δχ2¼3.1 for scales above 6Mpc=h that are directly in the cosmological measurements are used. analysis for the redMaGiC sample (see Table III for comparable results from the MagLim sample).
SUMMARY OF MEASUREMENT AND MODELING UNCERTAINTIES
The uncertainty about the correction of the shear response is determined using image simulations in MacCrann et al. propagated to the analysis using the multiplicative bias parameters, which are marginalized in the cosmological analysis. iii) TreeCorr approach: see Sec.III F. iv) Boost factors: see Sec.III B. Summary table of the effects included in the DES Y33×2pt fiducial measurements and model relevant to the inter-galaxy lensing probe and galaxies (top) and those not included (bottom) but that we test in both this paper and the DES Y33×2pt methodology paper in Krauseet al. [72]. In the first column we show the contribution of each of these effects in the measurement or in the best-fitting DES Y33×2pt model.
In the second column, we show the uncertainty in each of the effects, estimated by calculating Δχ2 between the best-fitting model and the model with a2σ deviation of the corresponding effect. In the third column of the upper part, we indicate whether the uncertainty propagates to the cosmological contours. To estimate Δχ2s, we use the inverse theoretical covariance with and without point mass marginalization, considering only the large scales used in the cosmological analysis for the galaxy-galaxy lensing part (above 6Mpc=h), which includes 248 points.
Source redshifts: we do not show the contribution of the source redshifts to the model, as they are significant, i.e. the model cannot be calculated without an estimated redshift distribution. We calculate the uncertainty by comparing the best-fitting model to values in the source redshift parameters that are 2σ away from the best-fitting values in the 3×2pt posterior. viii). To estimate the uncertainty in the baryonic effects on the galaxy-galaxy lensing probe, we compare the fiducial contamination obtained from the OWLS hydrodynamic simulation[93,94] with contamination from the EAGLE simulation[95].
CONCLUSIONS
We also find that the tangential shear measurements are robust to observational conditions and PSF model residuals, and find that the shear shear component is compatible with zero. In this work together with Krauseet al [72] we found that none of the higher-order effects or their combinations will affect our cosmological constraints by more than 0.3σ in the Ωm-σ8 plane. Therefore, the joint analysis also shows that our cross-component measurements are compatible with a vanishing signal.
When performing the angle bin averaging in Eq. (24) and (25), we did not take into account the variation in the pair counts due to the survey geometry, which is expected to affect mainly large scales. The variation of the window function within a corner box provides an upper bound on the impact of this effect on tangential shear modeling. Cross-component correlation matrix for the redMaGiC sample, considering the cross-covariance of all lens-source pairs using 1799 lognormal simulations combined with pocket knife resampling (see the text for details).
Comparison of the JK error bars calculated in this work as described in Section III F with the theory error bars of Friedrich et al.[68]. This plot shows the contribution of each of the components of our model in Fourier space at the best-fit values from the 3×2pt results for the MagLim sample. This is a subset of the covariance for the second lensing bin and each of the four source redshift bins.
