In this way, we consider not only the width of the lensing redshift distributions, but also lensing magnification and intrinsic stretching effects. In DES Y3REDMAGICgalaxies are used as a sample lens in the clustering and galaxy-galaxy lensing parts of the 3×2pt cosmological analysis [32,34]. The DES Y3 source galaxy sample, described in Gatti et al.[49], includes a subset of the DES Y3 Gold sample.
Σ−1l;scrit;effj : ð5Þ From this equation it is clear that the main dependence of the ratios depends on the redshift distributions of both the lens and the source samples. We then describe in detail the complete modeling of the ratios that we use in this work. The model of the ratio for the lens redshift bin between source redshift binsjandk can be expressed as.
MEASUREMENT AND COVARIANCE OF THE RATIOS
In Table II we summarize the downscaling described in this section for each of the ratio combinations. Cr¼JCγ˜JT; ð26Þ where J is the Jacobian of the ratio transformation as a function of the scale from Eq. 24), rðli;sj;skÞ, and can be calculated exactly using the theoretical model for the lens measurements. Because the covariance for the ratio is a function of the scale, the estimate of the mean ratio with minimum variance is given by.
Figure 4 shows values of the fiducial estimated lens shear ratios for both our simulated data and the real, unblinded data. We then describe the covariance estimation of the ratios and assess the performance of our estimator. We use that to calculate the 9×9 covariance of the ratios, as shown in Figure 16 in Appendix A.
Independence between small and large scales In this section we discuss why the SR probability is independent of the 2pt probability. The correlation of the SR probability with the ð3×Þ2pt probability will mostly come from galaxy-to-galaxy lensing 2pt measurements. Since shear ratios are a non-linear transformation of galaxy-to-galaxy lensing measurements, it is important to check the Gaussianity assumption with respect to the likelihood.
We have a number of realizations of the lens measurements, drawn from the theory curves and the corresponding covariance, and for each of them we have a set of nine FIG. Figure 4 shows the noiseless (or true) ratios of the model,frg0, together with the estimated mean and standard deviation of the noisy ratios,frgs.
VALIDATION OF THE MODEL
Summary of posteriors on model parameters corresponding to source redshifts, cutoff calibration, and lensing redshifts for various SR-only tests described in Sec.Vand combinations from Sec.VI. This plot summarizes the posteriors on the two internal parameters of the alignment model that are bounded by ratios, for the various SR-only tests described in Sec.V, using simulated noise-free data vectors. To test the impact of these effects on the ratios, we produce a set of simulated galaxy–galaxy lensing data vectors including the effects of baryons and non-linear galaxy biases as described above, and produce the corresponding set of shear ratios.
At small scales (between 2 and 6Mpc=h) we see very small deviations of the HOD-simulated ratios compared to the fiducial ones (Δχ2¼0.22 for nine data points), which do not significantly change the constraints on the model parameters using HOD-derived ratios. Effects of HOD modeling and HOD evolution on displacement ratios, for both small and large angular scales. Boost factors are the measurement correction needed to account for the impact of lensed source clusters on the redshift distributions.
In Fig.9 we show the difference in the ratios when we include or not the correction of the driving factor and find that it has a small impact on the ratios compared to their uncertainty, with Δχ2¼0.16. The fact that the driving factors do not have a large impact on the ratios gives us an indication that. Influence of various effects on lensing ratios, including cosmological dependence (see Sec.V E), driving factors (see Sec. V F) and reduced shear source magnification (see Sec.V G).
Here we extend this model to the lens ratio and show the small differences they produce at the ratios in Fig. 9, with Δχ2¼0.09 for nine data points. In this section we have so far considered various physical effects and tested their impact on the conditions at the level of theory, for example by changing the input power spectrum used to generate galaxy–galaxy lensing estimates.
COMBINATION WITH OTHER PROBES AND EFFECT ON COSMOLOGICAL CONSTRAINTS
In this section, we test the impact of higher-order lensing effects on our relational model, such as using the reduced-shear approximation and not including source magnification in our model. For the source magnification coefficients, we use the values calculated in Elvin-Poole et al. Reduced shear contamination results in only aΔχ2=0.02, so most of the change comes from the source magnification part.
In addition, the tests in this part will be subject to noise in the measurement of the lens signal and the ratios, due to shot noise and shape noise in the lens sample, in contrast to the tests above which were performed with noiseless theoretical ratios. In Fig.6 we include the results of the tests using N-body simulations, called SR Buzzard for the fiducial small-scale ratios and SR Buzzard LS for the large-scale SR test. The results are in line with the other tests in this section, showing the robustness of the SR constraints also on N-body simulations (taking into account the fact that the Buzzard constraints include noise in the measurements, as mentioned above) .
It can be seen from Fig. 10 that the improvement in cosmology comes mainly from the large improvement in constraining the IA modeling amplitudes. For source redshift parameters, SR improves the constraints of the first three source bins by 9%, 14%, and 4%, respectively. A powerful and robust way of extracting cosmological information from galaxy imaging surveys involves the perfect combination of three two-point functions, which is now the standard in the field and is called 3×2pt analysis.
The effect of adding SR to the DES Y33×2pt analysis is similar to the 2×2pt case. For example, for source redshift parameters, SR improves the constraints of the second source bin by more than 15%.
RESULTS WITH THE DES Y3 DATA In this section we will present and validate the con-
Allowed range and priors of model parameters for DES Y3 data chains executed in Sec.VII. Regarding the mild tension between SR and pre-redshift for the MAGLIM sample, we refer to the DES Collaboration [33] for results demonstrating the consistency of cosmological constraints with and without SR. In addition to the source redshift parameters, other parameters that are significantly constrained by the SR are the model amplitude IA, aIA1 and aIA2 (see Sec.III B for a description).
The similarity between these constraints demonstrates the robustness of the IA SR constraints, which play an important role in combination with cosmic shear and other 2pt functions. The SR methods described in this work are part of the solid DES Y3 cosmological analysis, and therefore the SR measurements are used as an additional probability in addition to the other 2pt functions. Average source redshift constraints of different SR configurations, using the DES Y3 redshift prior (SOMPZþWZ), comparing the fiducial small-scale constraints with those of the LS SR, for the two independent lens galaxy samples, REDMAGIC.
The contours in the plot are all placed at the origin of the ΔΩm-ΔS8 plane, so the graph only shows the effect of SR on the size of the contours, but does not include information on the central values. The gain in constraining power from adding the SR likelihood to the data is consistent with our findings on the simulated noise-free data (Sec. VI and Fig. 10), indicating the robustness of the simulated analysis in reproducing the DES Y3 data. . Changes in the DES Y3 data constraints on the cosmological parameters S8 and Ω with the addition of SR to the cosmic shear measurement (1×2pt).
All contours in the graph are placed at the origin of the ΔΩm-ΔS8 plane, so that the graph only shows the impact of SR on the size of the contours, but does not contain information about the central values of parameters or shifts between them. For a discussion of IAs in the context of the 3×2pt analysis, see the DES Collaboration[33].
We perform extensive tests of the small-scale modeling of the shear ratios by characterizing the impact of various effects, such as the inclusion of baryonic physics in the power spectrum, nonlinear galaxy biasing, the effect of HOD modeling description and lens magnification. One of the main advantages of SR is its weak sensitivity to small-scale model uncertainties, compared to pure inter-galaxy lensing measurements. Furthermore, SR is more sensitive to the mean redshift than to the width or shape of the entire redshift distribution, complementing other methods (such as cross-correlation clustering) that are more sensitive to other moments of these distributions.
National Science Foundation, Ministry of Science and Education of Spain, UK Science and Technology Facilities Council, Higher Education Funding Council for England, National Center for Supercomputing Applications at the University of Illinois at Urbana-Champaign, Kavli Institute of Cosmological Physics at the University of Chicago, Center for Cosmology and Astro-Particle Physics at Ohio State University, Mitchell Institute for Fundamental Physics and Astronomy at Texas A&M University, Financiadora de Estudos e Projetos, Fundação Carlos Chagas Filho de Amparo `a Pesquisa do Estado do Rio de Janeiro, Conselho Nacional de Desenvolvimento Científico e Tecnológico and Minist´erio da Ciência, Tecnologia e Inovação, Deutsche Forschungsgemeinschaft and Collaborating Institutions in the Dark Energy Survey. APPENDIX A: COVARIANCE OF THE SHEAR RATIO Figure 16 shows the covariance of the measured ratios, for the REDMAGIC and MAGLIM ratios, following the procedure described in Sec.IVA 4. In Fig.17, for completeness, we show the influence of SR in limiting the of the five parameters of the IA model (described in Sec.III) when combined with other 2pt functions.
The multipole space profile of the galaxy distribution is related to u¯jκðl; M; zÞ and is given by. Constraints on the five parameters of the IA model described in Section III given the combination of SR and the other 2pt functions, using simulated DES Y3 data. For the 2-halo term, the effective linear bias of the dark matter haloes can be written as
We compare the case of assuming a constant HOD in a redshift bin in the top panel and including the evolution of the Ncen and Nsat parameters in each redshift bin in the bottom panel. We find a small impact of the small-scale physics, especially on the large displacement ratios as quantified in Δχ2 mentioned in the legend of the plot.
