Dark Energy Survey year 1 results: Galaxy-galaxy lensing

We present galaxy-galaxy lensing measurements from 1321 sq. deg. of the Dark Energy Survey (DES) Year 1 (Y1) data. The lens sample consists of a selection of 660,000 red galaxies with high-precision photometric redshifts, known as redMaGiC, split into five tomographic bins in the redshift range $0.15<z<0.9$. We use two different source samples, obtained from the Metacalibration (26 million galaxies) and im3shape (18 million galaxies) shear estimation codes, which are split into four photometric redshift bins in the range $0.2<z<1.3$. We perform extensive testing of potential systematic effects that can bias the galaxy-galaxy lensing signal, including those from shear estimation, photometric redshifts, and observational properties. Covariances are obtained from jackknife subsamples of the data and validated with a suite of log-normal simulations. We use the shear-ratio geometric test to obtain independent constraints on the mean of the source redshift distributions, providing validation of those obtained from other photo-$z$ studies with the same data. We find consistency between the galaxy bias estimates obtained from our galaxy-galaxy lensing measurements and from galaxy clustering, therefore showing the galaxy-matter cross-correlation coefficient $r$ to be consistent with one, measured over the scales used for the cosmological analysis. The results in this work present one of the three two-point correlation functions, along with galaxy clustering and cosmic shear, used in the DES cosmological analysis of Y1 data, and hence the methodology and the systematics tests presented here provide a critical input for that study as well as for future cosmological analyses in DES and other photometric galaxy surveys.

Figure 1

(Top panel): Redshift distributions of redMaGiC lens galaxies divided in tomographic bins (colors) and for the combination of all of them (black). The $n(z)$’s are obtained stacking individual Gaussian distributions for each galaxy. (Bottom panel): The same, but for our two weak lensing source samples, Metacalibration and im3shape, using the BPZ photometric redshift code.

Figure 2

Tangential shear measurements for Metacalibration and im3shape together with the best-fit theory lines from the DES Y1 multiprobe cosmological analysis [25]. Scales discarded for the cosmological analysis, smaller than $12h^{-1}\mathrm{Mpc}$ in comoving distance, but which are used for the shear-ratio test, are shown as shaded regions. Unfilled points correspond to negative values in the tangential shear measurement, which are mostly present in the lens-source combinations with low signal-to-noise due to the lenses being at higher redshift than the majority of sources. HiDens, HiLum and HigherLum correspond to the three redmagic samples (High Density, High Luminosity and Higher Luminosity) described in Sec. 3a.

Figure 3

Correlation matrices obtained from the jackknife method on the data (top-left panel), from the mean of jackknife covariances using 100 FLASK realizations (top-middle panel) and from the 1200 lognormal simulations FLASK (top-right panel), for an example redshift bin ($0.3<z_l<0.45$ and $0.63<z_s<0.90$). In the bottom-middle and bottom-right panels, we show the differences between the covariance matrices shown in the upper panels normalized by the uncertainty on the difference, for the same example redshift bin. On the bottom-left panel, we display the normalized histograms of these differences ($20\times 20$ for each covariance, corresponding to 20 angular bins) for all the $5\times 4$ lens-source redshift bin combinations, compared to a Gaussian distribution centered at zero with a width of one.

Figure 4

Comparison of the diagonal elements of the covariance obtained from the jackknife method on the data (Data JK), from the mean of jackknife covariances using 100 FLASK realizations (FLASK JK) and from the 1200 lognormal simulations flask (FLASK True), for all the lens-source combinations.

Figure 5

(Top panel): Cross-component of the galaxy-galaxy lensing signal with random points subtraction for one lens-source redshift bin combination. (Bottom panel): The null ${\chi }^2$ histogram from all $5\times 4$ lens-source redshift bins combinations computed with the jackknife covariance corrected with the Hartlap factor [65], compared to the ${\chi }^2$ distribution with 20 degrees of freedom corresponding to 20 angular bins. We find the cross-component to be consistent with zero.

Figure 6

PSF residuals for PSFEx model, using a single non-tomographic lens bin, including random-point subtraction. It is consistent with a null measurement and much smaller than the signal.

Figure 7

S/N (left) and size (right) splits tests for Metacalibration and im3shape, using scales employed in the cosmology analysis ($>12h^{-1}\mathrm{Mpc}$). (Top panels): Redshift distributions of the lens and source samples used for this test. (Bottom panels): Comparison between the ratio of ${\mathrm{\Sigma }}_{\text{crit},\text{eff}}^{-1}$ using the above redshift distributions (boxes) to the ratio between the amplitudes coming from the fit of the tangential shear measurement for each half to the smooth template from the lognormal simulations (points).

Figure 8

Results for the tests involving area splits in halves of different observational systematics maps in the $r$ band, with angular scales used in the cosmology analysis ($12h^{-1}\mathrm{Mpc}$). We compare the ratio of ${\mathrm{\Sigma }}_{\text{crit},\text{eff}}^{-1}$ (boxes) using the redshift distributions for each split to the ratio between the amplitudes coming from the fit of the tangential shear measurement for each half to the smooth template derived from the lognormal simulations (points), following the same procedure as for the S/N and size splits, described in Sec. 5c and shown in Fig. 7.

Figure 9

Comparison between the mean ratio of tangential shear measurements using 1200 independent log-normal simulations and the ones calculated from theory, for all lens-source bin ratio combinations sharing the same lens bin. The error bars correspond to the standard deviation of the measurement on individual simulations, thus being representative of the errors that we will obtain from the data.

Figure 10

Boost factor correction accounting for clustering between lenses and sources in each lens-source bin used in this analysis. Non-shaded scales correspond to scales used in the DES Y1 cosmological analysis, while shaded regions are used for the shear-ratio geometrical test in this section. Boost factors are unity or percent-level for the former, but can be significantly larger for the latter in some cases, and hence they are applied in our analysis of the shear-ratio test.

Figure 11

Comparison between the ratio of tangential shear measurements on Metacalibration (blue points) to the ones calculated from theory, both without applying any shift to the original source $n(z{)}^{\prime }s$ (dashed orange line) and applying the best-fit shifts with a $1\sigma$ uncertainty band (gray band).

Figure 12

Comparison of the constraints obtained on the source redshift distribution shifts using different methods: Shear-ratio test, photo-$z$ studies in the COSMOS field (COSMOS, [34]) and cross-correlation redshifts (WZ, [35, 36]).

Figure 13

Prior and posterior distributions for multiplicative shear biases ($m$) for the first three source bins defined in this work (Fig. 1). The shear-ratio test appears to be informative on the multiplicative shear biases for the second and third source bins, reducing the prior width by as much as 20%, even though posteriors are all consistent with the priors at better than $1\text{−}\sigma$ level.

Figure 14

Comparison of the galaxy bias results obtained from galaxy clustering measurements ($b_A$, [37]) and from the galaxy-galaxy lensing measurements in this work ($b_{\times }$), by fixing all cosmological parameters to the $3\times 2$ cosmology best-fit from [25]. The vertical dotted lines separate the three redMaGiC samples, which have different luminosity thresholds $L_{\min }$, defined in Sec. 3a.

Figure 15

Cross-correlation coefficient $r$ between galaxies and dark matter obtained by comparing the galaxy bias from galaxy clustering ($b_A$) and from galaxy-galaxy lensing only ($b_{\times }$), fixing all cosmological parameters to three different cosmologies from DES Y1 cosmological results [25]: (i) 3x2 best-fit (All), (ii) $\omega (\theta )+{\gamma }_t$ best-fit, and (iii) cosmic shear best-fit.

Figure 16

Relative signal-to-noise ratio of lensing signal recovered when weighting sources uniformly (commonly called ${\gamma }_{\mathrm{t}}$, circles) and with “$\mathrm{\Delta }\mathrm{\Sigma }$ weighting” according to a DES-like photometric redshift point estimate (squares) with ${\sigma }_p=-0.1(1+z)+0.12(1+z{)}^2$ scatter around the true redshift [34]. The point estimate is used to select source bins of width $\mathrm{\Delta }z=0.25$.

Figure 17

Tangential shear around random points for Metacalibration and im3shape.

Figure 18

We show the impact the random point subtraction has on the tangential shear measurement and its corresponding jackknife covariance matrix for an example redshift bin ($0.3<z_l<0.45$ and $0.63<z_s<0.90$ for Metacalibration).

Figure 19

Metacalibration responses scale dependence and mean values. We compare the responses averaged in 20 log-spaced angular bins between 2.5 and 250 arcmin in each lens-source redshift bin combination ($R_{\mathrm{nk}}$) to the average of the responses in each source redshift bin ($R_{\mathrm{mean}}$). The maximum difference between them is at the 0.2% level.