Wide-field lensing mass maps from Dark Energy Survey science verification data: Methodology and detailed analysis

Weak gravitational lensing allows one to reconstruct the spatial distribution of the projected mass density across the sky. These “mass maps” provide a powerful tool for studying cosmology as they probe both luminous and dark matter. In this paper, we present a weak lensing mass map reconstructed from shear measurements in a $139{\mathrm{deg}}^2$ area from the Dark Energy Survey (DES) science verification data. We compare the distribution of mass with that of the foreground distribution of galaxies and clusters. The overdensities in the reconstructed map correlate well with the distribution of optically detected clusters. We demonstrate that candidate superclusters and voids along the line of sight can be identified, exploiting the tight scatter of the cluster photometric redshifts. We cross-correlate the mass map with a foreground magnitude-limited galaxy sample from the same data. Our measurement gives results consistent with mock catalogs from $N$-body simulations that include the primary sources of statistical uncertainties in the galaxy, lensing, and photo-$z$ catalogs. The statistical significance of the cross-correlation is at the $6.8\sigma$ level with 20 arcminute smoothing. We find that the contribution of systematics to the lensing mass maps is generally within measurement uncertainties. In this work, we analyze less than 3% of the final area that will be mapped by the DES; the tools and analysis techniques developed in this paper can be applied to forthcoming larger data sets from the survey.

Figure 1

Distributions of the single-point photo-$z$ estimates for the background and foreground samples used in this paper are shown in the top panel, overlaid by the lensing efficiency [Eq. (10)] corresponding to the background sample. The background and the foreground main sample uses the mean of the PDF from BPZ for single-point estimates, while the LRG redshift estimate comes independently from Redmagic (see Sec. 3a3). The bottom panel shows the corresponding $n(z)$ of the background and foreground main sample given by BPZ. These come from the sum of the PDF for all galaxies in the samples.

Figure 2

The upper left panel shows the $E$ modes of the weak lensing convergence map. The upper right shows the weighted foreground galaxy map from the main sample, or ${\kappa }_{g,\text{main}}$. The lower two panels show the product maps of the $E$-mode (left) and $B$-mode (right) convergence map with the ${\kappa }_{g,\text{main}}$ map. All maps are generated with a 5 arcmin pixel scale and 20 arcmin Gaussian smoothing. Red areas corresponds to overdensities and blue areas to underdensities in the upper panels. White regions correspond to the survey mask. The scale of the Gaussian smoothing kernel is indicated by the Gaussian profile on the upper right corner.

Figure 3

The top panel shows the S/N map for the mass map in Fig. 2 estimated via randomized errors. Note that due to the Gaussian smoothing kernel, there is some mixing of scales which leads to higher contrasts in the cores of over- and underdense regions compared to top-hat smoothing. The bottom panel shows the normalized S/N distributions for both maps, overlaid by those measured from simulations described in Sec. 6b. The red dashed lines in both bottom panels show a Gaussian fit to the $B$-mode S/N.

Figure 4

The DES SV mass map along with foreground galaxy clusters detected using the Redmapper algorithm. The clusters are overlaid as black circles with the size of the circles indicating the richness of the cluster. Only clusters with richness greater than 20 and redshift between 0.1 and 0.5 are shown in the figure. The upper right corner shows the correspondence of the optical richness to the size of the circle in the plot. It can be seen that there is significant correlation between the mass map and the distribution of galaxy clusters. Several superclusters (black squares) and voids (white squares) can be identified in the joint map.

Figure 5

Left: the blue curve in each of the 4 panels shows the weighted redshift distribution of galaxy clusters counts with optical richness $\lambda >5$ at the 4 different locations in the mass map of Fig. 4 corresponding to large convergence peak locations. The RA, Dec coordinates of these pointings are shown in the top right corner of each panel and the field numbers are listed on the top left corner. The counts are calculated for a 1 deg radius area, and the histograms are weighted by $\lambda$ and the lensing efficiency to properly represent the mass distribution and the lensing probed by the mass map. The thick grey line indicates the corresponding average number count in the full map. The redshift range above $z=0.6$ is marked with the shaded grey area, as these ranges overlap with the background sample. Right: a candidate supercluster is shown by zooming in on a narrow redshift range of field 2 (red band in upper right panel on the left) where a peak in the cluster counts occurs. Each circle indicates the location of a galaxy belonging to a Redmapper cluster. The large spatial extent (a transverse distance of 10 Mpc is indicated in the panel) and the irregular shape characteristic of three-dimensional superclusters is evident.

Figure 6

Left: same as the left panel of Fig. 5 but plotted for voids identified in the mass map. There are typically fewer than average clusters over much of the line of sight which also contains some deep underdense regions at specific redshifts. At the higher redshifts, there are also above average cluster counts, but since the redshift range overlaps with the source galaxy sample, the interpretation of the structures is more complicated. Right: radial distribution of the Redmagic LRGs for field 5 in the left panel (red bands in upper left panel). The data are consistent with the existence of two voids modeled by the “top-hat” void model of width 190 and $120\mathrm{Mpc}/h$, respectively.

Figure 7

This figure shows the Pearson correlation coefficient between foreground galaxies and convergence maps as a function of smoothing scale for the ngmix galaxy catalog. The solid and open symbols show the $E$- and $B$-mode correlation coefficients, respectively. The black circles are for the main foreground sample and the red circles for foreground LRGs. The grey shaded regions show the $1\sigma$ bounds for $E$- and $B$-mode correlations from simulations for the main foreground sample with the same pixelization and smoothing (see Sec. 6b for details). We do not show the similar simulation results for the LRG sample. The detection significance for the correlation is in the range $\sim 5–7\sigma$ at different smoothing scales. The green points show the correlation between $E$ and $B$ modes of the mass map. The various $B$-mode correlations are consistent with zero. Uncertainties on all measurements are estimated based on jackknife resampling.

Figure 8

Same as Fig. 7 but using the im3shape galaxy catalog.

Figure 9

Maps from simulations that are designed to mimic the data in our analysis. The simulations are generated for a field of size $15\times 17.6{\mathrm{deg}}^2$ with similar redshift and magnitude selections for the foreground and the background sample as the data. The true $\kappa$ and ${\kappa }_g$ maps are shown in the first row, where ${\kappa }_g$ is modeled for the main foreground sample. The reconstructed ${\kappa }_E$ and ${\kappa }_B$ maps from the true $\gamma$ are shown in the first two panels of the second row, followed by the ${\kappa }_E$ and ${\kappa }_B$ maps reconstructed from the ellipticity ($ϵ$) values. The last row first shows the ${\kappa }_E$ and ${\kappa }_B$ constructed from $ϵ$ with photo-$z$ uncertainties, then the same maps with an SV survey mask applied. The last two panels on the bottom most closely match the data.

Figure 10

Pearson correlation coefficient ${\rho }_{X{\kappa }_g}$ between the different simulated maps shown in Fig. 9 as a function of smoothing scale. $X$ represents the different $\kappa$ maps as listed in the legend. This plot is the simulation version of Fig. 7, where one can see how the measured values in the data could have been degraded due to various effects. The qualitative trend of the correlation coefficients as a function of smoothing scale is consistent with that observed in data. When reconstructing ${\kappa }_E$ from the true $\gamma$ small errors are introduced due to the nonlocal reconstruction, lowering the correlation coefficient by a few percent. Adding shape noise to the shear measurement lowers the signal significantly, with the level of degradation dependent on the smoothing scale. Adding photo-$z$ uncertainties changes the signal by a few percent. Finally, placing an SV-like survey mask changes the signal by $\sim 10\%$. The black curve with its error bars corresponds to the shaded region in Fig. 7.

Figure 11

The normalized cross-correlation coefficient ${\widehat{\rho }}_{{\kappa }_E{\kappa }_g;\mathrm{\Theta }}$ is shown for 20 different systematic uncertainty parameters. The systematics parameters, represented by $\mathrm{\Theta }$, are listed in Table 2 and shown for two smoothing scales. The ${\widehat{\rho }}_{{\kappa }_E{\kappa }_g;\mathrm{\Theta }}$ values are normalized by ${\widehat{\rho }}_{{\kappa }_E{\kappa }_g}$ to show the relative magnitude of the systematic and the signal. The red dashed line indicates where the systematic is 5% of ${\widehat{\rho }}_{{\kappa }_E{\kappa }_g}$. The error bars are estimated from resampling the foreground and background galaxy sample in patches of size $10{\mathrm{deg}}^2$. The left panel is calculated for ngmix while the right panel is for im3shape.

Figure 12

Pearson correlation coefficient ${\rho }_{{\kappa }_E\mathrm{\Theta }}$ where $\mathrm{\Theta }$ represents the quantities listed in Table 2. We show the statistics for two smoothing scales and for both ngmix (left) and im3shape (right). The right-most points in both panel correspond to the detection signal in Fig. 7 and Fig. 8. The error bars are estimated from resampling the foreground and background galaxy sample in patches of size $10{\mathrm{deg}}^2$. Note that this is a different statistic from that in Fig. 11, thus the $y$-axis values are not directly comparable.

Figure 13

Galaxy number density as a function of the seeing in the area of consideration. The black line shows the mean and standard deviation (multiplied by 10 for easy visualization) of the scatter plot in 15 seeing bins.

Figure 14

The systematics map for ${\kappa }_E$ (left) and ${\kappa }_g$ (right) shown is compiled using a linear combination of 20 principal components extracted from the systematics maps listed in Table 2.