Origin of weak lensing convergence peaks

Weak lensing convergence peaks are a promising tool to probe nonlinear structure evolution at late times, providing additional cosmological information beyond second-order statistics. Previous theoretical and observational studies have shown that the cosmological constraints on ${\mathrm{\Omega }}_m$ and ${\sigma }_8$ are improved by a factor of up to $\approx 2$ when peak counts and second-order statistics are combined, compared to using the latter alone. We study the origin of lensing peaks using observational data from the $154{\mathrm{deg}}^2$ Canada-France-Hawaii Telescope Lensing Survey. We found that while high peaks (with height $\kappa >3.5{\sigma }_{\kappa }$, where ${\sigma }_{\kappa }$ is the rms of the convergence $\kappa$) are typically due to one single massive halo of $\approx 10^{15}{M}_{\odot }$, low peaks ($\kappa \lesssim {\sigma }_{\kappa }$) are associated with constellations of 2–8 smaller halos ($\lesssim 10^{13}{M}_{\odot }$). In addition, halos responsible for forming low peaks are found to be significantly offset from the line of sight towards the peak center (impact parameter $\gtrsim$ their virial radii), compared with $\approx 0.25$ virial radii for halos linked with high peaks, hinting that low peaks are more immune to baryonic processes whose impact is confined to the inner regions of the dark matter halos. Our findings are in good agreement with results from the simulation work by Yang et al. [Phys. Rev. D 84, 043529 (2011)].

Figure 1

Reconstructed ${\kappa }_{\mathrm{lens}}$ map from shear measurements (left) and ${\kappa }_{\mathrm{proj}}$ map from projected foreground halos (right), for the CFHTLenS W1 field. Both maps are smoothed with an 8.9 arcmin Gaussian window.

Figure 2

Peaks (black filled circles) found in ${\kappa }_{\mathrm{proj}}$ maps are overlaid on ${\kappa }_{\mathrm{lens}}$ maps, for CFHTLenS W1, W2, W3, W4 fields (upper left, upper right, lower left, and lower right, respectively). Circle sizes represent the height of peaks. ${\kappa }_{\mathrm{proj}}$ maps are smoothed with a 5.3 arcmin Gaussian window, while ${\kappa }_{\mathrm{lens}}$ maps with a 8.9 arcmin window. These two different smoothing scales are used for the purpose of visual display.

Figure 3

Cross-correlations of the ${\kappa }_{\mathrm{proj}}$ and ${\kappa }_{\mathrm{lens}}$ maps (red circle) and of the ${\kappa }_{\mathrm{proj}}$ and ${\kappa }_{\mathrm{B}-\text{mode}}$ maps (black diamonds), with analytical Gaussian error estimates. The correlation between the ${\kappa }_{\mathrm{proj}}$ and ${\kappa }_{\mathrm{lens}}$ maps has a significance of 24.1.

Figure 4

The top panel shows peak counts from ${\kappa }_{\mathrm{lens}}$ maps (filled green circles), compared with averaged peak counts from 500 random noise maps (dashed curves), created by rotating galaxies by a random angle. The bottom panel shows their difference. The error bars are the standard deviation on 500 random realizations. Maps are smoothed with a 1 arcmin Gaussian window and have rms of ${\sigma }_{\kappa }=0.036$. ${\kappa }_{\mathrm{lens}}$ peak counts deviate from the random case significantly ($\mathrm{SNR}=6.2$).

Figure 5

Top panel: Cross-correlations of ${\kappa }_{\mathrm{proj}}$ maps and ${\kappa }_{\mathrm{lens}}$ peaks. Filled red circles show the relation for all ${\kappa }_{\mathrm{lens}}$ peaks ($\mathrm{SNR}=16.1$). Open red circles include only low ${\kappa }_{\mathrm{lens}}$ peaks ($<3.5{\sigma }_{\kappa }$), where the signal, though slightly reduced, remains significant ($\mathrm{SNR}=14.0$). Bottom panel: Cross-correlation of ${\kappa }_{\mathrm{proj}}$ peaks and ${\kappa }_{\mathrm{lens}}$ peaks, with $\mathrm{SNR}=23.7$ (all peaks, red filled circle) and $\mathrm{SNR}=21.9$ (low peaks only, red open circle). We also show results of null tests (filled and open black diamonds for all and low peaks, respectively), where we replace ${\kappa }_{\mathrm{lens}}$ peaks by ${\kappa }_{\mathrm{B}-\text{mode}}$ peaks. All maps are smoothed with an 1.0 arcmin Gaussian window.

Figure 6

The number of halos needed to account for $>50\%$ of the peak height (red circles) for ${\kappa }_{\mathrm{proj}}$ peaks. We also show the same quantity, but for 10,000 random directions that are not peaks (green diamonds). The shade in the background is the two-dimensional probability distribution for all peaks. The error bar is the standard deviation of all peaks within each $\kappa$ bin.

Figure 7

Same as Fig. 6 but with the peaks extracted from ${\kappa }_{\mathrm{lens}}$ maps.

Figure 8

Examples of peaks in ${\kappa }_{\mathrm{lens}}$, located at the center of each $5\times 5{\mathrm{arcmin}}^2$ panel. Red (blue) represents higher (lower) convergence value. The left panel shows a typical high peak with a relatively circular shape, suggesting a single massive halo. In comparison, most low peaks (showing in the other three panels) reside in complex regions where several peaks are cluttered together, or filamentlike structures are seen. The peak height (${\kappa }_{\mathrm{peak}}$) is marked at the top of each panel.

Figure 9

Properties of halos that contribute $>50\%$ of the total convergence of ${\kappa }_{\mathrm{proj}}$ peaks, as a function of peak height: (a) average halo mass of contributing halos, (b) comoving distance dispersion along the line of sight, (c) average angular separation between the halos and the center of the peak, in unit of arcmin, and (d) that in unit of the halo virial radius.

Figure 10

Peaks (black filled circles) found in ${\kappa }_{\mathrm{lens}}$ maps are overlaid on ${\kappa }_{\mathrm{proj}}$ maps, for CFHTLenS W1, W2, W3, W4 fields (upper left, upper right, lower left, and lower right, respectively). Circle sizes represent the height of peaks. ${\kappa }_{\mathrm{lens}}$ maps are smoothed with a 5.3 arcmin Gaussian window, while ${\kappa }_{\mathrm{proj}}$ maps with a 8.9 arcmin window. These two different smoothing scales are used for the purpose of visual display.