Multi-scale weak lensing detection of galaxy clusters with source redshift tomography

Abstract

Recently, a number of methods have emerged to detect galaxy clusters solely through their weak lensing signal. Using the recently-introduced wavelet multi-scale detection method, we focus here on the potential for the use of tomographic information of the source galaxies to increase the number of weak lensing detections. We apply the $z_{s,\mathrm{min}}$-cut technique, consisting of the combination of weak lensing peak detections emerging from lensing maps obtained using different source redshift bins, to mock data sets of progressively increasing sophistication. The source redshift distribution is chosen to be $Euclid$-like, with a maximum depth of $z_{s,\mathrm{max}}=3$, and overlapping tomographic redshift bins are constructed by progressively increasing the minimum source redshift $z_{s,\mathrm{min}}$. Considering all possible detection combinations from one to four tomographic bins, we find that a single source redshift bin, with $z_{s,\mathrm{min}}=0.4$, performs as well as the combination of multiple redshift bins. By running detections on synthetic clusters of varying complexity -- from isolated Navarro Frenk White haloes to haloes embedded in and formed within N-body cosmological simulations, and considering both true and photometric source redshifts -- we show that while large-scale structure contamination and photometric redshift errors reduce the potential gains of the tomographic approach, the dominant limitation is the accumulation of spurious detections across redshift bins, leading to decreased purity at a fixed detection threshold.

Figures (12)

• Figure 1: (a) Mass–redshift ($M_{200\mathrm{c}}$–$z_l$) plane for one simulated field, showing all haloes in the simulation catalogue (grey dots). Haloes selected by the mass–redshift cut defined in Eq. \ref{['eq:diagonal_cut']} (red dashed line) are highlighted in blue. (b) Redshift distribution of the clusters selected by the mass–redshift cut, shown as the mean over all simulated fields (black line), with the 16th–84th percentile range indicated by the blue shaded region. (c) Mock $\kappa_E$ convergence field populated by NFW haloes with mass, redshift, and angular positions from the selected halo catalogue. (d) Same mock convergence field, with added shape noise. (e) Original N-body $\kappa_E$ from which the halo catalogue was extracted.
• Figure 2: Multi-scale peak detections, shown on a patch of an N-body convergence field in the W2, W3, and W4 scales: respectively (a), (b), and (c)). Detection peaks are circled with a radius matching the typical size of the given wavelet scale (red: W2, cyan: W3, and green: W4). The detection threshold was set on W2 as $4.6\sigma$, and the convergence map was generated using the full source redshift distribution (i.e. $z_{s,\mathrm{min}}=0$).
• Figure 3: Merging of multi-scale detections on W234 (W2+W3+W4). Pink squares mark the final merged detection positions. Thick white circles indicate haloes matched to detections; thin white circles show haloes rejected by the S/N matching when multiple candidates fall within the matching radius. Unmatched haloes are shown as dashed grey circles. Circle sizes scale with $\theta_{200}$. The detection threshold is $4.6\sigma$ on W2, and the convergence map uses the full source redshift distribution ($z_{s,\mathrm{min}}=0$).
• Figure 4: Left: Source redshift distributions for tomographic bins defined by lower redshift cuts $z_s \ge z_{s,\mathrm{min}}$ (vertical dashed lines). Solid curves show the resulting true-redshift distributions when bins are selected using photometric redshifts, highlighting inter-bin leakage due to photometric redshift uncertainties. Right: lensing efficiency kernels as a function of lens redshift for each source bin, weighted by the shape noise contribution.
• Figure 5: Histogram of the number of detections and associations on NFW mock convergence maps, produced with bins of lens redshift and source redshift. The full bars show the detections matched to the haloes input from the catalogue, while the hashed bars show the share of detections that were not matched, i.e., spurious detections. The colours show the contributions of each wavelet scale (red: W2, cyan: W3, green: W4) to the total detections/associations (grey). On top of each bar, we display purity (P) and completeness (C). The detection threshold was set on W2 as $4.6\sigma$.