The Massive and Distant Clusters of WISE Survey 2: Detection of splashback radii in galaxy cluster total light stacks

TL;DR

This work reports the first detection of splashback radii in total light stacks built from WISE/W1 and W2 imaging of 83,345 MaDCoWS2 clusters across $0.5 \le z \le 1.92$. Using bootstrap realizations, the authors extract projection-based splashback radii and compare them to independent cross-correlation results, finding general consistency albeit with larger uncertainties. The analysis emphasizes background subtraction as a principal systematic and demonstrates the method's advantage at high redshift, where the stacking approach remains sensitive to flux from faint cluster members and intracluster light. The study also explores an application to the stellar mass in the infalling region, showing a redshift-dependent increase in the outskirts’ stellar mass fraction, highlighting the method’s potential for studying cluster outskirts and galaxy evolution in dense environments.

Abstract

The splashback radius, the radius of the apocenter of the first orbit of infalling material, is a measurable quantity marking the boundary between a galaxy cluster and its infalling region. We report detections of splashback radii in total light stacks, i.e. image stacks centered on the cores of galaxy clusters. Our analysis uses Wide-field Infrared Survey Explorer (WISE) W1 and W2 images of 83,345 candidate clusters at $0.5 \lesssim z \lesssim 1.9$ from the Massive and Distant Clusters of WISE Survey 2 (MaDCoWS2). The clusters are organized in stacks by redshift and signal-to-noise ($S\slash N$) ratios. We adopt a statistical approach, using 1000 bootstrap realizations to determine the median projected splashback radius and its confidence interval in a given bin. We compare our splashback radii with the measurements made by K. Thongkham et al. on a similar sample of MaDCoWS2 clusters using galaxy-cluster cross-correlation and find that they are consistent, although our method yields larger error bars. Our main systematic error is the accuracy of the background subtraction, but its impact remains small: the consistency of K. Thongkham et al. and our results suggests that neither method suffers from large systematics. The sensitivity of total light stacking to the contribution of faint galaxies can be advantageous to locate splashback radii when only the brightest galaxies are detected in individual images, such as at high redshifts. We present a potential application of this new technique to probe the evolution of the stellar mass in cluster infalling regions.

Figures (6)

• Figure 1: The photometric redshift and $S\slash N$ subdivisions used in this work. The cluster sample is represented by hexagons, color-coded by counts. The main redshift divisions are indicated as rectangles delimited by full lines, with the height of the rectangle giving the maximum S/N in a redshift bin. The dashed lines show the $S\slash N$ subdivisions, with values listed in Table \ref{['tab_binning']}.
• Figure 2: Left: Non-cumulative mean surface brightness of the $\overline{z} = 1.77$, $5.0 \leq S\slash N < 5.25$ bootstraps (variance-weighted mean of W1 and W2). The confidence interval of the splashback radius is shaded in pink, and its median location indicated by a darker line. The edges of the prior are indicated in dark green. Center: Logarithmic slope of the surface brightness. Right: Histogram of the positions of the splashback radii in the W1+W2 bootstraps with the confidence interval shaded in pink. The text on the top right indicates the percentage of bootstraps with a detected feature. Bottom panels: same as the top panel, for the $\overline{z} = 1.09$, $5.25 \leq S\slash N < 5.91$ bootstraps.
• Figure 3: Comparison between our splashback radii, color-coded by $S\slash N$ bins, and thongkham_massive_2026 2D splashback radii (open symbols). For $z\geq 0.5$, we offset thongkham_massive_2026 values by $\Delta z=0.025$ to limit overlaps. We also include the two highest redshift bins of murata_splashback_2020 as filled black symbols.
• Figure 4: Splashback radius measurements for the $\overline{z} = 0.72$, $5.25 \leq S\slash N < 5.91$ bootstraps. The confidence interval of the splashback radius is shaded in pink if the determination is reliable (see Section \ref{['ssec_splashback']}) and hatched if it is not. Left: Nominal background determination. Center: Same as left panel, but introducing a systematic 2.5% undersubtraction of the residual background. The new confidence interval is shaded or hatched in blue, with the new median indicated by a blue line. The median of the original distribution is indicated by a pink line. Right: mean surface brightness with a systematic 2.5% oversubtraction of the residual background. The new confidence interval (in blue) is not deemed reliable though the new median and original median have the same value, i.e. the blue line is under the pink line.
• Figure 5: The stellar mass (not deprojected) beyond the splashback radius (out to 3 Mpc) divided by the stellar mass within the splashback radius. The stellar mass in the outskirts increases with redshift with respect to the central mass.