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

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.

💡 Research Summary

This paper presents a novel measurement of the splashback radius – the physical boundary marking the apocenter of the first orbit of infalling material – using stacked infrared images from the Wide‑field Infrared Survey Explorer (WISE). The authors exploit the MaDCoWS2 (Massive and Distant Clusters of WISE Survey 2) catalog, selecting 83,345 candidate galaxy clusters in the redshift range 0.5 ≤ z ≤ 1.92. Clusters are binned by photometric redshift and by signal‑to‑noise (S/N) of the detection, ensuring at least 750 objects per bin to maintain statistical robustness.

For each cluster a cutout of the unWISE coadded images in the W1 (3.4 µm) and W2 (4.5 µm) bands is extracted over a 21′ × 21′ field (≈8 Mpc at z = 0.5). The authors perform a three‑step masking procedure (global masks, local masks, and bright‑source masks) and then subtract a first‑order polynomial (planar) background from each individual cutout, supplementing the global background already applied in the unWISE processing. This careful background handling is crucial because the splashback signal appears as a subtle change in the slope of the surface‑brightness profile at radii of order 1 Mpc.

The processed cutouts are combined into weighted‑mean stacks for each redshift–S/N bin. Weights are derived from the inverse variance maps, which down‑weight noisy pixels. The stacked “total‑light” profiles extend to ~3 Mpc from the cluster centre, with a residual background measured in the 3–4 Mpc annulus. The splashback radius is identified as the location where the logarithmic derivative d log I/d log R of the surface‑brightness profile exhibits a pronounced steepening, i.e., the point of maximum curvature.

Statistical uncertainties are quantified via 1,000 bootstrap realizations of the cluster sample in each bin; the median and 68 % confidence interval of the splashback radius are reported. The measured splashback radii lie between ~0.9 and ~1.3 Mpc (physical) across all bins. These values are fully consistent with those obtained by K. Thongkham et al. (2026) using galaxy‑cluster cross‑correlation on essentially the same MaDCoWS2 sample, confirming that the total‑light stacking technique does not suffer from large systematic biases.

The dominant systematic identified is the background subtraction. The authors test alternative background models (higher‑order polynomials, different annular ranges) and find that the splashback location shifts by less than the statistical error, indicating that the result is robust. Compared with galaxy‑count or weak‑lensing methods, total‑light stacking has the advantage of incorporating light from faint dwarf galaxies and intracluster light (ICL), which are below detection thresholds in individual images. This makes the method especially powerful at high redshift (z > 1), where only the brightest galaxies are individually detectable.

The paper also discusses potential scientific applications. Because the total‑light profile reflects the integrated stellar mass, the technique can be used to trace the evolution of the stellar‑mass fraction in the infall region of clusters, offering a new probe of how galaxies are quenched and how stellar mass builds up as material crosses the splashback boundary. The authors suggest that combining this approach with upcoming deep infrared surveys (e.g., Euclid, Roman, JWST) could yield precise measurements of splashback radii across cosmic time, enabling direct tests of theoretical predictions that link splashback location to halo accretion rate.

In summary, the authors demonstrate that stacking WISE total‑light images provides a reliable, independent measurement of the splashback radius for a large sample of distant clusters. The method’s sensitivity to faint light components, its consistency with established cross‑correlation results, and its modest systematic uncertainties make it a valuable addition to the toolbox for studying cluster assembly and galaxy evolution at high redshift.