The Massive and Distant Clusters of WISE Survey 2: Splashback Radii to z=1.65 from Galaxy Density Profiles

TL;DR

This work measures the splashback radius in the MaDCoWS2 cluster sample out to $z\,\approx\,1.65$ by cross-correlating clusters with CatWISE2020 galaxies and fitting a two-component density model (orbiting plus infalling) via Bayesian MCMC to extract $r_{ m sp}$. The analysis reveals a distinct splashback feature across all subsamples, with $r_{ m sp}$ increasing in comoving units with redshift and scaling with $S/N_{ m P}$, and derives $M_{200m}$ from $r_{ m sp}$ using a simulation-based relation, though these masses are systematically lower than weak-lensing calibrations. The authors discuss the need for robust mass calibration—potentially from future weak-lensing measurements with Euclid, Rubin, and Roman—to fully leverage $r_{ m sp}$ as a cluster-mass proxy. They also compare their results to DR2 mass–S/N$_{ m P}$ relations and prior literature, highlighting selection effects and baryonic physics as possible sources of discrepancy and emphasizing the value of upcoming wide-field data for improved cosmological constraints.

Abstract

The Massive and Distant Clusters of WISE Survey 2 (MaDCoWS2) is a WISE-selected catalog of galaxy clusters at $0.1<z<2$ covering an effective area of $>6000$ deg$^2$. In this paper, we derive splashback radii for this cluster ensemble from galaxy density profiles and constrain the mass threshold of the survey as a function of redshift. We use MaDCoWS2 cluster candidates at $0.4\leq z \leq 1.65$ divided into subsamples with different signal-to-noise (S/N$_{\rm P}$) and redshifts, cross-correlated with galaxies from the CatWISE2020 catalog, to obtain average surface density profiles. We perform a Markov Chain Monte Carlo analysis to derive parameter estimates for theoretical models consisting of orbiting and infalling terms. A distinct splashback feature is detected in all subsamples. The measured splashback radii span from $0.89^{+0.02}_{-0.02}h^{-1}$ comoving Mpc/cMpc ($0.61^{+0.02}_{-0.02}h^{-1}$ proper Mpc/pMpc) at $\overline{z}=0.45$ to $1.27^{+0.05}_{-0.05}h^{-1}$ cMpc ($0.53^{+0.04}_{-0.04}h^{-1}$ pMpc) at $\overline{z}=1.54$. We also find that splashback radii increase with $S/N_{\rm P}$ at fixed redshift. The resultant splashback radii constrain the redshift dependence of the mass of MaDCoWS2 clusters at fixed $S/N_{\rm P}$. We calculate $M_{\rm 200m}$ from the radii using a relation based on a cosmological simulation. MaDCoWS2 $M_{\rm 200m}$ values derived from the simulation-based relation are lower than the expected values based on weak-lensing observations. More robust mass constraints will come from calibrating splashback radii derived from galaxy density profiles with weak lensing shear profiles from facilities such as $\textit{Euclid}$, Rubin, and $\textit{Roman}$.

Figures (8)

• Figure 1: Sample selection of the cluster candidates used in the analysis of this paper. The cluster sample is displayed in hexagonal bins with a bin size of $0.05$ in cluster redshift on the x-axis and $0.5$ in S/N$_{\rm P}$ on the y-axis. S/N$_{\rm P}$ and $z$ are the signal-to-noise ratio and photometric redshift of the clusters. Bin colors indicate the number of clusters. The solid red lines display the binning scheme for subsamples shown in Table \ref{['Tab:cluster sample']}. The red squares indicate $\overline{\text{S/N}}_{\rm P}$ and $\overline{z}$ of the subsamples.
• Figure 2: Galaxy surface density versus comoving projected radius (left column), galaxy density versus comoving three-dimensional radius (middle column), and logarithmic derivative of galaxy density versus comoving three-dimensional radius (right column) of MaDCoWS2 clusters with $5\leq$ S/N$_{\rm P}$$<7$. Each row displays a different redshift subsample as listed in Table \ref{['Tab:cluster sample']}. The surface density measurements as described in § \ref{['subsec:measurement']} are shown as data points in the left column. The solid lines in the left column are the best fit to galaxy surface density from the model fitting scheme in § \ref{['sec:Model fitting']}. The solid lines in the right column show the three-dimensional splashback radii ($r_{\rm sp}$). For reference, dashed lines show the profiles and splashback radius of the lowest redshift bin in the higher redshift subsamples. We input all fit parameters in our MCMC samples to the model in § \ref{['sec:Model']} and generate the curves in the middle columns. The curves in the right column correspond to the best-fit parameters, and to the 0th and 100th percentiles of the parameter distribution.
• Figure 2: Continued)
• Figure 3: Galaxy surface density (left column), galaxy density (middle column), and logarithmic derivatives of galaxy density (right column) similar to Figure \ref{['fig:dens1']}, but for subsamples with $7\leq$ S/N$_{\rm P}$$<9$.
• Figure 4: Galaxy surface density (left column), galaxy density (middle column), and logarithmic derivatives of galaxy density (right column) similar to Figure \ref{['fig:dens1']}, but for subsamples with S/N$_{\rm P}$$\geq 9$.