Selecting Clusters and Protoclusters via Stellar Mass Density: I. Method and tests on Mock HSC-SSP catalogs

TL;DR

This work tackles the challenge of identifying galaxy clusters and protoclusters in wide-area optical surveys up to $z\sim 2$ by first locating the dominant galaxy within each structure via local stellar mass density contrasts. It introduces a density-contrast–based probabilistic framework that assigns dominance and cluster membership, using PCcones mocks built from the Millennium simulation and L-GALAXIES to calibrate the model. Key contributions include a robust pre-selection of dominant galaxies, a probabilistic dominance function, probabilistic cluster membership and richness estimates, and calibrated halo mass–richness relations across redshift bins; the results show $\gtrsim 65\%$ purity for $P_{\rm dominant}>0.5$ and $\sim 80\%$ purity with $50\%$ completeness for $M_{\rm halo} \ge 10^{14}\,M_\odot$, with completeness rising to $\approx 100\%$ for $M_{\rm halo} \ge 10^{14.5}\,M_\odot$. The method does not rely on the red sequence and is designed to be applicable to HSC-SSP and other multi-band surveys, providing a practical path to study high-redshift structure growth and galaxy evolution; a companion paper will apply the method to real HSC-SSP data and compare with other cluster catalogs and X-ray detections.

Abstract

We present an algorithm designed to identify galaxy (proto)clusters in wide-area photometric surveys by first selecting their dominant galaxy-i.e., the Brightest Cluster Galaxy (BCG) or protoBCG-through the local stellar mass density traced by massive galaxies. We focus on its application to the Hyper Suprime-Cam Subaru Strategic Program (HSC-SSP) Wide Survey to detect candidates up to $\rm z \sim 2$. In this work, we apply the method to mock galaxy catalogs that replicate the observational constraints of the HSC-SSP Wide Survey. We derive functions that describe the probability of a massive galaxy being the dominant galaxy in a structure as a function of its stellar mass density contrast within a given redshift interval. We show that galaxies with probabilities greater than 50\% yield a sample of BCGs/protoBCGs with $\gtrsim 65\%$ purity, where most of the contamination arises from galaxies in massive groups below our cluster threshold. Using the same threshold, the resulting (proto)cluster sample achieves 80\% purity and 50\% completeness for halos with $M_{\rm{halo}} \geq 10^{14} \ M_{\odot}$, reaching nearly 100\% completeness for $M_{\rm{halo}} \geq 10^{14.5} \ M_{\odot}$. We also assign probabilistic membership to surrounding galaxies based on stellar mass and distance to the dominant galaxy, from which we define the cluster richness as the number of galaxies more likely to be true members than contaminants. This allows us to derive a halo mass-richness relation. In a companion paper, we apply the algorithm to the HSC-SSP data and compare our catalog with others based on different cluster-finding techniques and X-ray detections.

Figures (14)

• Figure 1: Number density of structures as a function of redshift in the PCcones mocks. Red (blue) line denotes the median number density galaxy clusters (protoclusters), while the shaded area is limited by 16th and 84th percentiles, considering 10 different lightcones with $\rm 36 \ deg^{2}$ each. We are defining galaxy clusters as structures with halo mass $M_{\rm{halo}} \geq 10^{14} \ M_{\odot}$ and galaxy protoclusters as structures with halo mass below this threshold, which will surpass this value at some point in their future at z $>$ 0. The large error bars at low redshifts for clusters are primarily due to cosmic variance. At low redshift, the survey volume per unit redshift is smaller, which enhances the impact of large-scale structure fluctuations on the measured cluster number densities.
• Figure 2: Top: Structure's halo mass functions for different redshift intervals depicted in the legend. The solid line is simply connecting the points, while the dotted lines are modified Normal distributions fits. Bottom: Halo mass as a function of the redshift. Each point denotes the halo mass where the modified Normal distributions reach their peak. The line denotes a power-law fit with 3 free parameters to these data. The function with the fitted parameters is showed in the upper right of this panel.
• Figure 3: Sample fraction with measured W1 values as a function of the true redshift (left panel) and true stellar mass (right). Blue dots denote all mock objects while red stars represent BCGs.
• Figure 4: From left to right: the first row of plots shows the estimated stellar mass ($\rm M_{\star, phot}$) of galaxies, $\sigma_{NMAD}$ (Eq. \ref{['eq: nmad']}), $Bias$ (Eq. \ref{['eq: bias']}), and $f_{out}$ (Eq. \ref{['eq: f_out']}), respectively, as a function of the mock stellar mass ($\rm M_{\star, true}$). Gray dots and lines represent all objects from the test sample. Orange (green) dots and lines stand for true mock BCGs with (without) W1 unWISE band information. Red lines stand for all true mock BCGs. Second row of plots shows the results for photometric redshift estimates ($\rm z_{phot}$) as a function of $\rm z_{true}$, analogous to the stellar mass estimates in the first row. Blue dots and lines denote all objects in the test sample. The purple line represents the results obtained by nishizawa20. The dashed line in the second plot ($\sigma_{NMAD} vs. z_{true}$) denotes the results obtained by W&H21. Third row of plots is analogous to the second row, now including only BCGs after pre-selecting galaxies above a given threshold in photometric stellar mass (as described in Section \ref{['sec: presel']}).
• Figure 5: BCG $i$-band magnitude, $r - i$ observed frame color, and stellar mass as function of redshift. For the mocks, we utilized perturbed magnitudes and photometric stellar masses and redshifts (Sections \ref{['sec: pccones']} and \ref{['sec: photoz']}) for true mock BCGs. Points denote the median properties within a given redshift bin, and the bars are the dispersions bounded by the 16th and 84th percentiles. BCGs from CAMIRA oguri14, W&H21 wh21, and redMaPPer rykoff14 catalogs are represented in the plots by blue, green, and orange colors, respectively, while mock BCGs are denoted by red color. Also, redMaPPer galaxies were cross-matched with the HSC-SSP Wide Survey to compare the measurements in the same photometric system. A slight horizontal shift was applied to the different markers to improve visualization.