Hidden Connections: Tracing the BCG Stellar Mass-Halo Mass Relation in the SDSS-GalWCat19 Cluster Catalog

Abstract

The stellar-to-halo mass (SMHM) relation of brightest cluster galaxies (BCGs) provides key insight into the connection between BCG growth and the assembly of their host halos. We analyze this relation using the spectroscopic SDSS GalWCat19 cluster catalog, selecting 996 systems with log(M200) >= 13.6, log(Mstar) >= 10.5, and 0.02 <= z <= 0.125 to limit evolutionary effects and ensure stellar-mass completeness. We fit lognormal scaling relations with a Markov Chain Monte Carlo (MCMC) framework that accounts for measurement uncertainties and intrinsic scatter. For the fiducial SMHM relation, <log Mstar | M200> = alpha + beta log(M200/Mpiv) with log(Mpiv) = 14.2, we find a shallow slope beta = 0.17 +/- 0.03, normalization alpha = 11.04 +/- 0.01, and intrinsic scatter sigma_int = 0.19 +/- 0.01 dex. Recasting the relation in normalized form reduces the scatter to 0.16 +/- 0.01 dex, while including the magnitude gap M14 further reduces it to 0.14 +/- 0.01 dex. Variations in richness, redshift, and mass thresholds produce systematic shifts that are small compared to the statistical uncertainties, indicating that our inferred relations are robust to plausible selection choices. The reduced scatter when including M14 supports a picture in which BCG stellar mass reflects both halo mass and halo assembly history.

Figures (6)

• Figure 1: Left: Distribution of galaxy cluster masses $M_{200}$ as a function of redshift for our sample of 1185 clusters. The sample is approximately complete for clusters with $\log{M_{200}} \geq 13.6$ [$h^{-1} \ M_{\odot}$] in the redshift range $0.02 \leq z \leq 0.125$. Right: Distribution of BCG stellar masses $\mathrm{M}_{\ast}$ versus redshift. To ensure completeness, we select BCGs with $\log{\mathrm{M}_{\ast}} \geq 10.5$ [$h^{-2} \ M_{\odot}$]. In both panels, the color bar indicates the magnitude gap $M_{14}$, defined as the brightness difference between the BCG and the fourth brightest galaxy member.
• Figure 2: Left: Distribution of the stellar-to-halo mass ratio, $\log{(M_\ast/M_{200})}$, as a function of cluster mass, $\log{M_{200}}$. Right: Distribution of $\log{(M_\ast/M_{200})}$ versus the magnitude gap $M_{14}$ between the BCG and the fourth brightest galaxy member. In both panels, the color bar indicates the value of $M_{14}$.
• Figure 3: BCG stellar mass--halo mass relations for our cluster sample. Left: The standard $\mathrm{SMHM}$ relation showing $\log M_\ast$ as a function of $\log M_{200}$. Middle: $\mathrm{SMHM}_N$ relation showing $\log(M_\ast/M_{200})$ as a function of $\log M_{200}$, illustrating the declining stellar mass fraction with increasing halo mass. Right: $\mathrm{SMHM}^G_N$ relation, where $\log(M_\ast/M_{200})$ is plotted against $\log{M_{200}} - M_{14}$. In all panels, gray points show individual clusters with $1\sigma$ error bars. Solid lines indicate the best-fit relations, and the shaded regions denote the $1\sigma$, $2\sigma$, and $3\sigma$ confidence intervals.
• Figure 4: Comparison between our derived BCG stellar mass-to-halo mass relations at $z \sim 0.1$ and several published models and observations. Left: $\log M_\ast$ versus $\log M_{200}$ relation ($\mathrm{SMHM}$). Right: $\log(M_\ast/M_{200})$ versus $\log M_{200}$ relation ($\mathrm{SMHM}_N$). The black solid line represents our best-fit relation, with the shaded region indicating the $1\sigma$ uncertainty. The red solid line denotes the direct observational measurement from Erfanianfar19, while the colored dashed curves show empirical models from Behroozi13c, Moster13, Kravtsov18, and Behroozi19.
• Figure A1: Impact of varying selection thresholds on the SMHM relations. Each row shows the best-fit SMHM (left), SMHM$_N$ (middle), and SMHM$^G_N$ (right) relations for different cuts in richness ($N_{\mathrm{mem}}$, top row), lower redshift ($z_{\mathrm{lower}}$, middle row), and upper redshift ($z_{\mathrm{upper}}$, bottom row). Color scales indicate the threshold values used. The relations remain nearly unchanged across the tested ranges, demonstrating that systematic effects from these selection criteria are small.