Strong Conformity and Assembly Bias: Towards a Physical Understanding of the Galaxy-Halo Connection in SDSS Clusters

TL;DR

This paper introduces a new method to understand the galaxy-halo connection in SDSS clusters by analyzing conformity and assembly bias, revealing their impact on cluster properties and cosmology.

Contribution

The study develops a novel approach to measure conformity between BCG stellar mass and satellite richness, and models assembly bias effects, advancing understanding of galaxy-halo relationships.

Findings

Detected halo mass-dependent conformity with correlation coefficient 0.60.

Resolved the 'halo mass equality' conundrum in cluster studies.

Predicted assembly bias effects consistent with observations.

Abstract

Understanding the physical connection between cluster galaxies and massive haloes is key to mitigating systematic uncertainties in next-generation cluster cosmology. We develop a novel method to infer the level of conformity between the stellar mass of the brightest central galaxies~(BCGs) $M_*^{BCG}$ and the satellite richness $\lambda$, defined as their correlation coefficient $\rho_{cc}$ at fixed halo mass, using the abundance and weak lensing of SDSS clusters as functions of $M_*^{BCG}$ and $\lambda$. We detect a halo mass-dependent conformity as $\rho_{cc}{=}0.60{+}0.08\ln(M_h/3{\times}10^{14}M_{\odot}/h)$. The strong conformity successfully resolves the "halo mass equality" conundrum discovered in Zu et al. 2021 -- when split by $M_*^{BCG}$ at fixed $\lambda$, the low and high-$M_*^{BCG}$ clusters have the same average halo mass despite having a $0.34$ dex discrepancy in average $M_*^{BCG}$. On top of the best-fitting conformity model, we develop a cluster assembly bias~(AB) prescription calibrated against the CosmicGrowth simulation, and build a conformity+AB model for the cluster weak lensing measurements. Our model predicts that with a ${\sim}20\%$ lower halo concentration $c$, the low-$M_*^{BCG}$ clusters are ${\sim}10\%$ more biased than the high-$M_*^{BCG}$ systems, in excellent agreement with the observations. We also show that the observed conformity and assembly bias are unlikely due to projection effects. Finally, we build a toy model to argue that while the early-time BCG-halo co-evolution drives the $M_*^{BCG}$-$c$ correlation, the late-time dry merger-induced BCG growth naturally produces the $M_*^{BCG}$-$\lambda$ conformity despite the well-known anti-correlation between $\lambda$ and $c$. Our method paves the path towards simultaneously constraining cosmology and cluster formation with future cluster surveys.