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

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) $M_{\ast }^{BCG}$ and the satellite richness $\hat{I}»$, defined as their correlation coefficient $\ddot{I}{}_{cc}$ at fixed halo mass, using the abundance and weak lensing of SDSS clusters as functions of $M_{\ast }^{BCG}$ and $\hat{I}»$. We detect a halo mass-dependent conformity as $\ddot{I}{}_{cc}=0.60+0.08\ln (M_h/3\times 10^{14}{M}_{\odot }/h)$. The strong conformity successfully resolves the "halo mass equality" conundrum discovered in Zu et al. 2021 -- when split by $M_{\ast }^{BCG}$ at fixed $\hat{I}»$, the low and high-$M_{\ast }^{BCG}$ clusters have the same average halo mass despite having a $0.34$ dex discrepancy in average $M_{\ast }^{BCG}$. 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-$M_{\ast }^{BCG}$ clusters are $\sim 10\%$ more biased than the high-$M_{\ast }^{BCG}$ 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 $M_{\ast }^{BCG}$-$c$ correlation, the late-time dry merger-induced BCG growth naturally produces the $M_{\ast }^{BCG}$-$\hat{I}»$ conformity despite the well-known anti-correlation between $\hat{I}»$ and $c$. Our method paves the path towards simultaneously constraining cosmology and cluster formation with future cluster surveys.

Final MN accepted version (w/ Fig 6 replaced)