Ying Zu, Yunjia Song, Zhiwei Shao, Xiaokai Chen, Yun Zheng, Hongyu Gao, Yu Yu, Huanyuan Shan, Yipeng Jing, Strong conformity and assembly bias: towards a physical understanding of the galaxy–halo connection in SDSS clusters, Monthly Notices of the Royal Astronomical Society, Volume 511, Issue 2, April 2022, Pages 1789–1807, https://doi.org/10.1093/mnras/stac125

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 bright central galaxies (BCGs) |$M_*^{\texttt {BCG}}$| and the satellite richness λ, defined as their correlation coefficient ρcc at fixed halo mass, using the abundance and weak lensing of SDSS clusters as functions of |$M_*^{\texttt {BCG}}$| and λ. We detect a halo mass-dependent conformity as ρcc = 0.60 + 0.08ln (Mh/3 × 1014h−1M⊙). The strong conformity successfully resolves the ‘halo mass equality’ conundrum discovered in Zu et al. – when split by |$M_*^{\texttt {BCG}}$| at fixed λ, the low- and high-|$M_*^{\texttt {BCG}}$| clusters have the same average halo mass despite having a 0.34-dex discrepancy in average |$M_*^{\texttt {BCG}}$|⁠ . 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 an |${\sim }20{{\ \rm per\ cent}}$| lower halo concentration c, the low-|$M_*^{\texttt {BCG}}$| clusters are |${\sim }10{{\ \rm per\ cent}}$| more biased than the high-|$M_*^{\texttt {BCG}}$| systems, in good 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 |$M_*^{\texttt {BCG}}$| -c correlation, the late-time dry merger-induced BCG growth naturally produces the |$M_*^{\texttt {BCG}}$| -λ conformity despite the well-known anticorrelation between λ and c. Our method paves the path towards simultaneously constraining cosmology and cluster formation with future cluster surveys.

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