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 cosmology. We develop a novel method infer level of conformity stellar mass bright central (BCGs) $M_*^{\texttt {BCG}}$ satellite richness ?, defined as their correlation coefficient ?cc at fixed halo mass, using abundance weak lensing SDSS clusters functions ?. detect mass-dependent = 0.60 + 0.08ln (Mh/3 × 1014h?1M?). The strong successfully resolves ‘halo equality’ conundrum discovered Zu et al. – when split by low- high-$M_*^{\texttt have same average despite having 0.34-dex discrepancy {BCG}}$. On top best-fitting model, we assembly bias (AB) prescription calibrated against CosmicGrowth simulation build AB model for measurements. Our predicts that with an ${\sim }20{{\ \rm per\ cent}}$ lower concentration c, low-$M_*^{\texttt are }10{{\ more biased than systems, good agreement observations. also show observed unlikely due projection effects. Finally, toy argue while early-time BCG–halo co-evolution drives {BCG}}$-c correlation, late-time dry merger-induced BCG growth naturally produces {BCG}}$-? well-known anticorrelation ? c. paves path towards simultaneously constraining cosmology formation future surveys.