Halo Assembly Bias using properties of central galaxies in SDSS redMaPPer clusters

The clustering of dark matter halos depends on the assembly history of halos at fixed halo mass; a phenomenon referred to as \textit{halo assembly bias}. Halo assembly bias is readily observed in cosmological simulations of dark matter. However, it is difficult to detect it in observations. The identification of galaxy or cluster properties correlated with the formation time of the halo at fixed halo mass and the ability to select galaxy clusters free from projection effects are the two most significant hurdles in the observational detection of halo assembly bias. The latter, in particular, can cause a misleading detection of halo assembly bias by boosting the amplitude of lensing and clustering on large scales. This study uses twelve different properties of central galaxies of SDSS redMaPPer clusters derived from spectroscopy to divide the clusters into sub-samples. We test the dependence of the clustering amplitude on these properties at fixed richness. We first infer halo mass and bias using weak lensing signals around the clusters using shapes of galaxies from the SDSS survey. We validate the bias difference between the two subsamples using cluster-galaxy cross-correlations. This methodology allows us to decouple the contamination due to the projection effects from the halo assembly bias signals. We do not find any significant evidence of a difference in the clustering amplitudes correlated with any of our explored properties. Our results indicate that central galaxy properties may not correlate significantly with the halo assembly histories at fixed richness.