On the Assembly Bias of Cool Core Clusters Traced by H$alpha$ Nebulae

Do cool-core (CC) and noncool-core (NCC) clusters live in different environments? We make novel use of H$alpha$ emission lines in the central galaxies of redMaPPer clusters as proxies to construct large (1,000u0027s) samples of CC and NCC clusters, and measure their relative assembly bias using both clustering and weak lensing. We increase the statistical significance of the bias measurements from clustering by cross-correlating the clusters with an external galaxy redshift catalog from the Sloan Digital Sky Survey III, the LOWZ sample. Our cross-correlations can constrain assembly bias up to a statistical uncertainty of 6%. Given our H$alpha$ criteria for CC and NCC, we find no significant differences in their clustering amplitude. Interpreting this difference as the absence of halo assembly bias, our results rule out the possibility of having different large-scale (tens of Mpc) environments as the source of diversity observed in cluster cores. Combined with recent observations of the overall mild evolution of CC and NCC properties, such as central density and CC fraction, this would suggest that either the cooling properties of the cluster core are determined early on solely by the local (u003c200 kpc) gas properties at formation or that local merging leads to stochastic CC relaxation and disruption in a periodic way, preserving the average population properties over time. Studying the small-scale clustering in clusters at high redshift would help shed light on the exact scenario.