Testing the Large-Scale Environments of Cool-core and Noncool-core Clusters with Clustering Bias

There are well-observed differences between cool-core (CC) and non-cool-core (NCC) clusters, but the origin of this distinction is still largely unknown. Competing theories can be divided into internal (inside-out), in which internal physical processes transform or maintain the NCC phase, and external (outside-in), in which the cluster type is determined by its initial conditions, which in turn lead to different formation histories (i.e., assembly bias). We propose a new method that uses the relative assembly bias of CC to NCC clusters, as determined via the two-point cluster-galaxy cross-correlation function (CCF), to test whether formation history plays a role in determining their nature. We apply our method to 48 ACCEPT clusters, which have well resolved central entropies, and cross-correlate with the SDSS-III/BOSS LOWZ galaxy catalog. We find that the relative bias of NCC over CC clusters is $b = 1.42 \pm 0.35$ ($1.6\sigma$ different from unity). Our measurement is limited by the small number of clusters with core entropy information within the BOSS footprint, 14 CC and 34 NCC. Future compilations of X-ray cluster samples, combined with deep all-sky redshift surveys, will be able to better constrain the relative assembly bias of CC and NCC clusters and determine the origin of the bimodality.