Title: The SRG/eROSITA All-Sky Survey: Exploring halo assembly bias with X-ray selected superclusters

Abstract: We explore halo assembly bias on cluster scales using large samples of superclusters. Leveraging the largest-ever X-ray galaxy cluster and supercluster samples obtained from the first SRG/eROSITA all-sky survey, we construct two subsamples of galaxy clusters which consist of supercluster members (SC) and isolated clusters (ISO) respectively. After correcting the selection effects on redshift, mass, and survey depth, we compute the excess in the concentration of the intracluster gas of isolated clusters with respect to supercluster members, defined as $\delta c_{\rm gas} \equiv c_{\rm gas,ISO}/c_{\rm gas,SC}-1$, to investigate the environmental effect on the concentration of clusters, an inference of halo assembly bias on cluster scales. We find that the average gas mass concentration of isolated clusters is a few percent higher than that of supercluster members, with a significance of $2\sigma$. The result on $\delta c_{\rm gas}$ varies with the overdensity ratio $f$ in supercluster identification, cluster mass proxies, and mass ranges, but remains positive in all the measurements. We measure slightly larger $\delta c_{\rm gas}$ when adopting a higher $f$ in supercluster identification. $\delta c_{\rm gas}$ is also larger for low-mass clusters, and almost negligible for high-mass clusters. We perform weak lensing analyses to compare the total mass concentration of the two classes and find a similar trend as obtained from gas mass concentration. Our results are consistent with the prediction of HAB on cluster scales, where halos located in denser environments are less concentrated, and this trend is stronger for low-mass halos than for massive halos. These phenomena can be interpreted by the fact that clusters in denser environments such as superclusters have experienced more mergers than isolated clusters in their assembling history.