Identification of Superclusters and their Properties in the Sloan Digital Sky Survey Using WHL Cluster Catalog

Superclusters are the largest massive structures in the cosmic web on tens to hundreds of megaparsecs (Mpc) scales. They are the largest assembly of galaxy clusters in the Universe. Apart from a few detailed studies of such structures, their evolutionary mechanism is still an open question. In order to address and answer the relevant questions, a statistically significant, large catalog of superclusters covering a wide range of redshifts and sky areas is essential. Here, we present a large catalog of 662 superclusters identified using a modified $\textit{ Friends of Friends}$ algorithm applied on the WHL (Wen-Han-Liu) cluster catalog within a redshift range of $0.05 \le z \le 0.42$. We name the most massive supercluster at $z \sim 0.25$ as $\textit{Einasto Supercluster}$. We find that the median mass of superclusters is $\sim 5.8 \times 10^{15}$ M$_{\odot}$ and median size $\sim 65$ Mpc. We find that the supercluster environment slightly affects the growth of clusters. We compare the properties of the observed superclusters with the mock superclusters extracted from the Horizon Run 4 cosmological simulation. The properties of superclusters in mocks and observations are in broad agreement. We find that the density contrast of a supercluster is correlated with its maximum extent with a power law index, $\alpha \sim -2$. The phase-space distribution of mock superclusters shows that, on average, $\sim 90\%$ part of a supercluster has a gravitational influence on its constituents. We also show mock halos' average number density and peculiar velocity profiles in and around the superclusters.