The evolution of high-density cores of the BOSS Great Wall superclusters

High-density cores (HDCs) of galaxy superclusters that embed rich clusters and groups of galaxies are the earliest large objects to form in the cosmic web, and the largest objects that may collapse in the present or future. We study the dynamical state and possible evolution of the HDCs in the BOSS Great Wall (BGW) superclusters at redshift $z \approx 0.5$ in order to understand the growth and evolution of structures in the Universe. We derived the density contrast values for the spherical collapse model in a wide range of redshifts and used these values to study the dynamical state and possible evolution of the HDCs of the BGW superclusters. The masses of the HDCs were calculated using stellar masses of galaxies in them. We found the masses and radii of the turnaround and future collapse regions in the HDCs and compared them with those of local superclusters. We determined eight HDCs in the BGW superclusters. The masses of their turnaround regions are in the range of $M_{\mathrm{T}} \approx 0.4 - 3.3\times~10^{15}h^{-1}M_\odot,$ and radii are in the range of $R_{\mathrm{T}} \approx 3.5 - 7 h^{-1}$Mpc. The radii of their future collapse regions are in the range of $R_{\mathrm{FC}} \approx 4 - 8h^{-1}$Mpc. Distances between individual cores in superclusters are much larger: of the order of $25 - 35h^{-1}$Mpc. The richness and sizes of the HDCs are comparable with those of the HDCs of the richest superclusters in the local Universe. The BGW superclusters will probably evolve to several poorer superclusters with masses similar to those of the local superclusters. This may weaken the tension with the $\Lambda$CDM model, which does not predict a large number of very rich and large superclusters in our local cosmic neighbourhood, and explains why there are no superclusters as elongated as those in the BGW in the local Universe.