Fundamental plane of groups and clusters of galaxies: distances and peculiar velocities of superclusters of galaxies on small scales

We have studied the relationships between the basic properties of 172 groups and clusters of galaxies based on archival data from the SDSS, 2MASX, and NED catalogs. The measured parameters ($\log R_e$, $\langle \log I_e \rangle $ and $\log \sigma$ of the clusters of galaxies determine the fundamental plane (FP) in the near infrared: $\log R_e=0.98(\pm0.06)\,\log \sigma-0.56(\pm0.04)\langle \log \langle I_e \rangle \rangle+3.57(\pm0.07)$, which can be used to determine the distances of the galaxy systems. The root-mean-square deviation of the FP zero-point is 0.07, which corresponds to an error of 16% in determining the distance of the group or cluster of galaxies. For the first time we have measured the peculiar velocities of the superclusters of galaxies. The mean peculiar velocity of the 5 superclusters of galaxies relative to the CMB is $+75\pm360$ km/s.