Fundamental Plane of Groups and Clusters of Galaxies: Distances and Peculiar Velocities of Superclusters of Galaxies on Small Scales

This work is a continuation of the work of Kopylova and Kopylov (2016) to build a fundamental plane (FP) of groups and clusters of galaxies -- here a sample of galaxies systems is increased from 94 to 172 objects. We have studied the ratios between the basic characteristics of groups and clusters of galaxies according to the archival data of SDSS, 2MASX and NED catalogs. Measured parameters ($\log L_K$, $\log R_e$ and $\log \sigma$) of clusters of galaxies determine the fundamental plane in the near infrared region: $L_K \propto R_e^{0.77\pm0.09} \sigma^{1.44\pm0.12}$. The form of the FP of groups/clusters is consistent with the FP of the early -- types of galaxies (SDSS, $r$-band) determined in the same way. Direct regression relative to the padius $\log r_e$ in the kpc gives a projection of the FP -- $\log R_e=0.98(\pm0.06)\,\log \sigma-0.56(\pm0.04)