Abstract
This work is a continuation of the work of Kopylova and Kopylov published in 2016 on constructing the fundamental plane (FP) of groups and clusters of galaxies. In this article, the sample of galaxy systems has been increased from 94 to 172 objects. We have studied the relationships between the main characteristics of groups and clusters of galaxies using archival data from the SDSS, 2MASX, and NED catalogs. The measured parameters ( \(\log L_{K}\) , \(\log R_{e}\) and \(\log\sigma\) ) of galaxy clusters define the fundamental plane in the near-infrared region: \(L_{K}\propto R_{e}^{0.77\pm 0.09}\sigma^{1.44\pm 0.12}\) . The shape of the FP of groups and clusters is consistent with the FP of early-type galaxies (SDSS, \(r\) -filter), determined in the same way. Regression against \(\log R_{e}\) in kpc gives the projection of the FP: \(\log R_{e}=0.98(\pm 0.06)\,\log\sigma-0.56(\pm 0.04)\langle\log I_{e}\rangle+3.57(\pm 0.07)\) , which can be used to determine the distances of galaxy systems. The \(rms\) scatter of the zero point is 0.07, which is equivalent to a 16 \(\%\) error in determining the distance to a group or cluster of galaxies. For the first time, we have determined the average relative FP distances and peculiar velocities of five large superclusters of galaxies. According to our estimates, the average peculiar velocity of these superclusters relative to the CMB is \(+75\pm 360\) km s \({}^{-1}\) .
