Distances of Galaxy Groups and Clusters Measured Using Fundamental Planes

In this paper, we continue our research on constructing the optimal fundamental plane (FP) of galaxy groups and clusters for measuring their distances. This work was carried out using archival data from the SDSS and 2MASX catalogs. We present the fundamental planes (scaling relations of dynamical and photometric parameters) of 205 galaxy groups and clusters ( $$z<0.15$$ ). We found that in the near infrared ( $$K$$ -filter), the distribution of galaxy clusters is well approximated by three-parameter planes of the form $$R_{e}\propto\sigma^{1.01\pm 0.05}\langle I_{e}\rangle{{}^{-0.32\pm 0.03}}$$ and $$R_{e}\propto N^{0.43\pm 0.01}\langle I_{e}\rangle^{-0.40\pm 0.02}$$ and a four-parameter plane of the form $$R_{e}\propto\sigma^{0.15\pm 0.06}\langle I_{e}\rangle^{-0.39\pm 0.02}N^{0.38\pm 0.02}$$ . The fundamental planes have logarithmic standard deviations of 0.060, 0.036, and 0.035. If we use the fundamental planes to measure distances of galaxy systems, these deviations correspond to 14 $$\%$$ and 8 $$\%$$ errors in the distance of a single cluster. Using the four-parameter fundamental plane, we obtained the scatter of the Hubble constant $$H_{0}=70\pm 5.6\text{ km s}^{-1}$$ Mpc $${}^{-1}$$ . Using three fundamental planes of galaxy clusters, it was found that the velocity of the average drift motion in the three-degree cosmic microwave background (CMB) system of five superclusters of galaxies from the SDSS region is $$\langle V_{\textrm{pec}}\rangle={+}241\pm 180\text{ km s}^{-1}$$ .