Estimation of the Hubble constant from the scatter of the fundamental plane distances of groups and clusters of galaxies ($71.1\pm 2.8$ km s$^{-1}$ Mpc$^{-1}$)

To determine the peculiar velocities of galaxy clusters relative to the Hubble Flow, we need to measure the distances of galaxy systems using some method that is sensitive to their distances. The fundamental plane (FP) of early-type galaxies is one such method and is widely used for such problems. Using the FP, we determined the angular distances of 140 groups and galaxy clusters in the local Universe ($z<$ 0.15) and constructed a Hubble diagram between distances and radial velocities in the CMB reference frame in the framework of the flat $\Lambda$CDM model ($\Omega_{\rm m}=0.3$, $H_0=70$ km s$^{-1}$ Mpc$^{-1}$). We obtained the average deviation of the relative distances $\gamma$ from the Hubble dependence for this model $\langle\Delta \gamma\rangle$=$-0.0066\pm0.0023$ ($N$ = 140). The minimum deviation we found corresponds to the value of the Hubble constant $71.1$ km s$^{-1}$ Mpc$^{-1}$. We found that the logarithmic standard scatter of the relative distances of groups and clusters of galaxies on the Hubble diagram (subtracting peculiar velocities) is $\pm0.0173$ ($N$ = 140), which corresponds to the deviation of the Hubble constant $71.1\pm2.8$ km s$^{-1}$ Mpc$^{-1}$. For a sample of galaxy clusters ($N$ = 63) with X-ray luminosity in the range (0.15–4)$\times10^{44}$ erg/s, we obtained $71.1\pm2.1$ km s$^{-1}$~Mpc$^{-1}$.