Halo Radius (Splashback Radius) of Groups and Clusters of Galaxies on small scales

We report the results of a study of the distribution of galaxies in the projection along the radius (R ≤ 3R200c) for 157~groups and clusters of galaxies in the local Universe (0.01 < z < 0.10) with line-of-sight velocity dispersions~200~km~s⁻¹ < σ < 1100~km~s⁻¹. We introduce a new observed boundary for the halos of clusters of galaxies, which we identify with the splashback radius Rₛₚ. We also identified the core of groups/clusters of galaxies with the radiusRc. These radii are determined by the observed integrated distribution of the number of galaxies as a function of squared angular radius from the center of the group/cluster, which (usually) coincides with the brightest galaxy. We found for the entire sample that the boundary of dark matter Rₛₚ for groups/clusters of galaxies is proportional to the radius R200c of the virialized region. We measured the mean radius Rₛₚ = 1.14±0.02~Mpc for groups of galaxies (σ ≤ 400~km~s⁻¹) and Rₛₚ = 2.00±0.07~Mpc for clusters of galaxies (σ > 400~km~s⁻¹). The mean ratio of radii is Rₛₚ/R200c = 1.40±0.02}, or Rₛₚ/R₂₀₀ₘ = 0.88±0.02.