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 ($R \leqslant 3{{R}_{{200{\text{c}}}}}$) for 157 groups and clusters of galaxies in the local Universe (0.01 < $z$ < 0.10) with line-of-sight velocity dispersions 200 < $\sigma$ < 1100 km s^–1. We introduce a new observed boundary for the halos of clusters of galaxies, which we identify with the splashback radius ${{R}_{{{\text{sp}}}}}$. We also identified the core of groups/clusters of galaxies with the radius ${{R}_{{\text{c}}}}$. 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 ${{R}_{{{\text{sp}}}}}$ for groups/clusters of galaxies is proportional to the radius ${{R}_{{{\text{200}}}}}$ of the virialized region. We measured the mean radius $\langle {{R}_{{{\text{sp}}}}}\rangle = 1.14 \pm 0.02$ Mpc for groups of galaxies ($\sigma \leqslant 400$ km s^–1) and $\langle {{R}_{{{\text{sp}}}}}\rangle = 2.00 \pm 0.07$ Mpc for clusters of galaxies ($\sigma > 400$ km s^–1). The mean ratio of radii is $\langle {{{{R}_{{{\text{sp}}}}}} \mathord{\left/ {\vphantom {{{{R}_{{{\text{sp}}}}}} {{{R}_{{{\text{200c}}}}}}}} \right. \kern-0em} {{{R}_{{{\text{200c}}}}}}}\rangle = 1.40 \pm 0.02$, or $\langle {{{{R}_{{{\text{sp}}}}}} \mathord{\left/ {\vphantom {{{{R}_{{{\text{sp}}}}}} {{{R}_{{{\text{200m}}}}}}}} \right. \kern-0em} {{{R}_{{{\text{200m}}}}}}}\rangle = 0.88 \pm 0.02$.