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 $$\langle {{{{R}_{{{\text{sp}}}}}} \mathord{\left/ {\vphantom {{{{R}_{{{\text{sp}}}}}} {{{R}_{{{\text{200m}}}}}}}} \right. \kern-0em} {{{R}_{{{\text{200m}}}}}}}\rangle = 0.88 \pm 0.02$$ .