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The splashback radius of groups and clusters of galaxies at low redshifts

We present a study of the distribution of galaxies along the radius of 157 groups and clusters of galaxies (200~km~s$^{-1}$ < $σ$ < 1100~km~s$^{-1}$) of the local Universe (0.01 < $z$ < 0.1). We introduced a new boundary of galaxy systems and identified it with the splashback radius $R_{sp}$. We also identified the central region of galaxy systems with a radius of $R_c$. These radii are defined by the observed integrated distribution of the total number of galaxies depending on the squared distance from the center of the groups/clusters coinciding, as a rule, with the brightest galaxy. We show that the radius $R_{sp}$ is proportional to the $R_{200c}$ (radius of the virialized region of a galaxy cluster) and to the radius of the central region $R_c$ with a slope close to 1. Among the obtained dependences of the radii on X-ray luminosity, the $\log R_{sp}$ - $\log L_X$ relation has the lowest scatter. We measured $<R_{sp}>$ = $1.67\pm0.05$~Mpc for the total sample, $<R_{sp}>$ = $1.14\pm0.14$~Mpc for galaxy groups with $σ\leq$ 400~km~s$^{-1}$, $<R_{sp}>$ = $2.00\pm0.20$~Mpc for galaxy clusters with $σ$ > 400~km~s$^{-1}$. We found the average ratio of the radii $R_{sp}/R_{200c} = 1.40\pm0.02$ or $R_{sp}/R_{200m} = 0.88\pm0.02$.}