Galaxy cluster A2142: halo boundary, `red sequence', properties of
  galaxies according to SDSS
  The paper presents the results of studying the dynamics of galaxies,
properties of early-type galaxies, properties of galaxies with the quenched
star formation (QGs) in the A 2142 based on the archival data from the Sloan
Digital Sky Survey. We found the observed halo boundary, the splashback radius
$R_{sp}$, which is equal to 4.12 Mpc ($M_r < -20\,.\!\!^{\rm m}3$) and 4.06 Mpc
($M_r < -21\,.\!\!^{\rm m}3$) over the integral distribution of the number of
galaxies as a function of the squared distance from the center. We have studied
how early-type galaxies are distributed in the center and in the outskirts of
the cluster ($R/R_{200}$ < 3, $M_r < -20\,.\!\!^{\rm m}3$) and plotted the red
sequence in the form of (g - r) = $(-0.024\pm0.001)M_r + (0.441\pm0.005$).
Among all the cluster galaxies, the galaxies with the quenched star formation (
$- 12\,yr^{- 1} < \log sSFR < - 10.75\,yr^{- 1}$) make up about one third. We
have found that the fraction of QGs beyond the splashback $R_{sp}$ is the same
as in the field at the same z with coordinates of the center of $16\,.\!\!^{\rm
h}5$, $31^{\circ}$ and a size of $300'$. For galaxies with the stellar masses
$\log M_*/M_{\odot}$ = [10.5;11.0] (this is the main mass range of QGs), after
entering the cluster, there is a decrease in the radii $R_{90,r}$ by about 30\%
when moving towards the center.
