Catalogue of Clusters that are Members of Superclusters

Abstract

An attempt is made to establish the membership of Abell clusters in superclusters of galaxies. The relation

$$ \log \;z = - 3.637 + (0.135\pm 0.014)\;{m_{{10}}} = (0.179\pm 0.030)\;\;\log \;P $$

((1))

is used to calibrate the distances to the clusters of galaxies with two redshift estimates. One is m₁₀, the magnitude of the ten-ranked galaxy, and the other is the “mean population,” P, defined by:

$$ P = p/2{\pi^2}, $$

((2))

, where p = 40, 65, 105 . . . galaxies for richness groups 0, 1, 2 . . . , and r is the apparent radius in degrees given by:

$$ r = 0.0286(1 + z_1 )^{2/z_1 } . $$

((3))

. The first iteration for redshift, z₁, is obtained from m₁₀ alone:

$$ {\text{z}}_{\text{1}} {\text{ = - 4}}{\text{.568 + 0}}{\text{.261m}}_{{\text{10}}} {\text{.}} $$

. The standard deviation for Eq. (1) is 0.105, the number of clusters with known velocities is 342 and the correlation coefficient between observed and fitted values is 0.921. With z_i from Eq. (1), we define Cartesian galactic coordinates X_i = R_ih^-1 cosB_i cosL_i, Y_i = R_ih^-1 cosB_i sinL_i, Z_i = R_ih^-1 sinB_i for each Abell cluster, i = 1,...,2712, where R_i is the distance to the cluster (Mpc), and H_o = 100 h km s^-1 Mpc^-1.