Subclustering might help to solve the virial theorem paradox for systems of galaxies by hiding a major part of the potential energy in gravitationally bound subsystems. We have shown (Ozernoy and Reinhardt 1976, Astr. Astrophys., 52, 31) that even in groups of galaxies there is mass segregation, in the sense that bright group members tend to be concentrated towards the centre. Recently Wesson and Lermann (1977, Astrophys. Sp. Sci., 46, 327), realizing the importance of subclustering, proposed a quantitative method for estimating its effect on the stability of systems of galaxies. However, their assumption about the frequency of subsystems of multiplicity n is not in accord with Holmberg's (1962) result. the mean frequency of galaxies in pairs is 0.37 for the Turner and Gott groups (1976) and 0.23 for the de Vauceulours groups (1976), in good agreement with the value of 0.25 required by Holmberg's distribution. Assuming Holmberg's frequency of gravitationally bound subsystems and that they are homogeneously distributed throughout the system, we have for the ratio of the total potential energy of a system of N equal masses Ω to the potential energy calculated in the usual way neglecting subclustering Ωs, Ω/Ωs≈ 1+(Rc)/(<r2>N), if the velocity dispersion <σr2(n)> = constant. Here Rc is the effective radius of the system and <r2> the mean distance of binaries. the assumption σr2(n) = const is reasonable for n ≤ 7, when Holmberg's distribution holds, since σr2(2) = 203 km s−1 according to Karachentsev (1974), and increases to only ≃ 1000 km s−1 for rich clusters. Since Karachentsev's data give an <r2> = 33 kpc for HO = 55 km s−1 Mpc−1, we have Ω/Ωs≈ 4 for groups of galaxies with Rc≈ 1 Mpc and N = 10. Thus it seems that subclustering cannot remove the mass discrepancy for rich clusters and for groups only in moderate cases.
Buckling And Postbuckling Of An Imperfect Plate Subjected To The Shear Load
