Three-point correlation function of galaxy clusters in cosmological models: a strong dependence on triangle shape

Jun, 1995
11 pages
Published in:
  • Mon.Not.Roy.Astron.Soc. 277 (1995) 630
e-Print:

Citations per year

19962002200820142020210
Abstract: (arXiv)
In this paper, we use large \pppm N-body simulations to study the three-point correlation function ζ\zeta of clusters in two theoretical models. The first model (LCDM) is a low-density flat model of Ω0=0.3\Omega_0=0.3, Λ0=0.7\Lambda_0=0.7 and h=0.75h=0.75, and the second model (PIM) is an Einstein-de-Sitter model with its linear power spectrum obtained from observations. We found that the scaled function Q(r,u,v)Q(r,u,v), which is defined as the ratio of ζ(r,ru,ru+rv)\zeta (r, ru, ru+rv) to the hierarchical sum ξ(r)ξ(ru)+ξ(ru)ξ(ru+rv)+ξ(ru+rv)ξ(r)\xi (r)\xi (ru)+ \xi (ru) \xi (ru+rv) +\xi (ru+rv)\xi (r) (where ξ\xi is the two-point correlation function of clusters), depends weakly on rr and uu, but very strongly on vv. Q(r,u,v)Q(r,u,v) is about 0.2 at v=0.1v=0.1 and 1.8 at v=0.9v=0.9. A model of Q(r,u,v)=Θ101.3v2Q(r,u,v)=\Theta 10^{1.3v^2} can fit the data of ζ\zeta very nicely with Θ0.14\Theta\approx 0.14. This model is found to be universal for the LCDM clusters and for the PIM clusters. Furthermore, Q(r,u,v)Q(r,u,v) is found to be insensitive to the cluster richness. We have compared our N-body results with simple analytical theories of cluster formation, like the peak theories or the local maxima theories. We found that these theories do not provide an adequate description for the three-point function of clusters. We have also examined the observational data of ζ\zeta presently available, and have not found any contradiction between the observations and our model predictions. The vv-dependence of qq in a projected catalogue of clusters is shown to be much weaker than the vv-dependence of QQ found in the three-dimensional case. It would be important to search for the vv-dependence of QQ in redshift samples of rich clusters.