ThreePoint Correlation Function of Galaxy Clusters in Cosmological Models  a Strong Dependence on Triangle Shapes
Abstract
In this paper, we use large P^3^M Nbody simulations to study the three point correlation function {ζ of clusters in two theoretical models. The first model (LCDM) is a lowdensity flat model of {OMEGA}_0_ = 0.3, {LAMBDA}_0_ = 0.7 and h = 0.75, and the second model (PIM) is an Einsteinde Sitter model with its linear power spectrum obtained from observations We find that the scaled function Q(r, u, v), which is defined as the ratio of ζ(r, ru, ru + rv) to the hierarchical sum ξ(r)ξ(ru) + ξ(ru)ξ(ru + rv) + ξ(ru + rv)ξ(r) (where ξ is the twopoint correlation function of clusters), depends weakly on r and u, but very strongly on v. Q(r, u, v) is about 0.2 at v = 0.1 and 1.8 at v = 0.9. A model of Q(r, u, v) = {THETA}10^1.3_v_^2^ can fit the data of ζ very nicely with {THETA} ~ 0.14. This model is found to be universal for the LCDM clusters and for the PIM clusters. Furthermore, Q(r, u, v) is found to be insensitive to the cluster richness. We compare our Nbody results with simple analytical theories of cluster formation, like the peak theories or the local maxima theories. We find that these theories do not provide an adequate description for the threepoint function of clusters. We also examine the observational data of ζ presently available, and do not find any contradiction between the observations and our model predictions. The v dependence of 4 in a projected catalogue of clusters is shown to be much weaker than the vdependence of Q found in the threedimensional case. This is probably the reason why the vdependence of Q has not been found in an angular correlation function analysis of the Abell catalogue. The vdependence found in this paper might be an important feature of clusters formed in the Gaussian gravitational instability theories. Therefore it would be important to search for the vdependence on Q in redshift samples of rich clusters.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 November 1995
 DOI:
 10.1093/mnras/277.2.630
 arXiv:
 arXiv:astroph/9506134
 Bibcode:
 1995MNRAS.277..630J
 Keywords:

 Astrophysics
 EPrint:
 11 pages, uuencoded compressed tar psfile. 2 tables and 8 figures included. The ps file (without uuencoding compressing) can also be obtained by anonymous ftp at ftp://ibm3.mpagarching.mpg.de/pub/jing/9506134.ps