The three-point correlation function for Abell clusters - Observations and simulations

Abstract

We have done a three-dimensional study of the three-point correlation function of Abell clusters and compared this with Park's 1990 biased cold dark matter (CDM) simulations, fitting the results with formulae of the form ζ(r_12_,r_13_,r_23_) = Q_11_[ζ(r_12_)ζ(r_13_) +ζ(r_12_)ζ(r_23_)+ζ(r_13_)ζ(r_23_)] + Q_111_[ζ(r_12_)ζ(r_13_)ζ(r_23)]. For the observations the maximum likelihood fits are Q_11_= 0.85 and Q_111_ = 0.0 in excellent agreement with the result of Toth, Hollosi, and Szalay's 1989 two- dimensional study. For Park's simulation we find maximum likelihood fits of Q_11_ = 0.9 and Q_111_ = 0.0 in excellent agreement with the observational result. Thus the standard biased CDM gravitational instability model reproduces the observed form of the three-point correlation function for Abell clusters remarkably well.