PERCOLATION TECHNIQUE FOR GALAXY CLUSTERING

We study percolation in mass and galaxy distributions obtained in thre e-dimensional simulations of the CDM, C + HDM, and the power law (n = - 1) models in the OMEGA = 1 universe. Percolation statistics is used here as a quantitative measure of the degree to which a mass or galaxy distribution is of a filamentary or cellular type. We have developed a very fast code (based on the 1985 algorithm described by Stauffer) w hich calculates the statistics of clusters along with the direct detec tion of percolation. We found that two parameters-mu(infinity). (eq.  3!), characterizing the size of the largest cluster, and mu2 (eq. 4!) , characterizing the weighted mean size of all clusters excluding the largest one-are extremely useful for evaluating the percolation thresh old. An advantage of using these parameters is their low sensitivity t o boundary effects. We show that both the CDM and the C + HDM models a re extremely filamentary both in mass and galaxy distribution. The per colation thresholds for the mass distributions are p(c) = 0.023 +/- 0. 005 in the C + HDM and p(c) = 0.044 +/- 0.005 in CDM models compared t o p(c) = 0.16 for a Gaussian random field. For galaxy samples with a f ew thousand galaxies the thresholds are P(c,C+HDM) = 0.06 +/- 0.02 and P(c,CDM) = 0.10 +/- 0.02 compared to p(c) = 0.31 for a Poisson distri bution. Percolation in regions having the shape of a parallelepiped is discussed in the context of the applications of percolation statistic s to real galaxy catalogs.