Percolation Technique for Galaxy Clustering
Abstract
We study percolation in mass and galaxy distributions obtained in threedimensional 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) which calculates the statistics of clusters along with the direct detection of percolation. We found that two parameters μ_infinity_ (eq. [3]), characterizing the size of the largest cluster, and μ^2^ (eq. [4]), characterizing the weighted mean size of all clusters excluding the largest oneare extremely useful for evaluating the percolation threshold. An advantage of using these parameters is their low sensitivity to boundary effects. We show that both the CDM and the C + HDM models are extremely filamentary both in mass and galaxy distribution. The percolation 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 to P_c_ = 0.16 for a Gaussian random field. For galaxy samples with a few 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 distribution. Percolation in regions having the shape of a parallelepiped is discussed in the context of the applications of percolation statistics to real galaxy catalogs.
 Publication:

The Astrophysical Journal
 Pub Date:
 August 1993
 DOI:
 10.1086/172975
 Bibcode:
 1993ApJ...413...48K
 Keywords:

 Dark Matter;
 Galactic Clusters;
 Galactic Structure;
 Mass Distribution;
 Percolation;
 Three Dimensional Models;
 Astrophysics;
 GALAXIES: CLUSTERING;
 COSMOLOGY: LARGESCALE STRUCTURE OF UNIVERSE;
 METHODS: NUMERICAL;
 COSMOLOGY: THEORY;
 COSMOLOGY: DARK MATTER