Astronomy and Astrophysics – Astrophysics
Scientific paper
1997-04-14
Astronomy and Astrophysics
Astrophysics
MNRAS LaTex style, 12 pages, 7 PostScript figures embedded, accepted by MNRAS
Scientific paper
We investigate properties of the correlation function of clusters of galaxies using geometrical models. On small scales the correlation function depends on the shape and the size of superclusters. On large scales it describes the geometry of the distribution of superclusters. If superclusters are distributed randomly then the correlation function on large scales is featureless. If superclusters and voids have a tendency to form a regular lattice then the correlation function on large scales has quasi-regularly spaced maxima and minima of decaying amplitude; i.e., it is oscillating. The period of oscillations is equal to the step size of the grid of the lattice. We calculate the power spectrum for our models and compare the geometrical information of the correlation function with other statistics. We find that geometric properties (the regularity of the distribution of clusters on large scales) are better quantified by the correlation function. We also analyse errors in the correlation function and the power spectrum by generating random realizations of models and finding the scatter of these realizations.
Einasto Jaan
Einasto Maret
Frisch Pierre
Gottlöber Stefan
Müller Volker
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