Journal Article

Searching for the scale of homogeneity

Vicent J. Martínez, María-Jesús Pons-Bordería, Rana A. Moyeed and Matthew J. Graham

in Monthly Notices of the Royal Astronomical Society

Published on behalf of The Royal Astronomical Society

Volume 298, issue 4, pages 1212-1222
Published in print August 1998 | ISSN: 0035-8711
Published online August 1998 | e-ISSN: 1365-2966 | DOI: http://dx.doi.org/10.1111/j.1365-8711.1998.01730.x
Searching for the scale of homogeneity

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Abstract

We introduce a statistical quantity, known as the K function, related to the integral of the two-point correlation function. It gives us straightforward information about the scale where clustering dominates and the scale at which homogeneity is reached. We evaluate the correlation dimension, D2, as the local slope of the log-log plot of the K function. We apply this statistic to several stochastic point fields, to three numerical simulations describing the distribution of clusters and finally to real galaxy redshift surveys. Four different galaxy catalogues have been analysed using this technique: the Center for Astrophysics I, the Perseus-Pisces redshift surveys (these two lying in our local neighbourhood), the Stromlo-APM and the 1.2-Jy IRAS redshift surveys (these two encompassing a larger volume). In all cases, this cumulant quantity shows the fingerprint of the transition to homogeneity. The reliability of the estimates is clearly demonstrated by the results from controllable point sets, such as the segment Cox processes. In the cluster distribution models, as well as in the real galaxy catalogues, we never see long plateaus when plotting D2 as a function of the scale, leaving no hope for unbounded fractal distributions.

Keywords: methods: statistical; galaxies: clusters: general; large-scale structure of Universe

Journal Article.  0 words. 

Subjects: Astronomy and Astrophysics

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