Introduction to Correlation Properties of Galaxy Distribution
Statistical analysis of spatial galaxy distribution is usually performed through the two point function ξ(r). This analysis allows one to determine a correlation length r 0 (ξ(r 0) = 1), which separates a correlated regime (r < r 0) from an uncorrelated one (r > r 0). Some years ago we criticized this approach and proposed a new one based on the concepts and methods of modern Statistical Physics. Here we present an introduction to these methods and report the results of the analysis to all the available three dimensional catalogues of galaxies and clusters, ie CfA, Perseus-Pisces, SSRS, IRAS, Stromlo-APM, LEDA, Las Campanas and ESP for galaxies and Abell and ACO for clusters. All the data analyzed are consistent with each other and show fractal correlations (with dimension D ≃ 2) up to the deepest scales probed until now (1000h –1Mpc) and even more as indicated from the new interpretation of the number counts. The very first consequence of this result is that the usual statistical methods (as for example ξ(r)), based on the assumption of homogeneity, are therefore inconsistent for all the length scales probed until now. In the range of self-similarity theories should shift from “amplitudes” to “exponents”. These facts lead to fascinating conceptual implications about our knowledge of the universe and to a new scenario for the theoretical challenge in this field.
KeywordsFractal Dimension Correlation Length Correlation Property Conditional Density Luminosity Function
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