K-minus Estimator Approach to Large Scale Structure

Abstract

Self similar 3D distributions of point-particles, with a given quasifractal dimension D, were generated on a Menger sponge model and then compared with \textit{2dfGRS} and \textit{Virgo project} data \footnote{http://www.mso.anu.edu.au/2dFGRS/, http://www.mpa-garching.mpg.de/Virgo/}. Using the principle of local knowledge, it is argued that in a finite volume of space only the two-point minus estimator is acceptable in the correlation analysis of self similar spatial distributions. In this sense, we have simplified the Pietronero-Labini correlative analysis by defining a K-minus estimator, which when applied to 2dfGRS data revealed the quasifractal dimension $D\approx 2$ as expected. In our approach the K-minus estimator is used only locally. Dimensions between D = 1 and D = 1.7, as suggested by the standard $\xi (r)$ analysis, were found to be fallacy of the method. In order to visualize spatial quasifractal objects, we created a small software program called \textit{RoPo} (''Rotate Points''). This program illustrates and manifests local correlative analysis in which the visual inspection emerged as a first step and a key part of the method. Finally, we discuss importance and perspective of the visual inspection on available real and simulated distributions. It is also argued that results of contemporary cosmological simulations do not faithfully represent real data, as they show a formation of ever increasing collapsars. We consent that 2dfGRS data are reminiscent of some kind of underlying turbulence like effects in action.