Breaking the self-averaging properties of spatial galaxy fluctuations in the Sloan Digital Sky Survey - Data Release Six

Statistical analyses of finite sample distributions usually assume that fluctuations are self-averaging, i.e. that they are statistically similar in different regions of the given sample volume. By using the scale-length method, we test whether this assumption is satisfied in several samples of the Sloan Digital Sky Survey Data Release Six. We find that the probability density function (PDF) of conditional fluctuations, filtered on large enough spatial scales (i.e., r>30 Mpc/h), shows relevant systematic variations in different sub-volumes of the survey. Instead for scales r<30 Mpc/h the PDF is statistically stable, and its first moment presents scaling behavior with a negative exponent around one. Thus while up to 30 Mpc/h galaxy structures have well-defined power-law correlations, on larger scales it is not possible to consider whole sample average quantities as meaningful and useful statistical descriptors. This situation is due to the fact that galaxy structures correspond to density fluctuations which are too large in amplitude and too extended in space to be self-averaging on such large scales inside the sample volumes: galaxy distribution is inhomogeneous up to the largest scales, i.e. r ~ 100 Mpc/h, probed by the SDSS samples. We show that cosmological corrections, as K-corrections and standard evolutionary corrections, do not qualitatively change the relevant behaviors. Finally we show that the large amplitude galaxy fluctuations observed in the SDSS samples are at odds with the predictions of the standard LCDM model of structure formation.(Abridged version).Comment: 32 pages, 28 figures, accepted for publication in Astronomy and Astrophysics. A higher resolution version is available at http://pil.phys.uniroma1.it/~sylos/fsl_highlights.html . Version v2 has been corrected to match the published on

Scale-invariance of galaxy clustering

Some years ago we proposed a new approach to the analysis of galaxy and cluster correlations based on the concepts and methods of modern statistical Physics. This led to the surprising result that galaxy correlations are fractal and not homogeneous up to the limits of the available catalogs. The usual statistical methods, which are based on the assumption of homogeneity, are therefore inconsistent for all the length scales probed so far, and a new, more general, conceptual framework is necessary to identifythe real physical properties of these structures. In the last few years the 3-d catalogs have been significatively improved and we have extended our methods to the analysis of number counts and angular catalogs. This has led to a complete analysis of all the available data that we present in this review. The result is that galaxy structures are highly irregular and self-similar: all the available data are consistent with each other and show fractal correlations (with dimension $D \simeq 2$) up to the deepest scales probed so far (1000 \hmp) and even more as indicated from the new interpretation of the number counts. The evidence for scale-invariance of galaxy clustering is very strong up to 150 \hmp due to the statistical robustness of the data but becomes progressively weaker (statistically) at larger distances due to the limited data. In 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.Comment: Latex file 165 pages, 106 postscript figures. This paper is also available at http://www.phys.uniroma1.it/DOCS/PIL/pil.html To appear in Physics Report (Dec. 1997