Cold uniform spherical collapse revisited

We report results of a study of the Newtonian dynamics of N self-gravitating particles which start in a quasi-uniform spherical configuration, without initial velocities. These initial conditions would lead to a density singularity at the origin at a finite time when N \rightarrow \infty, but this singularity is regulated at any finite N (by the associated density fluctuations). While previous studies have focussed on the behaviour as a function of N of the minimal size reached during the contracting phase, we examine in particular the size and energy of the virialized halo which results. We find the unexpected result that the structure decreases in size as N increases, scaling in proportion to N^{-1/3}, a behaviour which is associated with an ejection of kinetic energy during violent relaxation which grows in proportion to N^{1/3}. This latter scaling may be qualitatively understood, and if it represents the asymptotic behaviour in N implies that this ejected energy is unbounded above. We discuss also tests we have performed which indicate that this ejection is a mean-field phenomenon (i.e. a result of collisionless dynamics).Comment: 10 pages, 9 figures; proceedings of "Invisible Universe" conference, Paris, July 200

Fractal correlations in the CfA2-South redshift survey

We report our analysis of the properties of galaxy clustering for a new redshift sample of galaxies, the CfA2-South catalog, using statistical methods which do not rely on the assumption of homogeneity. We find that, up to ~ 20 Mpc/h, which is the largest scale to which correlation properties can be reliably inferred, the galaxy clustering is scale-invariant and characterized by a fractal dimension D=1.9 \pm 0.1. Further there is no statistical evidence for homogeneity at any of the larger scales (up to ~150 Mpc/h) probed more weakly by the catalog. These results means that characteristic ``correlation lengths'' for the clustering of galaxies derived using standards methods of analysis are not meaningful. Further the results are very consistent with those obtained from many other catalogs using the methods adopted here, which show the D =2 fractal continuing to beyond 100 Mpc/h. The incompleteness of the relevant data conjectured by various authors to give rise to such behaviour is therefore proved to have no significant effect (up to 20 Mpc/h) on the measured correlations.Comment: 18 pages, latex, 1 postscript figure, also available at http://www.phys.uniroma1.it/DOCS/PIL/pil.html Accepted for publication in Astrophysical Journal Letter

Scaling in cosmic structures

The study of the properties of cosmic structures in the universe is one of the most fascinating subject of the modern cosmology research. Far from being predicted, the large scale structure of the matter distribution is a very recent discovery, which continuosly exhibits new features and issues. We have faced such topic along two directions; from one side we have studied the correlation properties of the cosmic structures, that we have found substantially different from the commonly accepted ones. From the other side, we have studied the statistical properties of the very simplified system, in the attempt to capture the essential ingredients of the formation of the observed structures.Comment: 10 pages, 3 figures. Accepted for pubblication in Fractals