arXiv subjects

F. Sylos Labini

Publications and source records attributed to F. Sylos Labini.

40 records · Page 3Linked to original sources

arXiv1995

Power spectrum for fractal distributions

We study the behaviour of the power spectrum (PS) in the case of fractal structures. We show that in this case the main observational features of the PS, the large scale flattening and the scaling of the amplitude with sample depth, are related to finite size effects, due to the fractal nature of galaxy distribution in the sample. Comparing with the recent results of the PS for the CfA2 we conclude that this catalog is consistent with the fractal description.

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arXiv1995

Spatial and Luminosity Properties of the Perseus-Pisces Redshift Survey

We analyze the spatial and the luminosity properties of the Perseus-Pisces redshift survey. We find that the two point correlation function (CF) $Γ(r)$ is a power law up to the sample effective depth ($\sim 30 h^{-1}Mpc$), showing the fractal nature of the galaxy distribution in this catalog. The fractal dimension turns out to be $D \approx 2$. We also consider the CF $ξ(r)$ and in particular the behavior of the "{\it correlation length}" $r_0$ ($ξ(r_{0})\equiv 1$) as function of the sample size. In this respect we find, unambiguously, that the luminosity segregation effect is not supported by any experimental evidence. In addition we have studied the galaxian number-density ($n(r)$) and number-counts ($N(m)$) in the VL subsamples finding a good agreement with the properties of a fractal distribution. In particular our conclusion is that the $n(r)$ relation allows to extend the analysis of the fractal nature up to a deeper depth than that reached by the CF analysis, and, we find evidence for fractal properties up to the limiting depth of $120-140 h^{-1} Mpc$. We stress that the $N(m)$ relation must be studied in VL subsamples rather than in magnitude limited ones as usually done. Finally we have considered the correlations between galaxy positions and luminosities by means of the multifractal analysis. We find clear evidence for self-similar behavior of the whole luminosity-space distribution. These results confirm and extend those of Coleman \& Pietronero (1992).

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arXiv1995

Stochastic aggregation model for the multifractal distribution of matter

Two main features of the observable distribution of visible matter are the space correlations of galaxy positions and the mass function of galaxies. As discussed in Pietronero and Sylos Labini on this issue ([1], see also [2],[3]), the concept of multifractal (MF) distribution (including the masses) naturally unifies these two properties. Hence with the knowledge of the whole MF spectrum one obtains information on the correlations in space as well as on the mass function. From a theoretical point of view one would like to identify the dynamical process that leads to such a MF distribution. In order to gain some insight into this complex problem we have developed a simple stochastic model that includes some of the basic properties of aggregation process and allows us to pose a variety of interesting question concerning the possible dynamical origin of the MF distribution. The dynamics is characterised by some parameters, that have a direct physical meaning in term of cosmological processes. In this way we can relate the input parameters of the dynamics to the properties of the final configuration and produce a sort of phase diagram.

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arXiv1995

Cosmological Principle and the debate about Large Scale Structures distribution

The basic hypothesis of a post-Copernican Cosmological theory is that {\em all the points} of the Universe have to be essentially equivalent: this hypothesis is required in order to avoid any privileged {\em observer}. This assumption has been implemented by Einstein in the so-called Cosmological Principles (CP): {\em all the positions} in the Universe have to be essentially equivalent, so that the Universe is homogeneous. This situation implies also the condition of spherical symmetry about every point, so that the Universe in also Isotropic. There is a hidden assumption in the formulation of the CP in regard to the hypothesis that all the points are equivalent In fact, the condition that all the occupied points are statistically equivalent with respect to their environment correspond to the property of of Local Isotropy. It is generally believed that the Universe cannot be isotropic about every point without being also homogeneous [1]. Actually Local Isotropy does not necessarily implies homogeneity; in fact a topology theorem states that homogeneity is implied by the condition of local isotropy together with {\em the assumption of the analyticity or regularity} for the distribution of matter. Up to the seventies analyticity was an obvious implicit assumption in any physical problem. Recently however we have learned about intrinsically irregular structures for which analyticity should be considered as a property to be tested with appropriate analysis of experiment.

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