arXiv subjects

Francesco Sylos Labini

Publications and source records attributed to Francesco Sylos Labini.

87 records · Page 5Linked to original sources

arXiv2000

Scaling and fluctuations in galaxy distribution: two tests to probe large scale structures

We present a brief introduction to the statistical properties of systems with large fluctuations. We point out that for such systems the relevant statistical quantities are scaling exponents and the nature of fluctuations is completely different from the one belonging to system with small fluctuations. We then propose two test to be performed on galaxy counts data as a function of apparent magnitude, which may clarify in a direct way the nature of the large scale galaxy clustering

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arXiv2000

Persistent fluctuations and scaling properties in galaxy number counts

Counts of galaxies as a function of apparent magnitude are among the most time-honored observations in cosmology. In this Letter, we focus on some statistical properties of these counts which are fundamental in order to characterize the large scale correlations in the galaxy spatial distribution. There are, in fact, no longer doubts since two decades of the existence of very large scale structures. The still remaining problem concerns the correct characterization of their statistical properties. We propose to study two properties of galaxy counts data, in order to discriminate between a small scale (~ 5 - 20 Mpc/h) homogeneous distribution, and a fractal structure on large scales (~ 20 - 300 Mpc/h). Firstly, the average slope of the counts which can be associated to an eventual fractal dimension in real space by simple arguments. Secondly, we propose to study fluctuations of counts around the average behavior as a function of apparent magnitude in the whole magnitude range B_j > 11. These fluctuations can discriminate between a genuine fractal distribution and a homogeneous one. In fact, they are related to the very statistical properties of the spatial distribution, independently on cosmological corrections. More specifically, in a fractal distribution one expects to find persistent scale-invariant fluctuations around the average behavior, which do not decay with apparent magnitude. On the other hand, in an homogeneous distribution, on large enough scales, the relative variance of the counts should decrease exponentially with apparent magnitude. Smooth cosmological corrections cannot change such a behavior.

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arXiv2000

Fractal structures and the large scale distribution of galaxies

Galaxy structures are certainly fractal up to a certain crossover scale λ_0. A clear determination of such a scale is still missing. Usually, the conceptual and practical implications of this property are neglected and the structures are only discussed in terms of their global amplitude. Here we present a compact summary of these implications. First, we discuss the problem of the identification of the crossover scale λ_0 and the proper characterization of the scaling. We then consider the implications of these properties with respect to various physical phenomena and to the corresponding characteristic values, i.e. r_0, σ_8, Ω, etc. These implications crucially depend on the value of λ_0, but they are still important for a relatively small value, say λ_0 \approx 50 \hmp. Finally we consider the main theoretical consequences of these results.

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arXiv2000

Biasing in Gaussian random fields and galaxy correlations

In this letter we show that in a Gaussian random field the correlation length, the typical size of correlated structures, does not change with biasing. We interpret the amplification of the correlation functions of subsets identified by different thresholds being due to the increasing sparseness of peaks over threshold. This clarifies an long-standing misconception in the literature. We also argue that this effect does not explain the observed increase of the amplitude of the correlation function xi(r) when galaxies of brighter luminosity or galaxy clusters of increasing richness are considered.

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arXiv1999

Reconstructing the cosmological puzzle

In the debate about galaxy correlation there are different questions which can be addressed separately: Which are the statistical methods able to properly detect scale invariance and describe, in general, the properties of irregular and regular distributions? Which are the implications for cosmology of the fractal behavior of galactic structures, up to a certain scale lambda_0? Which is the homogeneity scale lambda_0, i.e. the scale beyond which galaxy distribution has an eventual crossover to homogeneity? These are three different, but related, problems, which must be considered in different steps, from the point of view of data analysis as well as from the theoretical perspective.

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arXiv1998

A Fractal Galaxy Distribution in a Homogeneous Universe?

In this letter we present an idea which reconciles a homogeneous and isotropic Friedmann universe with a fractal distribution of galaxies. We use two observational facts: The flat rotation curves of galaxies and the (still debated) fractal distribution of galaxies with fractal dimension D=2. Our idea can also be interpreted as a redefinition of the notion of bias.

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arXiv1998

On the fractal structure of the universe: methods, results and theoretical implication

The fact that galaxy distribution exhibits fractal properties is well established since twenty years. Nowadays, the controversy concerns the range of the fractal regime, the value of the fractal dimension and the eventual presence of a cross-over to homogeneity. Fractal properties maybe studied with methods which do not assume homogeneity a priori as the standard statistical methods do. We show that complementary to the adoption of new methods of analysis there are important theoretical implications for the usual scenario of galaxy formation. For example, we focus on the concept of bias and we show that it needs a basic revision even if future redshift surveys will be able to identify an eventual tendency to homogenization.

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arXiv1998

Scale invariance in galaxy structures: general concepts and application to the most recent data

The debate on the correlation properties of galaxy structures has having an increasing interest during the last year. In this lecture we discuss the claims of different authors who have criticized our approach and results. In order to have a clear cut of the situation, we focus mainly on galaxy distribution in the intermediate range of distances ~ 100 - 200 Mpc/h. In particular we discuss: (i) the validity of the actual data and the concept of "fair sample", (ii) the shift of r_0 with sample depth and luminosity bias, (iii) the value of the fractal dimension, (iv) the problem of the counts from a single point and the case of ESP, (iv) uniformity of angular catalogs. The detection of fractal behavior up to ~ 100 - 200 Mpc/h is enough to rise serious problems to the usual statistical methods used for the characterization of galaxy correlations, standard interpretation of galaxy distribution and theoretical models develoed. The clarification of the intermediate scale behavior is very instructive for the subsequent interpretation of the very large scale galaxy distribution.

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arXiv1998

Fractals and the galaxy distribution

There is a general agreement that galaxy structures exhibit fractal properties, at least up to some small scale. However the presence of an eventual crossover towards homogenization, as well as the exact value of the fractal dimension, are still a matter of debate. I summarize the main points of the this discussion, considering also some galaxy surveys which have recently appeared. Further I discuss the implications for the standard picture of the observed fractal behaviour in galaxy distribution. In particular I consider the co-existence of fractal structures and the linear Hubble-law within the same scales. This fact represents a challenge for the standard cosmology where the linear Hubble law is a strict consequence of homogeneity of the expanding universe. Finally I consider the comparison of CDM-like models with the data noting that the simulations are not able to reproduce the observed properties of galaxy correlations.

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arXiv1998

On the fractal structure of galaxy distribution and its implications for cosmology

Two fundamental empirical laws have been established in the analysis of galaxy space distribution. First, recent analyses have revealed that the three dimensional distribution of galaxies and clusters is characterized by large scale structures and huge voids: such a distribution shows fractal correlations up to the limits of the available samples. This has confirmed the earlier de Vaucouleurs power-law density - distance relation, now corresponding to a fractal structure with dimension $D \approx 2$, at least, in the range of scales $ \sim 1 ÷200 Mpc$ ($H_0 = 55 km/sec/Mpc$). An eventual cut-off towards homogenization has not been yet identified. Second, since Hubble's discovery, the linear redshift-distance law has been well established within $200 Mpc$ and also much deeper. The co-existence of these laws within the same scales is a challenge for the standard cosmology where the linear Hubble law is a strict consequence of homogeneity of the expanding universe. This puzzle is now sufficiently strong to raise doubts for the standard cosmology.

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arXiv1997

Angular Projections of Fractal Sets

We discuss various questions which arise when one considers the central projection of three dimensional fractal sets (galaxy catalogs) onto the celestial globe. The issues are related to how fractal such projections look. First we show that the lacunarity in the projection can be arbitrarily small. Further characteristics of the projected set---in particular scaling---depend sensitively on how the apparent sizes of galaxies are taken into account. Finally, we discuss the influence of opacity of galaxies. Combining these ideas, seemingly contradictory statements about lacunarity and apparent projections can be reconciled.

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arXiv1996

Multifractality as a Link Between Luminosity and Space Distribution of Visible Matter

We discuss how luminosity and space distribution of galaxies are naturally linked in view of their multifractal properties. In particular we show that the mass (luminosity) function corresponding to a multifractal distribution in a given observed volume, consists of a power law followed by an exponential cut-off. This implies that the amplitude $ϕ^*$ of the Schechter function scales with the sample depth, as confirmed by various observational data. This effect is analogous to the scaling of the space density due to the fractal nature of the space distribution. This has the important consequence that the luminosity function can be properly defined only in a volume limited sample. Also the so-called "luminosity segregation" and the concept of bias correspond to a natural consequence of multifractality. This implies however that they should be considered from a different perspective with respect to the usual one. Such a concept allows us to unify the space and luminosity distributions as being shaped by a single cause:multifractality which should therefore claim a central stage in theoretical investigations.

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arXiv1995

The power spectrum in a strongly inhomogeneous Universe

A crucial issue in cosmology is the determination of the fluctuation power spectrum.The standard picture of the matter clustering, the Cold Dark Matter model (and its variant), assumes that,on scales smaller than a certain ``flattening scale'' $λ_f$, the power spectrum increases with the scale, while on much larger scales it decreases so to match the tiny fluctuations observed in the microwave background. The standard picture also assumes that, once a statistically homogeneous sample is reached, the power spectrum amplitude is fixed, and any major variation should be attributed to luminosity segregation. However, the determination of $λ_f$ and of the absolute amplitude, if any, is still matter of debate. In particular, there is no consensus on whether the turnaround has been detected or not, and on the actual importance of the luminosity segregation effect. We show that, due to the finiteness of the sample the standard analysis of self-similar (fractal) distributions yields a turnaround for scales close to the survey scale, and a systematic amplitude shift with the survey scale. We point out that both features, bending and scaling, are in agreement with recent determination of the power spectrum, in particular with the CfA2 spectrum. We remark that the standard power spectrum is not a well defined statistical tool to characterize the galaxy distribution when a homogeneity scale has not been reached. In order to perform an analysis that does not imply any a priori assumption one should study the PS of the density, rather than the PS of the density contrast.

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arXiv1995

Isotropy, homogeneity and dipole saturation

A distribution of points that satisfies the property of local isotropy is not necessarily homogeneous: homogeneity is implied by the condition of local isotropy together with the assumption of analyticity or regularity. Here we show that the evidence of dipole saturation in galaxies (and clusters) catalogues, together with a monotone growth of the monopole, is an evidence of isotropy but not of homogeneity. This is fully compatible with a fractal structure which has the property of local isotropy, but it is non-analytic and non-homogeneous.

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arXiv1995

Multifractal properties of visible matter distribution: a stochastic model

Galaxies and clusters distributions show two major properties: (i) the positions of galaxies and clusters are characterized by a power law distribution indicating properties with respect to their positions. (ii) The distribution of masses is also characterized by a power law corresponding to self similarity of different nature. These two properties are naturally unified by the concept of multifractality. This concept naturally arises if the distribution of matter, as given by both positions and masses, has self similar properties. We discuss the experimental situation in this respect and we introduce a simple stochastic model based of the aggregation process of particles The aim of this model is to understand which characteristic properties of the aggregation probability can gives rise to multifractal distribution In particular we find that a crucial element in this respect is that the aggregation probability should depend on the environment of the aggregation region.

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