Finite size effects on the galaxy number counts: evidence for fractal behavior up to the deepest scale

Abstract

We introduce and study two new concepts which are essential for the quantitative analysis of the statistical quality of the available galaxy samples. These are the dilution effect and the small scale fluctuations. We show that the various data that are considered as pointing to a homogenous distribution are all affected by these spurious effects and their interpretation should be completely changed. In particular, we show that finite size effects strongly affect the determination of the galaxy number counts, namely the number versus magnitude relation ($N(<m)$) as computed from the origin. When one computes $N(<m)$ averaged over all the points of a redshift survey one observes an exponent $\alpha =D/5\approx 0.4$ compatible with the fractal dimension $D\approx 2$ derived from the full correlation analysis. Instead the observation of an exponent $\alpha \approx 0.6$ at relatively small scales, where the distribution is certainly not homogeneous, is shown to be related to finite size effects. We conclude therefore that the observed counts correspond to a fractal distribution with dimension $D\approx 2$ in the entire range $12 \ltapprox m \ltapprox 28$, that is to say the largest scales ever probed for luminous matter. In addition our results permit to clarify various problems of the angular catalogs, and to show their compatibility with the fractal behavior. We consider also the distribution of Radio-galaxies, Quasars and $\gamma$ ray burst, and we show their compatibility with a fractal structure with $D\approx 1.6÷1.8$. Finally we have established a quantitative criterion that allows us to define and {\em predict} the statistical validity of a galaxy catalog (angular or three dimensional).

42 Latex pages. Figures and macro are avaialable under request at [email protected]

References in corpus (3)

• A Possible Local Counterpart to the Excess Population of Faint Blue Galaxies
• FACTS AND IDEAS IN MODERN COSMOLOGY
• Do Gamma-Ray Burst Sources Repeat?

Cited by in corpus (14)

• Scale-invariance of galaxy clustering
• Cosmic clocks, cosmic variance and cosmic averages
• The fractal structure of the universe : a new field theory approach
• Energy Landscape of the Finite-Size Mean-field 3-Spin Spherical Model
• The power spectrum in a strongly inhomogeneous Universe
• Clustering of loose groups and galaxies from the Perseus--Pisces Survey
• Fractal Structures Driven by Self-Gravity: Molecular clouds and the Universe
• Boundary Corrections in Fractal Analysis of Galaxy Surveys
• Millennium Simulation Dark Matter Haloes: Multi-fractal and Lacunarity Analysis with Homogeneity Transition
• Are galaxy distributions scale invariant? A perspective from dynamical systems theory
• Spatial and Luminosity Properties of the Perseus-Pisces Redshift Survey
• Kinetic properties of fractal media
• Angular correlations of galaxy distribution
• An inhomogeneous universe with thick shells and without cosmological constant