FINITE-SIZE EFFECTS ON THE GALAXY NUMBER COUNTS - EVIDENCE FOR FRACTAL BEHAVIOR UP TO THE DEEPEST SCALE

We introduce and study two new concepts which are essential for the qu antitative analysis of the statistical quality of the available galaxy samples. These are the dilution effect and the small scale fluctuatio ns. We show that the various data that are considered as pointing to a homogenous distribution are all affected by these spurious effects an d their interpretation should be completely changed. In particular, we show that finite size effects strongly affect the determination of th e galaxy number counts, namely the number versus magnitude relation (N (< m)) as computed from the origin. When one computes N(<m) averaged o ver all the points of a redshift survey, one observes an exponent alph a = D/5 approximate to 0.4 compatible with the fractal dimension D app roximate to 2 derived from the full correlation analysis. Instead the observation of an exponent alpha approximate to 0.6 at relatively smal l scales, where the distribution is certainly not homogeneous, is show n to be related to finite size effects. We conclude therefore that the observed counts correspond to a fractal distribution with dimension D approximate to 2 in the entire range 12 less than or similar to m les s than or similar to 28, that is to say the largest scales ever probed for luminous matter. In addition our results permit to clarify variou s problems of the angular catalogs, and to show their compatibility wi th the fractal behaviour. We consider also the distribution of Radio-g alaxies, Quasars and gamma-ray bursts, and we show their compatibility with a fractal structure with D approximate to 1.6-1.8. Finally we ha ve established a quantitative criterion that allows us to define and p redict the statistical validity of a galaxy catalog (angular or three- dimensional).