Fractals vs. halos: Asymptotic scaling without fractal propertiesM. Bottaccio1, 2, M. Montuori1, 2 and L. Pietronero1, 3, 2
1 Centro per la Meccanica Statistica e la Complessità, Dipartimento di Fisica Università "La Sapienza" - P.le A. Moro, 2, 00185 Roma, Italy
2 Centro Studi e Ricerche e Museo della Fisica "E. Fermi" Compendio Viminale, Roma, Italy
3 CNR Istituto di Acustica "O. M. Corbino" V. del Fosso del Cavaliere 100, 00133 Roma, Italy
(Received 2 July 2003; accepted in final form 23 March 2004)
Precise analyses of the statistical and scaling properties of galaxy distribution are essential to elucidate the large-scale structure of the universe. Given the ongoing debate on its statistical features, the development of statistical tools permitting to discriminate accurately different spatial patterns is highly desiderable. This is specially the case when non-fractal distributions have power law two-point correlation functions, which are usually signatures of fractal properties. Here we review some possible methods used in the literature and introduce a new variable called "scaling gradient". This tool and the conditional variance are shown to be effective in providing an unambiguous way for such a distinction. Their application is expected to be of outmost importance in the analysis of upcoming galaxy catalogues.
98.65.-r - Galaxy groups, clusters, and superclusters; large scale structure of the Universe.
02.50.-r - Probability theory, stochastic processes, and statistics.
05.45.Df - Fractals.
© EDP Sciences 2004