Voids are a prominent feature of the galaxy distribution but their quantitative study is hindered by the lack of a precise definition of what constitutes a void. Here we propose a definition of voids in point distributions that uses methods of discrete sto
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SCALING OF VOIDS IN THE LARGE SCALE DISTRIBUTION OF MATTER Jose Gaite ————–Instituto de Matematicas y Fisica Fundamental,CSIC,Serrano 123,28006Madrid,Spain.jgaite@imaff.cfmac.csic.es Abstract V oids are a prominent feature of the galaxy distribution but their quantitative study is hindered by the lack of a precise definition of what constitutes a void.Here we propose a definition of voids in point distributions that uses methods of discrete stochastic geometry,in particular,Delaunay and V oronoi tessellations,and we construct a new void-finder.We then apply the void-finder to scaling point distributions.First,we find the voids of pure fractals with a transition to homogeneity and show that the rank ordering of the voids also scales (Zipf’s law)and,in addition,shows the transition to homogeneity.However,a pure fractal is arguably not a good model of the galaxy distribution,so we construct from a cosmological N -body simulation a bifractal mock galaxy sample representing two galaxy populations,which we identify as “wall”and “field”galaxies.The wall galaxy distribution fits a pure fractal with a transition to homogeneity and,furthermore,the rank ordering of its voids show a scaling range with the right slope plus a transition to homogeneity.Introduction
The standard statistical analysis of the distribution of galaxies consists in the derivation of the correlation functions,chiefly,the two-point correlation function ξ.The large value of this correlation function (ξ≫1)on small scales is interpreted as the tendency of galaxies to cluster strongly.The reverse side of strong clustering is the appearance of void regions,with essentially no galaxies.V oids have an intrinsic appeal,since our sensory system is well suited to perceive patterns,so we immediately perceive void shapes while looking at a point set.The observation of voids in the distribution of galaxies has led to the compilation of void catalogues and to their statistical analysis (Einasto,Einasto &Gramann,1989;V ogeley,Geller &Huchra,1991;El-Ad,Piran &da Costa,1997,Mueller et al.,2000;Hoyle &V ogeley,2002).A precise definition of void is however a delicate matter,and it is a moot point to determine to what
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