Scaling of voids in the large scale distribution of matter
Abstract
Description
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 stochastic geometry, in particular, Delaunay and Voronoi 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 shows a scaling range with the right slope plus a transition to homogeneity.
Contribution to "The Many Scales of the Universe - JENAM 2004, Astrophysics Reviews", eds. del Toro et al, proceedings of the conference held in Granada, kapproc style, 10 pages, 7 EPS figures
Contribution to "The Many Scales of the Universe - JENAM 2004, Astrophysics Reviews", eds. del Toro et al, proceedings of the conference held in Granada, kapproc style, 10 pages, 7 EPS figures