Applications of Minkowski Functionals to the Statistical Analysis of Dark Matter Models.pdf

Applications of Minkowski-Functionals to the Statistical Analysis of Dark Matter Models Michael Platz¨oder Max–Planck–Institut f¨ur Astrophysik 5 Postfach 1523, D-85740 Garching, F.R.G. 9 9 Thomas Buchert 1 p Theoretische Physik, Ludwig–Maximilians–Universit¨at e Theresienstr. 37, D-80333 M¨unchen, F.R.G. S 4 February 1, 2008 1 v 4 1 Abstract 0 9 A new method for the statistical analysis of 3-D point processes, based on the family of Minkowski- 0 Functionals , is explained and applied to modelled galaxy distributions generated by a toy-model 5 and cosmological simulations of the large-scale structure in the Universe. These measures are 9 / sensitive to both, geometrical and topological properties of spatial patterns and appear to be h very effective in discriminating different point processes. Moreover by the means of conditional p - subsampling, different building blocks of large-scale structures like sheets, filaments and clusters o can be detected and extracted from a given distribution. r t s a : 1 Introduction v i X r The still unsolved question of the origin and evolution of the Large-Scale Structure (LSS) of the a universe is a central topic in modern cosmology. The scientific approach to this problem is based on three columns: 1. The distribution of matter in the Universe is assumed to be traced by luminous galaxies. Thus, observation of