The topology of large-scale structure. I - Topology and the random phase hypothesis

Details The topology of large-scale structure. I - Topology and the random phase hypothesis The topology of large-scale structure. I - Topology and the random phase hypothesis

Oct 1987

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1987apj...321....2w&link_type=abstract

Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 321, Oct. 1, 1987, p. 2-27. Research supported by the University of Kansas.

Astronomy and Astrophysics

Astrophysics

76

Astronomical Models, Galactic Clusters, Galactic Evolution, Galactic Structure, Topology, Cosmology, Dark Matter, Density Distribution, Gravitational Fields, Neutrinos, Three Dimensional Models, White Noise

Scientific paper

Many models for the formation of galaxies and large-scale structure assume a spectrum of random phase (Gaussian), small-amplitude density fluctuations as initial conditions. In such scenarios, the topology of the galaxy distribution on large scales relates directly to the topology of the initial density fluctuations. Here a quantitative measure of topology - the genus of contours in a smoothed density distribution - is described and applied to numerical simulations of galaxy clustering, to a variety of three-dimensional toy models, and to a volume-limited sample of the CfA redshift survey. For random phase distributions the genus of density contours exhibits a universal dependence on threshold density. The clustering simulations show that a smoothing length of 2-3 times the mass correlation length is sufficient to recover the topology of the initial fluctuations from the evolved galaxy distribution. Cold dark matter and white noise models retain a random phase topology at shorter smoothing lengths, but massive neutrino models develop a cellular topology.

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