A quantitative approach to the topology of large-scale structure

Details A quantitative approach to the topology of large-scale structure A quantitative approach to the topology of large-scale structure

Aug 1987

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1987apj...319....1g&link_type=abstract

Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 319, Aug. 1, 1987, p. 1-8.

Astronomy and Astrophysics

Astrophysics

92

Astronomical Models, Galactic Clusters, Galactic Structure, Normal Density Functions, Topology, Cosmology, Dark Matter, Galactic Evolution, Gravitational Effects, Mass Distribution, Red Shift

Scientific paper

A quantitative measure of the topology of large-scale structure: the genus of density contours in a smoothed density distribution, is described and applied. For random phase (Gaussian) density fields, the mean genus per unit volume exhibits a universal dependence on threshold density, with a normalizing factor that can be calculated from the power spectrum. If large-scale structure formed from the gravitational instability of small-amplitude density fluctuations, the topology observed today on suitable scales should follow the topology in the initial conditions. The technique is illustrated by applying it to simulations of galaxy clustering in a flat universe dominated by cold dark matter. The technique is also applied to a volume-limited sample of the CfA redshift survey and to a model in which galaxies reside on the surfaces of polyhedral 'bubbles'. The topology of the evolved mass distribution and 'biased' galaxy distribution in the cold dark matter models closely matches the topology of the density fluctuations in the initial conditions. The topology of the observational sample is consistent with the random phase, cold dark matter model.

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