The statistics of maxima in primordial density perturbations

Statistics – Computation

Scientific paper

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Computational Astrophysics, Galactic Evolution, Gravitational Effects, Maxima, Normal Density Functions, Autocorrelation, Histograms, Mass Distribution

Scientific paper

The authors have investigated the hypothesis that protogalaxies/protoclusters form at the sites of maxima in a primoridal field of normally distributed density perturbations. Using a mixture of analytic and numerical techniques, they have studied the properties of the maxima, with the following results: (1) Maxima are surprisingly overdense, with a fairly narrow distribution of overdensities. (2) The shapes of the maxima depend on their heights. For asymptotically high maxima, all principal axes become equal. The typical maximum, however, is more nearly prolate with axial ratios 1:0.70:0.55, again quasi-independent of spectrum. (3) The clustering properties of maxima can differ from those of the density field as a whole. These results provide a natural mechanism for biased galaxy formation in which galaxies do not necessarily follow the large-scale density. Methods for obtaining the true autocorrelation function of the density field and implications for microwave background studies are discussed.

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