1997/11/17 by Ue-Li Pen, Ue‐Li Pen · 6 citations
Mathematics · Physics and Astronomy · #Astronomy and Astrophysical Research #Astrophysics #Dark matter #Galaxies: Formation, Evolution, Phenomena #Galaxy #Kurtosis #Mathematics #Matter power spectrum #Nonlinear system #Physics #Quantum mechanics #Redshift #Skewness #Spectral density #Statistical physics #Statistics #Stellar, planetary, and galactic studies #astro-ph
paper · pdf · doi:10.1086/306098
15 pages incl 2 figures, submitted to ApJ
arxiv created 1997/11/17 · openalex publication_date 1998/09/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We propose a strategy to measure the dark matter power spectrum using minimal assumptions about the galaxy distribution and the galaxy-dark matter cross-correlations. We argue that on large scales the central limit theorem generically assures Gaussianity of each smoothed density field, but not coherence. Asymptotically, the only surviving parameters on a given scale are galaxy variance σ, bias b = Ω 0.6 /β, and the galaxy-dark matter cross-correlation coefficient r . These can all be determined by measuring the quadrupole and hexadecapole velocity distortions in the power spectrum. Measuring them simultaneously may restore consistency between all β-determinations independent of galaxy type. The leading deviations from Gaussianity are conveniently parameterized by an Edgeworth expansion. In the mildly nonlinear regime, two additional parameters describe the full picture: the skewness parameter s and nonlinear bias b 2 . They can both be determined from the measured skewness combined with second-order perturbation theory or from an N -body simulation. By measuring the redshift distortion of the skewness, one can measure the density parameter Ω with minimal assumptions about the galaxy formation process. This formalism also provides a convenient parameterization to quantify statistical galaxy formation properties.