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Modeling the power spectrum of density fluctuations: A phenomenological approach
Branchini, Enzo; Guzzo, Luigi; Valdarnini, Riccardo
AA(SISSA - International School of Advanced Studies, Trieste, Italy), AB(SISSA - International School of Advanced Studies, Trieste, Italy), AC(SISSA - International School of Advanced Studies, Trieste, Italy)
Astrophysical Journal, Part 2 - Letters (ISSN 0004-637X), vol. 424, no. 1, p. L5-L8 (ApJL Homepage)
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NASA/STI Keywords:
Background Radiation, Big Bang Cosmology, Dark Matter, Fourier Transformation, Large Space Structures, Power Spectra, Radio Galaxies, Cosmic Background Explorer Satellite, Gravitational Waves, Infrared Astronomy Satellite, Infrared Astronomy Satellite, Nonlinear Evolution Equations, Red Shift, Space Density, Wavelengths
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We show how, based on considerations of the observed form of the galaxy two-point spatial correlation function xi(r), a very simplified -- yet surprisingly effective -- model for the linear density fluctuations power spectrum can be constructed. We first relate the observed large-scale shape of xi(r) to a power-law form for the power spectrum, P(k) proportional to k-2.2. For a plausible value of the bias parameter b = 1/sigma8 approximately equals 1.8, one has (delta rho/sigma)rms approximately 1 at r approximately equals 3.5 h-1 Mpc, suggesting that the change of slope observed in xi(r) around this scale marks the transition between the linear and nonlinear gravitational regimes. Under this working hypothesis, we use a simple analytical form to fit the large-scale correlations constraints together with the Cosmic Background Explorer Cosmic Microwave Background (COBE CMB) anisotropy measurement, thus constructing a simple phenomenological model for the linear power spectrum. Despite its simplicity, the model fits remarkably well directly estimated power spectra from different optical galaxy samples, and when evolved through an N-body simulation, it provides a good match to the observed galaxy correlations. One of the most interesting features of the model is the small-scale one-dimensional velocity dispersion produced: sigma1d = 450 km/s at 0.5 h-1 Mpc and sigma1d = 350 km/s for separations greater than or equal to 2 h-1 Mpc.

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