Modeling the power spectrum of density fluctuations : A phenomenological approach

We show how, based on considerations on 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) is-proportional-to k-2.2. For a plausible value of the bias parameter b = 1/sigma8 congruent-to 1.8, one has (deltarho/sigma)rms approximately 1 at r congruent-to 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 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-1 at 0.5 h-1 Mpc and sigma1d = 350 km s-1 for separations greater-than-or-equal-to 2 h-1 Mpc.