MODELING THE POWER SPECTRUM OF DENSITY-FLUCTUATIONS - A PHENOMENOLOGICAL APPROACH

We show how, based on considerations on the observed form of the galax y 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-pr oportional-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 obs erved in xi(r) around this scale marks the transition between the line ar and nonlinear gravitational regimes. Under this working hypothesis, we use a simple analytical form to fit the large-scale correlations c onstraints together with the COBE CMB anisotropy measurement, thus con structing a simple phenomenological model for the linear power spectru m. Despite its simplicity, the model fits remarkably well directly est imated power spectra from different optical galaxy samples, and when e volved through an N-body simulation, it provides a good match to the o bserved galaxy correlations. One of the most interesting features of t he model is the small-scale one-dimensional velocity dispersion produc ed: sigma1d = 450 km s-1 at 0.5 h-1 Mpc and sigma1d = 350 km s-1 for s eparations greater-than-or-equal-to 2 h-1 Mpc.