E. Branchini et al., MODELING THE POWER SPECTRUM OF DENSITY-FLUCTUATIONS - A PHENOMENOLOGICAL APPROACH, The Astrophysical journal, 424(1), 1994, pp. 120000005-120000008
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.