Large-scale power spectrum and cosmological parameters from SFI peculiar velocities

We estimate the power spectrum of mass density fluctuations from peculiar velocities of galaxies by applying an improved maximum likelihood technique to the new all-sky SFI catalog. Parametric models are used for the power spectrum and the errors, and the free parameters are determined by assuming Gaussian velocity fields and errors and maximizing the probability of the data given the model. It has been applied to generalized cold dark matter (CDM) models with and without COBE normalization. The method has been carefully tested using artificial SFI catalogs. The most likely distance errors are found to be similar to the original error estimates in the SFI data. The general result that is not very sensitive to the prior model used is a relatively high amplitude of the power spectrum. For example, at k = 0.1 h Mpc^-1 we find P(k)Ω^1.2 = (4.4 ± 1.7) × 10³(h^-1 Mpc)³. An integral over the power spectrum yields σ₈Ω^0.6 = 0.82 ± 0.12. Model-dependent constraints on the cosmological parameters are obtained for families of CDM models. For example, for COBE-normalized ACDM models (scalar fluctuations only), the maximum likelihood result can be approximated by Ωn²h^601.3 = 0.58 ± 0.11. The formal random errors quoted correspond to the 90% confidence level. The total uncertainty, including systematic errors associated with nonlinear effects, may be larger by a factor of ∼2. These results are in agreement with an application of a similar method to other data (Mark III).