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 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 ) \Omega ^ { 1.2 } = ( 4.4 \pm 1.7 ) \times 10 ^ { 3 } ( h ^ { -1 } { Mpc } ) ^ { 3 } .
An integral over the power spectrum yields \sigma _ { 8 } \Omega ^ { 0.6 } = 0.82 \pm 0.12 .
Model-dependent constraints on the cosmological parameters are obtained for families of CDM models .
For example , for COBE-normalized \Lambda CDM models ( scalar fluctuations only ) , the maximum-likelihood result can be approximated by \Omega n ^ { 2 } { h _ { 60 } } ^ { 1.3 } = 0.58 \pm 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 \sim 2 .
These results are in agreement with an application of a similar method to other data ( Mark III ) .