Correlation Analysis of SFI Peculiar Velocities

We present results of a statistical analysis of the SFI catalog of peculiar velocities, a recently completed survey of spiral field galaxies with I-band Tully-Fisher distances. The velocity field statistic utilized is the velocity correlation function, ψ1(r), originally introduced by Górski et al. The analysis is performed in redshift space so as to circumvent potential ambiguities connected with inhomogeneous Malmquist bias corrections. The results from the SFI sample are compared with linear-theory predictions for a class of cosmological models. We generate a large set of mock samples, extracted from N-body simulations, which are used to assess the reliability of our analysis and to estimate the associated uncertainties. We assume a class of cold dark matter–like power spectrum models, specified by σ8, the rms fluctuation amplitude within a sphere of 8 h-1 Mpc radius, and by the shape parameter, Γ. Defining η8 = σ8Ω, we find that the measured ψ1(r) implies a degenerate constraint in the (η8, Γ)-plane, with η8 = 0.3 ± 0.1(Γ/0.2)0.5 at the 2 σ level for the inverse Tully-Fisher (ITF) calibration presented in this paper. We investigate how much this constraint changes as we account for uncertainties in the analysis method and uncertainties in the distance indicator, and we consider alternative ITF calibrations. We find that both changing the error-weighting scheme and selecting galaxies according to different limiting line widths has a negligible effect. On the contrary, the model constraints are quite sensitive to the ITF calibration. The other ITF calibrations, by Giovanelli et al. and da Costa et al. both yield, for Γ = 0.2, a best-fit value of η8 ≃ 0.6.