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 (Haynes et al. 1999). The velocity field statistic utilized is the velocity correlation function, $\psi_1(r)$ (Gorski et al. 1989). 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. 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. Defining $\eta_8=\sigma_8\Omega_0^{0.6}$, we find that the measured $\psi_1(r)$ implies a degenerate constraint in the $\eta_8-\Gamma$ plane, with $\eta_8=(0.3 +/- 0.1) (\Gamma/0.2)^{0.5}$, at the $2\sigma$ level, for the inverse Tully-Fisher (ITF) calibration presented in this paper. Model constraints are quite sensitive to the ITF calibration. The other ITF calibrations by Giovanelli et al. (1997) and da Costa et al. (1998) both give, for $\Gamma=0.2$, $\eta_8\simeq 0.6$ as the best-fitting value.