Comparing the SFI Peculiar Velocities with the PSCz Gravity Field: a VELMOD analysis

We compare the peculiar velocities derived from the I-band Tully-Fisher (TF) relation for 989 field spiral galaxies in the SFI catalogue with the predicted velocity field derived from the IRAS PSCz galaxy redshift survey. We assume linear gravitational instability theory and apply the maximum likelihood technique, VELMOD, to SFI galaxies within cz<6000 km/s. The resulting calibration of the TF relation is consistent with a previous, independent calibration for a similar sample of spirals residing in clusters. Our analysis provides an accurate estimate of the quantity beta. Using the forward TF relation and smoothing the predicted velocity field with a Gaussian filter of radius 300 km/s, we obtain beta = 0.42 +/- 0.04 (1 sigma uncertainty). This value, as well as other parameters in the fit, are robust to varying the smoothing radius to 500 km/s and splitting the sample into spherical shells in redshift space. The one exception is the small-scale velocity dispersion, sigma_v, which varies from 200 km/s within cz= 4000 km/s 500 km/s at larger distance. For beta = 0.42, the residuals between the TF data and the PSCz gravity field are uncorrelated, indicating that the model provides a good fit to the data. More generally, a chi^2 statistic indicates that the PSCz model velocity field provides an acceptable (3 sigma) fit to the data for 0.3 < beta < 0.5.