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 PSC z galaxy redshift survey .
We assume linear gravitational instability theory and apply the maximum likelihood technique , VELMOD ( Willick et al . 1997b ) , to SFI galaxies within cz < 6000 km s ^ { -1 } .
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 _ { I } \equiv \Omega _ { m } ^ { 0.6 } / b _ { I } , where b _ { I } is the linear biasing parameter for IRAS galaxies .
Using the forward TF relation and smoothing the predicted velocity field with a Gaussian filter of radius 300 km s ^ { -1 } , we obtain \beta _ { I } = 0.42 \pm 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 ^ { -1 } and splitting the sample into spherical shells in redshift space .
The one exception is the small-scale velocity dispersion , \sigma _ { v } , which varies from \sim 200 km s ^ { -1 } within cz _ { LG } = 4000 km s ^ { -1 } to \sim 500 km s ^ { -1 } at larger distance .
For \beta _ { I } \simeq 0.42 , the residuals between the TF data and the PSC z gravity field are uncorrelated , indicating that the model provides a good fit to the data .
More generally , a \chi ^ { 2 } statistic indicates that the PSC z model velocity field provides an acceptable ( 3 \sigma ) fit to the data for 0.3 < \beta _ { I } < 0.5 .