The SFI++ consists of ~5000 spiral galaxies which have measurements suitable
for the application of the I-band Tully-Fisher (TF) relation. This sample
builds on the SCI and SFI samples published in the 1990s but includes
significant amounts of new data as well as improved methods for parameter
determination. We derive a new I-band TF relation from a subset of this sample
which consists of 807 galaxies in the fields of 31 nearby clusters and groups.
This sample constitutes the largest ever available for the calibration of the
TF template and extends the range of line-widths over which the template is
reliably measured. Careful accounting is made of observational and sample
biases such as incompleteness, finite cluster size, galaxy morphology and
environment. We find evidence for a type-dependent TF slope which is shallower
for early type than for late type spirals. The line-of-sight cluster peculiar
velocity dispersion is measured for the sample of 31 clusters. This value is
directly related to the spectrum of initial density fluctuations and thus
provides an independent verification of the best fit WMAP cosmology and an
estimate of Omega^0.6 sigma_8 = 0.52+/-0.06. We also provide an independent
measure of the TF zeropoint using 17 galaxies in the SFI++ sample for which
Cepheid distances are available. In combination with the ``basket of clusters''
template relation these calibrator galaxies provide a measure of H0 = 74+/-2
(random) +/-6 (systematic) km/s/Mpc.Comment: Accepted by ApJ (scheduled for 20 Dec 2006, issue 653). 21 pages (2
column emulateapj) including 12 figures. Version 2 corrects typos and other
small errors noticed in proof