  We demonstrate that the comparison of Tully-Fisher relations (TFRs) derived
from global HI line widths to TFRs derived from the circular velocity profiles
of dynamical models (or stellar kinematic observations corrected for asymmetric
drift) is vulnerable to systematic and uncertain biases introduced by the
different measures of rotation used. We therefore argue that to constrain the
relative locations of the TFRs of spiral and S0 galaxies, the same tracer and
measure must be used for both samples. Using detailed near-infrared imaging and
the circular velocities of axisymmetric Jeans models of 14 nearby edge-on Sa-Sb
spirals and 14 nearby edge-on S0s drawn from a range of environments, we find
that S0s lie on a TFR with the same slope as the spirals, but are on average
0.53+/-0.15 mag fainter at Ks-band at a given rotational velocity. This is a
significantly smaller offset than that measured in earlier studies of the S0
TFR, which we attribute to our elimination of the bias associated with using
different rotation measures and our use of earlier type spirals as a reference.
Since our measurement of the offset avoids systematic biases, it should be
preferred to previous estimates. A spiral stellar population in which star
formation is truncated would take ~1 Gyr to fade by 0.53 mag at Ks-band. If S0s
are the products of a simple truncation of star formation in spirals, then this
finding is difficult to reconcile with the observed evolution of the spiral/S0
fraction with redshift. Recent star formation could explain the observed lack
of fading in S0s, but the offset of the S0 TFR persists as a function of both
stellar and dynamical mass. We show that the offset of the S0 TFR could
therefore be explained by a systematic difference between the total mass
distributions of S0s and spirals, in the sense that S0s need to be smaller or
more concentrated than spirals.
