Formation of S0 galaxies through mergers. Evolution in the Tully-Fisher
  relation since $z\sim1$
  (Abridged version) We explore whether a scenario that combines an origin by
mergers at $z\sim$1.8-1.5 with a subsequent passive evolution of the resulting
S0 remnants since $z \sim$0.8-1 is compatible with observational data of S0s in
the Tully-Fisher relation (TFR). We studied a set of major and minor merger
experiments from the GalMer database that generate massive S0 remnants. We
analysed the location of these remnants in the photometric and stellar TFRs
assuming that they correspond to $z\sim0.8$ galaxies. We then estimated their
evolution in these planes over the last 7 Gyr. The results were compared with
data of real S0s and spirals at different redshifts. We also tested how the use
of Vcirc or Vrot,max affects the results. We found that just after $\sim$1-2
Gyr of coalescence, major mergers generate S0 remnants that are outliers of the
local photometric and stellar TFRs at $z\sim0.8$. After $\sim$4-7 Gyr of
passive evolution in isolation, the S0 remnants move towards the local TFR,
although the initial scatter among them persists. This scatter is sensitive to
the indicator used for the rotation velocity: Vcirc values yield a lower
scatter than when Vrot,max values are considered instead. In the planes
involving Vrot,max, a clear segregation of the S0 remnants in terms of the
spin-orbit coupling of the model is observed, in which the remnants of
retrograde encounters overlap with local S0s hosting counter-rotating discs.
The location of the S0 remnants at $z\sim 0$ agrees well with the observed
distribution of local S0 galaxies in the $\sigma_0$-$M_K$, Vcirc-$\sigma_0$ and
Vrot,max-$\sigma_0$ planes. Thus, massive S0 galaxies may have been formed
through major mergers that occurred at high redshift and have later evolved
towards the local TFR through passive evolution in relative isolation, a
mechanism that would also contribute to the scatter observed in this relation.
