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(Abridged version) We explore whether a scenario that combines an origin bymergers at $z\sim$1.8-1.5 with a subsequent passive evolution of the resultingS0 remnants since $z \sim$0.8-1 is compatible with observational data of S0s inthe Tully-Fisher relation (TFR). We studied a set of major and minor mergerexperiments from the GalMer database that generate massive S0 remnants. Weanalysed the location of these remnants in the photometric and stellar TFRsassuming that they correspond to $z\sim0.8$ galaxies. We then estimated theirevolution in these planes over the last 7 Gyr. The results were compared withdata of real S0s and spirals at different redshifts. We also tested how the useof Vcirc or Vrot,max affects the results. We found that just after $\sim$1-2Gyr of coalescence, major mergers generate S0 remnants that are outliers of thelocal photometric and stellar TFRs at $z\sim0.8$. After $\sim$4-7 Gyr ofpassive evolution in isolation, the S0 remnants move towards the local TFR,although the initial scatter among them persists. This scatter is sensitive tothe indicator used for the rotation velocity: Vcirc values yield a lowerscatter than when Vrot,max values are considered instead. In the planesinvolving Vrot,max, a clear segregation of the S0 remnants in terms of thespin-orbit coupling of the model is observed, in which the remnants ofretrograde encounters overlap with local S0s hosting counter-rotating discs.The location of the S0 remnants at $z\sim 0$ agrees well with the observeddistribution of local S0 galaxies in the $\sigma_0$-$M_K$, Vcirc-$\sigma_0$ andVrot,max-$\sigma_0$ planes. Thus, massive S0 galaxies may have been formedthrough major mergers that occurred at high redshift and have later evolvedtowards the local TFR through passive evolution in relative isolation, amechanism that would also contribute to the scatter observed in this relation.

Formation of S0 galaxies through mergers. Evolution in the Tully-Fisher relation since $z\sim1$