Context. Using the multi-integral-field spectrograph GIRAFFEat VLT, we previsouly derived the stellar-mass Tully-Fisher Relation(smTFR) at for a representative sample of 63 emission-line galaxies. We found thatthe distant relation is systematically offset by roughly a factor oftwo toward lower masses from the local relation. Aims. We extend the study of the evolution of the TFR byestablishing the first distant baryonic TFR in a CDFS subsample of35galaxies. We also investigate the underlying cause of the largescatter observed in these distant relations. Methods. To derive gas masses in distant galaxies, we estimate agas radius and invert the Schmidt-Kennicutt law between star formationrate and gas surface densities. We consider the influence of velocitydispersion on the scatter of the relation, using the kinematic tracer S suggested by Kassin and collaborators. Results. We find that gas extends farther out than the UV light from young stars, a median of 30%. We present the first baryonic TFR (bTFR) ever established at intermediate redshift and show that, within an uncertainty of 0.08dex, the zeropoint of the bTFR does not appear to evolve between and z= 0. On the other hand, we confirm that the difference between thelocal and distant smTFR is significant, even considering random andsystematic uncertainties, and that accounting for velocity dispersionleads to a significant decrease in the scatter of the distant relation.Conclusions. The absence of evolution in the bTFR over the past6Gyr implies that no external gas accretion is required fordistant rotating disks to sustain star formation until z = 0and convert most of their gas into stars. Finally, we confirm that thelarger scatter found in the distant smTFR, and hence in the bTFR, iscaused entirely by major mergers. This scatter results from a transferof energy from bulk motions in the progenitors, to random motions inthe remnants, generated by shocks during the merging. Shocks occurringduring these events naturally explain the large extent of ionized gasfound out to the UV radius in galaxies. All the results presented in this paper support the ``spiralrebuilding scenario'' of Hammer and collaborators, i.e., that a largefraction of local spiral disks have been reprocessed during majormergers in the past 8 Gyr. Key words: galaxies: evolution - galaxies: kinematics and dynamics -galaxies: high-redshift - galaxies: general - galaxies:interactions - galaxies: spiral.
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