The hierarchical build-up of the Tully-Fisher relation

We use the semi-analytic model GalICS to predict the Tully–Fisher relation in the B, I and K bands, and its evolution with redshift, up to z∼ 1. We refined the determination of the disc galaxies rotation velocity, with a dynamical recipe for the rotation curve, rather than a simple conversion from the total mass to maximum velocity. The new recipe takes into account the disc shape factor, and the angular momentum transfer occurring during secular evolution leading to the formation of bulges. This produces model rotation velocities that are lower by ∼30 km s−1 in case of Milky Way like objects, and ≤20–30 km s−1 for the majority of the spirals, amounting to an average effect of ∼20–25 per cent. We implemented stellar population models with a complete treatment of the thermally pulsing asymptotic giant branch, which leads to a revision of the mass-to-light ratio in the near-IR. Due to this effect, K-band luminosities increase by ∼0.5 at redshift z= 0 and by >1 at z= 3, while in the I band at the same redshifts the increase amounts to ∼0.3 and ∼0.5 mag. With these two new recipes in place, the comparison between the predicted Tully–Fisher relation with a series of data sets in the optical and near-infrared, at redshifts between 0 and 1, is used as a diagnostics of the assembly and evolution of spiral galaxies in the model. At redshifts 0.4 < z < 1.2 the match between the new model and data is remarkably good, especially for later-type spirals (Sb/Sc). At z= 0 the new model shows a net improvement in comparison with its original version of 2003, and in accordance with recent observations in the K band, the model Tully–Fisher also shows a morphological differentiation. However, in all bands the z= 0 model Tully–Fisher is too bright. We argue that this behaviour is caused by inadequate star formation histories in the model galaxies at low redshifts. The star formation rate declines too slowly, due to continuous gas infall that is not efficiently suppressed. An analysis of the model disc scalelengths, at odds with observations, hints to some missing physics in the modelling of disc formation inside dark matter haloes.