they would naturally produce a morphology-dependent TF relation. In other words, we want to find the physical parameters that uniquely characterise the Tully-Fisher manifold of spiral galaxies, by which a galaxy type is defined based on dynamics and physical parameters linked to its assembly history, rather than visual inspection.

![The Tully-Fisher relation for the semi-analytic model galaxies, divided according to morphology (*light blue, orange and red points* for Sc, Sb and Sa galaxies respectively), compared with the observed sample (*black squares*).[]{data-label="tfmodel"}](f2.eps)

We start by building the TF relation for the observed sample, plotted in Fig. (\[tfmodel\]) in terms of $W=2 V_{\rm C}$ and represented by the *black squares*. Note that the majority of the galaxies in the sample follow a reasonably-defined relation, but with a rather large scatter. In addition, there are numerous objects that significantly deviate from such behaviour. Fig. (\[tfmodel\]) also shows the Tully-Fisher relation for the model galaxies, divided according to morphology: *light blue, orange and red points* represent Sc, Sb and Sa galaxies respectively. As the bulge-to-disk mass ratio increases, the slope of the TF relation flattens, due to the combination of two effects: 1) the stellar populations in the bulge are on average older and 