et al. 2006) to define a dynamical parameter that characterises galaxy morphology, predicts the TF relation for different galaxy types and defines the spiral galaxy manifold. The model is built on cosmological simulations of structure formation, to model galaxy formation and evolution and build the theoretical TF relation. This tool is ideal for accounting for the merger history of galaxies and their complex star formation history, which is recorded in their rotation curve and stellar populations. We take particular care in producing dynamical and photometric quantities that can be directly compared with observations. With this tool, we analyse a unique dataset of galaxies: we build a sample of observed galaxies carrying the information on luminosity, circular velocity and central velocity dispersion, derived from the GALEX Arecibo SDSS Survey (Catinella et al. 2013). To this sample we apply our theoretical predictions.

In Section 2 we describe the model. In Section 3 we introduce our observational sample and present our main results. In Section 4 we discuss our findings and present our conclusions.

The model
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Semi-analytic models are a powerful tool for investigating the TF relation in a cosmological framework. They naturally interlink the dynamics of structure formation with the galaxy 