which determines the galaxy rotation curve. In the case of spiral galaxies, this is usually parameterised with the circular velocity at a given radius, and in the case of ellipticals, with the central velocity dispersion. Both these quantities have a monothonic dependence on luminosity, thus giving rise to the Tully-Fisher relation (TF; Tully $\&$ Fisher, 1977) for spirals, and the Faber-Jackson relation (FJ; Faber $\&$ Jackson 1976) for ellipticals.

However galaxy structure cannot be completely captured by such simple scalings, and the underlying complexity emerges with additional parameters. In the case of ellipticals, the triaxial mass distribution causes an expansion of the FJ relation into a third dimension, recasting it as a scaling between velocity dispersion $\sigma$, surface brightness $I_e$ and effective radius $r_e$, known as the Fundamental Plane (FP; Djorgovski $\&$ Davis 1987, Dressler et al. 1987), a manifestation of the virial theorem in observational quantities (see for instance Cappellari et al. 2006). The slope of the FP indicates that the structure of elliptical galaxies is not a self-similar scaled version of a single object as a function of mass.

In the case of spirals, the apparent simplicity of these systems is broken by the observational evidence of a 