Disc galaxies obey the Renzo's rule (Sancisi 2004): the shape of the luminosity profile and the shape of the rotation curve are closely related. In Lelli et al. 2013 we quantify this relation: the circular-velocity gradient (inner steepness of the rotation curve) correlates with the central surface brightness over several orders of magnitude. This is the inner galaxy counterpart of the Tully-Fisher relation!
