A scaling-relation for disc galaxies: circular-velocity gradient versus central surface brightness

For disc galaxies, a close relation exists between the distribution of light and the shape of the rotation curve. We quantify this relation by measuring the inner circular-velocity gradient d_{R}V(0) for spiral and irregular galaxies with high-quality rotation curves. We find that d_{R}V(0) correlates with the central surface brightness mu_{0} over more than two orders of magnitude in d_{R}V(0) and four orders of magnitudes in mu_{0}. This is a scaling-relation for disc galaxies. It shows that the central stellar density of a galaxy closely relates to the inner shape of the potential well, also for low-luminosity and low-surface-brightness galaxies that are expected to be dominated by dark matter.