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.