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 dRV(0) for spiral and irregular galaxies with high-quality rotation curves. We find that dRV(0) correlates with the central surface brightness μ0 over more than two orders of magnitude in dRV(0) and four orders of magnitudes in μ0. 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.