The effect of the disc on the rotation curves of spiral galaxies

We discuss the role of the galactic disc in the interpretation of the circular velocities of spiral galaxies at large galactocentric radii. The fractional amount of mass in the disc can be shown to be an increasing function of the luminosity. As a result, the shape of the rotation curve near the edge of the optical disc is expected to vary systematically with luminosity. Using a simple disc/halo model we find that in bright, disc-dominated galaxies the rotation curve should drop by a few tens of km s−1 immediately outside the disc, even in the presence of an extended dark halo. Only in faint, halo-dominated galaxies, do we expect the rotation curve to remain flat or even to rise beyond the optical radius. We find evidence for this behaviour in several published rotation curves. In the case of the Milky Way we show that if the disc dominates the gravitational potential in the inner regions, then the low mass estimated by Little & Tremaine from the dynamics of the outer satellites is consistent with a dark halo that extends beyond the region sampled. This and other available data are well fit by a model in which the luminous component of the Galaxy contributes ∼ 70 per cent of the mass at 12 kpc from the centre and the mass at large radii increases in proportion to the radius.