Look again at the rotation curve of this spiral galaxy. After it rises over the inner 5 kiloparsecs, it levels off (becoming "flat"), and then never declines. This simple fact has some amazing repurcussions.
Figure 3 - Rotation curve for NGC 2403.
Think about the rotation curve of a point mass. The circular velocity as a function of distance away from the mass can be calculated as
V=(GM/r) ½ ,and so as you move further away, the circular velocity drops as r -½ .Even if galaxies aren't point masses, once you get out far enough that most of the galaxy is inside your radius, the rotation curve should be dropping as r -½ . It doesn't. In the galaxy shown here, over 99% of the starlight lies inside 15 kpc, yet the rotation curve is still flat!
The flatness of spiral galaxy rotation curves is a extremely common; in fact, no spiral galaxy shows a r -½ falling rotation curve. This result led astronomers to the conclusion that there must be more mass than meets the eye in spiral galaxies -- in addition to being filled with stars, galaxies must have other unseen mass associated with them which provides enough mass to keep the rotation curves from falling. This mass has been dubbed "dark matter".