Measuring the velocities of stars as a function of their distance to the galaxy's center therefore allows to draw conclusions about the matter distribution inside the galaxy. The plot below shows an example of the velocity, v in km/s, as a function of the distanceto the center, R in kpc, for the galaxy NGC 3198
Naively one would expect one can estimate the rotation curves as follows. Most of the matter we see is located in the center of a galaxy. The gravitational field is weak enough so one can use the Newtonian limit. A star in the outer arms should thus roughly follow an orbit on which the attractive gravitational force balances the centripetal force. Requiring both to be equal one finds that the square of the stars velocities should drop with the inverse of the distance to the center:
If you look at the plot above however, you see that this is not what we observe. Instead, the velocity seems to become constant towards the outer regions. And the above example is not a single case. If you look at Begeman's paper, you will find many similar looking curves for spiral galaxies (for more recent measurements, see e.g. astro-ph/0107326).
The observations can be explained by assuming a significant amount of non-visible (dark) matter which is distributed through the galaxy. This dark matter is today the most widely accepted - though not the only - explanation for the rotational curves. The challenge here is that the ratio of dark matter to visible matter (the mass-to-light ratio, commonly denoted M/L) depends on the type of galaxy. E.g. globular clusters show little or no evidence for dark matter.
For other experimental evidence, see also our previous post on Dark Matter.
This post is part of our 2007 advent calendar A Plottl A Day.