What do rotation curves require of dark matter?

The extended rotation curves of spiral galaxies are asymptotically flat. This is the essential result of three decades of 21-cm line observations carried out with radio telescopes – single-dish as well as interferometers. Every astronomer and physicist is familiar with this result and its interpretation as visible spiral galaxies being embedded in a more extensive dark halo. But what does this imply about the distribution of dark matter within spiral galaxies? What is required of dark matter in order to explain this essential observation?

In Fig. 8.1 we see again the well-known example of a flat rotation curve, that of the spiral galaxy NGC 2403. This rotation curve has been derived from 21-cm line observations made more than 20 years ago at Westerbork WSRT by Kor Begeman, then a student in Groningen, and it is a clear example of a flat rotation curve which extends well beyond the bright inner regions of the galaxy. Also shown are the combined Newtonian rotation curves of the observable baryonic components of the galaxy – the stars and the gas (assuming that the light traces the mass of the visible disk). The discrepancy between the observations and predictions is very evident in this figure.

In the context of Newtonian dynamics, dark matter must make up this difference between observations and expectations. What sort of dark matter distribution is required in this case?