Undergrad Rotation curve in spiral velocity and uniform velocity dispersion

[Ranku]

The rotation curve of spiral galaxies shows uniform velocity dispersion in the outer reaches, which is taken as evidence of the presence and distribution of dark matter. My question: Does uniform velocity dispersion require the diffused distribution of dark matter, or could the distribution be, say, less diffused and more clustered, and there would still be uniform velocity dispersion, as long as there is the presence of dark matter?

 

[Ibix]

I don't think there's a general answer to that question. You'd have to plug a density distribution into the maths and see what orbits were implied.

Bear in mind that dark matter is influenced by gravity. You can probably find other density distributions that reproduce the same velocity curve for visible matter, but you have to show that the density distribution is consistent with the dynamics of dark matter.