>> so the rotation curve should approach the Keplerian limit...
I don't agree. If we treat the galaxy as a bunch of concentric rings, many of them are nowhere near far enough away to reach that "Keplerian" limit.
As an experiment I modeled a flat disk of uniformly distributed stars. Without doing a dynamic simulation one can do the n-body calculation to determine the total pull on each star and determine what its orbital velocity must be to go in a circular orbit. You find that the "galactic rotation curve" will have a velocity that actually increases all the way to the edge. Of course a uniform distribution is not what a real galaxy looks like, but I think we can all agree reality is somewhere between the uniform flat disk and the highly concentrated central mass. And the actual rotation curves are somewhere between Keplers and mine. I'd expect people to work backward from the rotation curves to determine the mass distribution and then try to understand why that isn't what is observed. I suppose that's just a different way to get at the same mystery.
I don't agree. If we treat the galaxy as a bunch of concentric rings, many of them are nowhere near far enough away to reach that "Keplerian" limit.
As an experiment I modeled a flat disk of uniformly distributed stars. Without doing a dynamic simulation one can do the n-body calculation to determine the total pull on each star and determine what its orbital velocity must be to go in a circular orbit. You find that the "galactic rotation curve" will have a velocity that actually increases all the way to the edge. Of course a uniform distribution is not what a real galaxy looks like, but I think we can all agree reality is somewhere between the uniform flat disk and the highly concentrated central mass. And the actual rotation curves are somewhere between Keplers and mine. I'd expect people to work backward from the rotation curves to determine the mass distribution and then try to understand why that isn't what is observed. I suppose that's just a different way to get at the same mystery.