I Do All Galaxies with Dark Matter Halos Have Flat Rotation Curves?

[strangerep]

[...] my own doodlings have shown that this certainly does not happen with a disc. [...]

FYI, you longer need to "doodle" with these sorts of nontrivial computations...

I just posted a thread about Jo Bovy's new interactive book on Galactic Dynamics. Among many other things, it covers detailed derivations for various galactic geometries, e.g., thin disk, thick disk, and others.

 

[Bandersnatch]

Why should vast majority of particles stream through the central area, i. e. have low periapse requiring low individual angular momentum? In case of no collisions, would there be any mechanism to clear out high periapse orbits?

Hey, thanks for this question. I've been trying to recall the argument for that, and I'm increasingly certain I've just pulled it out of my lower back at some point in the past and then started believing it.
Because as you say, it shouldn't be the case, should it? And in any case, the density being inversely dependent on the radius doesn't require 'the vast majority' of DM to be going through the central region. The vast majority of the mass should actually be in the halo, given the approx. 1/r density profile, since the volume obviously grows faster with r.

 

[snorkack]

Because as you say, it shouldn't be the case, should it? And in any case, the density being inversely dependent on the radius doesn't require 'the vast majority' of DM to be going through the central region. The vast majority of the mass should actually be in the halo, given the approx. 1/r density profile, since the volume obviously grows faster with r.

The entire mass is in the halo for the simple reason that the mass is infinite - 1/r density obviously means that the density diverges to infinity at r=0, while the mass diverges to infinity with r².
But note that for a spherically symmetric distribution of masses on circular orbits, the said spherical distribution is completely free and arbitrary.
Whereas eccentric orbits provide constraints on the relative densities of different shells. On the assumption that the orbits are incommensurate periods and the particles have spread uniformly around their orbits, we can figure out instant mass distribution from distribution of orbits.
If all orbits are high eccentricity, then every single particle spends most of time in the halo moving slowly, and a small fraction of time moving fast through the centre. But since the particles coming from different directions get together in the centre, what is the net result? Which distribution of orbits gives 1/r density?