This may be a nitpick (depending on what you are trying to achieve) but the scale density is not a "numerical fact" because it is degenerate with the scale radius when you express the NFW profile as you have done. For any set of data there is a range of pairs of values rho_0 and R_s that all fit...
I confess my knowledge of this area comes from working in the same department as people who study it rather than reading or publishing the literature, so its hard to point you at anything specific. Some folks I know who have worked on this are Andrew King, and his former student Chris Nixon. You...
This only applies to SMBHs in galaxies. Planetary systems are dynamically quite different.
I'm a little confused as to what you want me to demonstrate. Why should there be any alignment between rotation planes in this case?
Yes you do get finite masses integrating the NFW halo from r=0 due to the r^2 factor in the integral element. It's still not a good idea to use it near the central black hole.
Cosmological density profiles like NFW or Einasto (which is popular in N body simulations these days) are based on...
That's not a good idea. If you do that for, say, an NFW halo you get towards infinite density at the centre.
If you are referring to the black hole at the centre of our galaxy, there are stars that can be used as tracers of potential and thus could get you a dark matter distribution. However...
Elizabeth,
Regardless of what may be happening to spacetime in or near the central black hole of a galaxy, rotation velocities are measured at distances where the gravitational effect of the black hole is well into the Newtonian regime. Even if what you are describing could happen (and...