Dark Matter Halo and the Galactic Rotation Curve

What you are seeing: a 3D galactic disk with its dark-matter halo (transparent purple sphere) on the left, and the rotation curve $v_c(r)$ on the right. The bulge (gold), exponential disk (cyan), and NFW dark halo (purple) contributions to $v_c$ are plotted separately, with the total (white) on top. Toggle the dark halo off to see the flat plateau collapse into a Keplerian fall

Figure 1. Three-component galactic rotation curve (Hernquist bulge, exponential disk, NFW dark halo) with 3D disk + halo inset. Method: closed-form enclosed-mass integrals; v_c(r) = sqrt(G M(<r) / r).

M_DM80

concentration c12

scale radius r_s20

dark halo

presetvisible+dm

WHAT TO TRY

Switch the preset to visible matter only: the rotation curve falls off Keplerian past the disk edge. Add the dark halo and it flattens, the observation that demands dark matter.
Raise the halo mass M_DM: the plateau velocity climbs, and the dark-to-visible mass ratio grows. The flat curve needs most of the mass to be invisible and extended.
Tune the concentration c and scale radius r_s: the NFW halo reshapes the inner rise versus the outer plateau, the profile fitted to real galaxy rotation curves.