 Solution

Observed galaxy rotation curves commonly remain approximately flat across much of the measured outer luminous disk. A pure NFW profile is not an exactly flat curve: it rises in the inner cusp and ultimately declines. Nevertheless, its broad maximum can look nearly flat over a finite radial range, so observing a flat segment does not by itself exclude an NFW halo.

The measured circular speed responds to the total gravitational potential, including stars and gas as well as dark matter. For components in the same plane,For spherical components this reduces to $G{\sum }_j{M}_j(<r)/r$; a disk contribution must instead be computed from its actual disk potential. Baryonic mass can supply much of the inner rotation and modify the halo through slow contraction or more impulsive evolution. Thus the appropriate comparison is with the combined mass model, not an isolated halo-only curve. At arbitrarily large radius a finite isolated galaxy must eventually have a declining circular speed; an observed flat segment is not a claim of flat rotation to infinity.