Why Do Stars at the Edge of Galaxies Feel an Inward Pull from Dark Matter?

[Aschere]

I was wondering, if dark matter (DM) halos are spherical in nature and increase in density as a function of distance from the galactic core,

why does the density drop off so suddenly
and
why would stars on the edge of a galaxy feel an inward pull?

To elaborate on the 2nd question, if DM interacts only gravitationally and is more dense at the edge of the galaxy (or a radius from it), wouldn't stars want to be gravitationally tugged by the DM away from the galaxy and not towards the galactic core? Rotation curves suggest stars on the edges of spirals are being pulled 'inward', but the DM is in the opposite direction for that!

 

[Chronos]

DM does not clump in the manner that 'ordinary' baryonic matter does. The particles are weakly interactive with everything, including each other. For this reason, the DM universe is much 'younger' than the baryonic universe. It would be fascinating to observe the actual distribution.

 

[Wallace]

I was wondering, if dark matter (DM) halos are spherical in nature and increase in density as a function of distance from the galactic core,

The answer to the first question is a very cautious yes (since there is a lot about DM halos we do not understand fully) however to the second part of the question the answer is no. The density of dark matter (as we understand it) decreases monotonically with the radius of the halo. What is greater as you go out is the ratio of DM/baryons, but the actual density should be greater in the center.