[Pxtl]

Well, they say the DS would also have a decent amount of baryonic matter in it - some diffuse hydrogen and helium. If the pressure from the annihilations pushes the hydrogen and helium outwards, that could create some outward gravity to pull on the dark matter, right? Wait, except the outward gravitational pull inside of a hollow shell is zero because it all cancels.

Would there even be friction though? It sounds like the only interactions these hypothetical particles have is gravity and annihilation.

[Sharlin]

Yes, no friction for the DM particles. WIMP DM cannot collapse by shedding kinetic energy as heat like visible matter can. Thus the dark matter halos around galaxies. But gravity would still cause there to be a higher average density of DM inside and near the dark star (or indeed a modern-day galaxy) than far away from any massive objects.

[floxy]

>Yes, no friction for the DM particles

Chandrasekhar dynamical friction?

https://en.wikipedia.org/wiki/Dynamical_friction

[CydeWeys]

> If the pressure from the annihilations pushes the hydrogen and helium outwards, that could create some outward gravity to pull on the dark matter, right?

But it's not on net being pushed outwards. It's in equilibrium. The outward push is on average exactly canceled out by the baryonic matter falling inwards due to friction. If it weren't, then everything would get either denser/sparser until equilibrium were regained. The point is that the forces are working in such a way as to maintain a stable equilibrium, like in normal stars.