> If it interacts with visible matter gravitationally then why doesn't it take on the same distribution?
Because unlike visible matter, it does not interact in non-gravitational ways, even with itself.
Visible matter can clump to form planets and stars because when two particles of it are attracted enough to hit each other there is some interaction other than gravity, which helps eat some of their kinetic energy. In contrast, when that happens with two particles of dark matter, they just fly through each other, and if they were moving fast enough, never meet again.
There are non-gravitational interactions even at the galactic scale, even though they are very weak indeed compared to gravity. As our sun plows through space, the particles it's sphere of influence hits have a preferred range of velocities and directions, the "galactic rest". Over billions of years, this does influence where in the galaxy our sun is. Dark matter has no such influence on it.
Do we actually know that dark matter doesn't interact with itself or other matter, or do we just have an upper bound on how much it could potentially interact? And if so, roughly what is it?
Because unlike visible matter, it does not interact in non-gravitational ways, even with itself.
Visible matter can clump to form planets and stars because when two particles of it are attracted enough to hit each other there is some interaction other than gravity, which helps eat some of their kinetic energy. In contrast, when that happens with two particles of dark matter, they just fly through each other, and if they were moving fast enough, never meet again.
There are non-gravitational interactions even at the galactic scale, even though they are very weak indeed compared to gravity. As our sun plows through space, the particles it's sphere of influence hits have a preferred range of velocities and directions, the "galactic rest". Over billions of years, this does influence where in the galaxy our sun is. Dark matter has no such influence on it.