system
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human
Why doesn't dark matter clump into singularities?

With only some undergrad physics courses, I've asked a few cosmologists and particle physicists but could not get an answer and they suggested posting here.

Dark matter (as I understand it) is used (among other things) to explain the discrepancies between the rate of rotation of stars/galaxies near the edge of a cluster being observed as faster than prediction.

In order for this explanation to work, one must assume that a Dark matter "cloud" is relatively uniformly distributed over an area larger than the galaxy/cluster.  The explanations I've read about dark matter consistently mention its uniform distribution. 

However, why would such a massive particle stay uniformly distributed?  

Should not even the slightest irregularities (even the gravitational irregularities of the stars themselves) cause clumping of the dark matter?

Since dark matter is not affected by electromagnetic forces, as it clumps there is nothing to stop it from keep clumping (unlike stars/matter which have electromagnetic repulsion).  

Therefore, why wouldn't all dark matter eventually clump into a singularities, eventually coalescing into a single massive singularity?
gpt
First of all, dark matter is clumped, just not into compact bodies like planets and stars and black holes.  It would only be uniform over galactic distance scales - one of the signatures of dark matter searches are looking for are effects it may have on the sun via clumping in the core.

The reason you don't expect many dark matter singularities is that in order to get a cloud to collapse into a dense body, you have to have some mechanism to redistribute and radiate away momentum on some fast enough timescale.  If the dark matter particles only interact sufficiently weakly with one-another, you won't get this process to happen fast enough for the dark matter to settle into compact objects compared to the lifetime of the universe.  If you just have particles and gravity, then they zip past eachother in lots of fun and intricate ways, but they won't in general undergo collapse unless there's something that lets them get rid of their relative kinetic energy.

It's easier to think about in the limit of two bodies interacting only gravitationally: there are no solutions that involve collapse!  They either stay bound and orbit eachother (maybe even move through eachother - keep in mind we're saying *only* gravity for this thought experiment) or they have enough energy to escape - to get them to collapse to one spot they have to do something else besides gravity.  You need some kind of drag force.