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Dark matter supposed to be affected only by gravity and no other force. At the same time, however, dark matter forms halos around galaxies, that become visible examining how galaxies and clusters bend the light.

The question is now, what does prevent these huge clouds of dark matter from collapsing? A cloud of "normal" matter has an inner pressure from its temperature. The force working here would be the electromagnetic force because the atoms and molecules of "normal" matter repel each other (compare https://www.youtube.com/watch?v=bKldI-XGHIw Veritasium - Can We Really Touch Anything?) When it collapses as a cold cloud to form stars, the inner pressure is still working, it's heating up until it forms a star hot enough to start fusion fire.

When the star collapses because the pressure decreases after the core cools down after fusion slows down at the end of its life, quantum mechanical forces (Pauli principle) keep it from getting down any further until the mass is strong enough to overcome the Pauli forces and create a black hole.

Now why doesn't the same happen to dark matter if there's no other force that's affecting dark matter particles (whatever they might be) except for gravity? Inner pressure can't happen because electromagnetic forces don't work here. Pauli principle can't happen because for that it's not dense enough and would again need other forces to be exchanged between the particles.

Does that mean, that these DM particles have to be Bosons since they can go through each other and thus never lose any energy to each other do collapse further? However, gravity could produce some kind of inner friction too when one particle loses gravitational energy to another one passing by.

PS: I am not a physicist just interested in this stuff, thus I can't do the calculations for myself.

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Dark matter without strong self-interaction is indeed pressure-less, so it cannot form a static ball. However, since it does not interact with electromagnetism or give off any other kind of radiation, it also cannot lose energy. When normal matter clouds collapse to form stars it happens because the involved atoms and molecules can radiate away their energy and end up in a more tightly bound form. This is not available to the dark matter halo, where individual particles (whatever they are) will orbit in the joint gravitational field.

If enough dark matter was accidentally concentrated somewhere it would implode into a black hole, but since black holes are tiny on an astronomical scale this will just remove the super-dense part and leave the rest orbiting as normal (with a tiny fraction falling in over time).

Technically, dark matter form virialized halos. The virial theorem in mechanics states that when a lot of particles bound interact with each other by gravity the average movement energy tends to equal half of their average potential energy. That is, they form a density distribution with high density and speed in the core, surrounded by a loose and low-density cloud of more slowly moving particles.

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