I have read this question:
The only way you can do this is to remove kinetic energy from the system.
With normal matter this is done through electromagnetic interactions, which turn the kinetic energy of normal matter (protons, electrons etc.) into photons, which then escape from the system. Since these kinds of interactions do not occur for dark matter (by definition), then there is no way to get rid of kinetic energy and so the dark matter remains as a large "halo" around gravitationally clumping ordinary matter.
If dark matter only interacts with gravity, why doesn't it all clump together in a single point?
And this one:
A significant portion of the dark matter is known to be gravitationally bound to galaxies and relativistic velocities are far about the escape velocity and the stuff you propose would not remain bound.
Can dark matter be relativistic dust?
I assume that its speed with respect to the Sun will have a distribution with an rms of a few 100 km/s.
Can the Sun capture dark matter gravitationally?
In general particles created at the time of Big Bang are at non relativistic velocities at present .
What is meant by dark matter being non-relativistic and why is this?
The first one says that dark matter cannot lose kinetic energy through interactions.
As far as I understand, most ordinary matter moves at non-relativistic speeds around us because these are able to lose kinetic energy through interactions and thus we see objects made of these particles in the observable universe to be mostly non-relativistic (except for example neutrinos).
Now if dark matter cannot lose kinetic energy, then shouldn't it have most of its kinetic energy from the Big Bang and travel at relativistic speeds? The second one says dark matter is definitely non-relativistic.
Question:
If dark matter can't lose kinetic energy, then why is it not traveling at relativistic speeds?
Best Answer
If dark matter consists of particles that thermally decoupled from the rest of the universe very early, then its momentum distribution with respect to the comoving reference frame was fixed at that point.
As the universe expands, then the characteristic absolute scale of this momentum distribution decreases as the scale length grows.
One way of thinking about this is that the de Broglie wavelength of a particle $\lambda = h/p$, gets stretched by the universal expansion just like the wavelength of light. Hence the rms $p$ (with respect to the comoving reference frame) decreases and the particles become non-relativistic.