Orodruin said:
As was discussed already, CNB neutrinos can have a velocity as low as 0.00005c (for the upper range of allowed masses). The corresponding gamma factor would be of the order 1.000000001.
The problem is one of density, interaction strength, and the fact that coming from outside of a galaxy a neutrino will naturally have a higher speed than the escape velocity to begin with.
But for those neutrinos that make halos around galaxies, wouldn't their velocities be less than the escape velocity so that they would be gravitationally bounded to them? (As I think you said in post #24)
Also, what about bigger gravitationally bounded structures like galaxy clusters and superclusters? Would they also have "halos" made from denser neutrino distributions?
Finally, I contacted with Yvonne Wong on the paper that I cited before, asking her whether neutrinos would be gravitationally bound to other macroscopic structures (e.g. a galaxy, a dark matter halo...etc)
She said that neutrinos fall into the potential wells generated by the cold dark matter (CDM) halos. That is, the assumption is that there is a dominant CDM component that is able to form clumps (which is what observational evidence suggests anyway). So, with the additional attraction of the CDM halo, the neutrinos are able to form a kind of cloud around the CDM halo
If there were no existing CDM structure, then it is true that standard model neutrinos have far too much energy to forming clumps under their own gravity.
So the key thing seems to be the extra gravitational pull by dark matter that makes neutrinos gravitationally bounded to e.g. galaxies. Is that correct?
After that, I asked her two more questions related to we've discussed.
I asked her:
1. In the future of the universe, when neutrinos have cooled down into sufficiently slow speeds, could they clump together under their own gravity?
(After this discussion I expected the answer to be no, but just to confirm)
2. As you say Dark Matter could clump neutrinos together. However, let's say that Dark Matter is composed of particles that decay over long periods of time. Once Dark Matter has decayed and nothing is left, would neutrinos still be clumped under their own gravity (especially if they have sufficiently slow speed)?
She replied to question #1 that in the standard scenario, you should not find neutrinos collapsing under their own gravity even after they become slow enough (which is consistent to what was said here)
For clumps to form you would need density peaks, i.e., regions they act as gravitational sources. In the standard scenario, these are provided by cold dark matter. Now, of course, you could also imagine planets or black holes acting as density peaks, and we cannot preclude that neutrino clumps can form around these objects at a very late time. But we’ll still talking about neutrinos forming clumps around something else, rather than just neutrinos collapsing under their own gravity.
And to question #2 she said that in this scenario it would be possible to have pure neutrino clumps (assuming that the dark matter decays into something even lighter and more weakly interacting than neutrinos, so these particles just fly away).
(Note that when she says "clumps" I think she means "clouds" or "halos" of neutrinos rather than compact structures)
I think her answers were very insightful. Do you have any objections ti what she said? Was there anything wrong?
