# How do we know Dark Matter isn't simply Neutrinos?

What evidence is there that dark matter isn't one of the known types of neutrinos?

If it were, how would this be measurable?

• That'd be typical of neutrinos as well. Never doing what they're meant to... – qubyte Nov 19 '11 at 14:49
• This is a very very good question i've been doing myself all these years. – lurscher Nov 19 '11 at 18:33
• – Qmechanic Jul 4 '12 at 9:13

Dark matter can be hot, warm or cold. Hot means the dark matter particles are relativistic (kinetic energy on the order of the rest mass or much higher), cold means they are not relativistic (kinetic energy much less than rest mass) and warm is in between. It is known that the total amount of dark matter in the universe must be about 5 times the ordinary (baryonic) matter to explain the CMB as measured by WMAP.

However, cold dark matter must be a very significant component of the universe to explain the growth of structures from the small fluctuations in the early universe that grew to become galaxies and stars (see this reference). Thus cold dark matter is also required to explain the currently measured galactic rotation curves.

Now, the neutrino oscillation experiments prove that neutrinos have a non-zero rest mass. However, the rest masses must still be very small so they could only contribute to the hot dark matter. The reason they can only be hot dark matter is because it is assumed that in the early hot, dense universe, the neutrinos would have been in thermal equilibrium with the hot ordinary matter at that time. Since the neutrino's rest mass is so small, they would be extremely relativistic, and although the neutrinos would cool as the universe expands, they would have still been very relativistic at the time of structure formation in the early universe. Thus, they can only contribute to hot dark matter in terms of the early growth of structure formation. [Because of the expansion of the universe since then, the neutrinos should have cooled so much that they are non-relativistic today.]

According to this source:

Current estimates for the neutrino fraction of the Universe’s mass–energy density lie in the range 0.1% <∼ ν <∼ a few %, under standard assumptions. The uncertainty reflects our incomplete knowledge of neutrino properties.

So most cosmic neutrinos are probably less than 10% of the total dark matter in the universe. In addition most of the rest (of the non-neutrino) 90% of dark matter must also be cold dark matter - both in the early universe and even now.

• I've no idea from this answer why there cannot be enough cold neutrinos to explain galactic rotation curves – lurscher Nov 27 '11 at 5:26
• @lurscher - sorry I screwed up and had the same link in the 2nd and 3rd paragraphs. I corrected that just now, so please click on the link in the 2nd paragraph to read why the neutrinos would only be hot DM. Your speculation that the cross section might be much higher than what current electroweak theory would say it is might be true, but then that means neutrinos are not what we currently think they are. All we can say is that our current understanding of neutrinos means that they could only contribute to hot DM and that they could not give the cold DM needed for structure formation. – FrankH Nov 27 '11 at 6:34
• Ok, makes sense as long as we believe neutrinos don't have additional forces that make them lump together at low energies. – lurscher Nov 27 '11 at 14:53
• Yeah, it'd be a pretty weird Universe otherwise – user12345 May 22 '13 at 20:25
• @quuxman - I removed the broken link and added what I remember was the argument of what the link would have said. – FrankH Feb 14 '16 at 8:06

Hot dark matter could be partly neutrinos - but they (probably) don't interact enough to have been resposnible for initial galaxy formation.

• Am I mistaken to conclude that they'd also be unable to explain galaxy rotation curves? Those suggest a halo distribution of dark matter around the centres of galaxies. Neutrino's wouldn't have that spatial distribution, neither when formed in the big bang or in later nuclear reactions. – MSalters Nov 21 '11 at 9:53
• @MSalters: That is, in essence, the reason people distinguish between hot and cold dark matter. To explain both the structure of the cosmos and the rotation curves it has to cool enough to collect in/around galaxies. – dmckee --- ex-moderator kitten Jul 9 '12 at 17:57
• @MSalters Your question is worthy of further discussion. The current estimates of neutrino mass make them non-relativistic now, and capable of being captured by galaxies and clusters. Depending on the exact neutrino mass one could have neutrino density enhancements of factors of 10 around large galaxies. – Rob Jeffries Feb 20 '16 at 9:15
• However, this enhancement would still not provide anywhere near the mass required to explain galaxy rotation curves. – Rob Jeffries Feb 20 '16 at 9:17
• "they (probably) don't interact enough" due to high velocities? – SRS Jun 13 '18 at 9:58

Neutrinos from the big bang have been redshifted to ~2K = ~0.0002 eV, which is considerably lower than the current best upper bound on neutrino rest mass (0.1eV). We have no way to directly detect the flux of neutrinos at this low energy and the indirect methods at deducing it are tentative at best. So primordial neutrinos might indeed be a significant component of Cold/Warm dark matter. We don't know.

• When you refer to "neutrinos from the big bang," what history do you have in mind for them? Would they have gone through some period of thermal equilibrium and then become decoupled? If so, then wouldn't their abundance be constrained by known particle physics? – Ben Crowell Sep 12 '13 at 15:03
• Said upper bound would be extremely high because of neutrinos' extremely low probability of interacting with anything. And such an upper bound should be taken with a large grain of salt until someone unifies QM with relativity. I recall that it would take a light year of lead to block about half of any neutrino flux. Coincidentally, the mass of a cubic light year of lead at 11.3g/cm^3 would be within an order of magnitude of the total mass of the observable universe. I.e. a neutrino would have to cross most of the universe to be reabsorbed, on average. – Jonathan Ray Dec 23 '14 at 22:30
• but you wouldn't need a cubic light year of lead to block any given neutrino, just one light year times the cross-sectional area of the neutrino. although i guess what you are saying is, if you integrate across all primordial neutrinos, you have to have a cubic light year. – Michael Feb 4 '15 at 19:52
• But the same calculations that give you the temperature tell you how many there should be and hence $\Omega_{\nu}\sim 0.003$. – Rob Jeffries Feb 19 '16 at 20:51
• Yeah, this answer isn't right, the calculation yields $\Omega h^2 \simeq \frac{ \sum_i m_i}{93\text{ MeV}}$, see any review on this topic – innisfree Oct 18 '19 at 4:46

Cold neutrinos which clumped together would form a Fermi-Dirac condensate. Unlike electrons in an atom there would be no mutual repulsion and the quantum numbers could increase truly "astronomically". For a large concentrate all but the early neutrino contributors would be far from cold. Such a concentrate would behave like a huge heavy ball of unobservable, very rareified liquid which is exacty what you see in a barred spiral galaxy, the bar is in the liquid where g varies as r and the spiral arms are outside, subject to the inverse square law. Cold neutrinos may have been around since the early universe but another source could be black holes where they may pour out like Hawkinge radiation or as a result of accretion disc annihilation at the event horizon. Either way they would be very cold by the time they had crawled away from the hole.

• The electron electron repulsion doesn't change the atomic occupation number in any qualitative way, it only makes the atoms a little bigger than they would be otherwise, not by a factor of 10. The neutrinos are not assumed cold here, they would have to be moving absurdly slowly for that to happen. Neutrinos are not Hawking emitted until the black hole gets as small the compton wavelength of the neutrino, which isn't infinite (neutrinos are massive). – Ron Maimon Jul 9 '12 at 3:48