<p>It's an interesting but frustrating question. ;)</p>
<p>As you mentioned, we can't detect slow neutrinos. Direct detection of them may never be technically feasible. One answer of the linked question does mentions that there are some <em>possible</em> indirect detection techniques for neutrinos below current thresholds, but detecting the theoretically huge numbers of neutrinos &amp; antineutrinos released &amp; produced during a couple of phases of the Big Bang is a much harder proposition. Those neutrinos have experienced a far greater redshift than the cosmic microwave background. As another answer at that link mentions, the CNB (cosmic neutrino background) redshift is on the order of <span class="math-container">$10^{10}$</span>, compared to the 1100 or so of the CMB.</p>
<p>We can estimate numbers of low energy neutrinos, but there could be some factor that our theories have overlooked, so the numbers <em>might</em> be way off. However, cold slow neutrinos don't have much energy, so even in astronomically huge quantities they don't have much impact on spacetime curvature, certainly not enough to account for all the dark matter that we've indirectly detected via its mass.</p>
<p>According to Wikipedia's article on the <a href="https://en.wikipedia.org/wiki/Lambda-CDM_model" rel="nofollow noreferrer">Lambda CDM</a> cosmological model, the relic neutrinos <em>could</em> account for as much as 0.5% of the universes energy content. OTOH, that's more than the 0.01% due to EM radiation, which is dominated by CMB photons.</p>
<p>Our current most sensitive <a href="https://en.wikipedia.org/wiki/Neutrino_detector" rel="nofollow noreferrer">neutrino detection</a> reaction, the Alsace-Lorraine technique (so-named because it uses a gallium → germanium → gallium sequence) has a threshold of 233 keV. That is, the kinetic energy of those neutrinos is over a quarter of a million times their (rest) mass energy. And our detectors are lucky to catch about 1 neutrino per billion that pass through them. Note that 233 keV is less than half the rest mass energy of an electron (511 keV).</p>
<p>Neutrinos need to be very cold / redshifted to orbit anything (apart from black holes &amp; possibly neutron stars).  Bear in mind that even neutrinos with an eV or so of kinetic energy are <em>still</em> relativistic. So they can be deflected by galaxies and even stars, but they can't get into a closed orbit.</p>
<p>As I said earlier,  the CNB neutrinos are highly redshifted, and so (some of them) <em>can</em> be gravitationally bound to galaxies, and maybe even individual stars. So they are a component of dark matter, but a fairly small one.</p>
<hr />
<p>The bulk of the Big Bang neutrinos (and antineutrinos, the term &quot;neutrino&quot; can cover both types when the difference between them isn't relevant) in the CNB were released during neutrino decoupling, 1 second after the start of the big bang. From <a href="https://en.wikipedia.org/wiki/Neutrino_decoupling" rel="nofollow noreferrer">Wikipedia</a>:</p>
<blockquote>
<p>In Big Bang cosmology, neutrino decoupling was the epoch at which neutrinos ceased interacting with other types of matter, and thereby ceased influencing the dynamics of the universe at early times. Prior to decoupling, neutrinos were in thermal equilibrium with protons, neutrons and electrons, which was maintained through the weak interaction.</p>
<p>Decoupling occurred approximately at the time when the rate of those weak interactions was slower than the rate of expansion of the universe. Alternatively, it was the time when the time scale for weak interactions became greater than the age of the universe at that time. Neutrino decoupling took place approximately one second after the Big Bang, when the temperature of the universe was approximately 10 billion kelvin, or 1 MeV.</p>
</blockquote>
<p>After decoupling, some neutrinos and antineutrinos were released as neutrons converted to protons and vice versa. Proton → neutron conversion normally requires a high energy environment, because neutrons have more mass than protons. Conversely free neutrons are unstable, with a half-life of a little over 10 minutes. There were also some neutrinos produced during <a href="https://en.wikipedia.org/wiki/Big_Bang_nucleosynthesis" rel="nofollow noreferrer">Big Bang nucleosynthesis</a> (which ended about 20 minutes after the Big Bang), as hydrogen was converted to helium. BB nucleosynthesis cleaned up most of the remaining free neutrons.</p>

CC BY-SA 4.0
2020-11-19T23:48:56.683Z
The cosmic neutrino background is non-relativistic (or at least not highly relativistic).
ProfRob
CC BY-SA 4.0
2020-11-19T15:14:21.707Z
2020-11-20T01:16:57.273Z
2020-11-20T01:16:57.273Z
PM 2Ring
<p>These neutrinos would have to be really cold. The cosmic neutrino background is at 1.9K, and they are considered <em>hot</em> dark matter, because they would have been highly relativistic at the epoch of structure formation. To be considered cold dark matter, and also to be captured in orbits in galaxies, the neutrinos would have to be much colder - totally non-relativistic now.</p>
<p>Let's assume an average energy then of about 0.1 eV for each neutrino (similar to their likely rest mass energy). In order to account for <span class="math-container">$\Omega_{\rm CDM}\sim 0.3$</span> there would need to be <span class="math-container">$5\times 10^{10}$</span> per cubic metre, or about <span class="math-container">$10^{10}$</span> per cubic metre per flavour, <em>on average</em> over the universe.</p>
<p>To account for dark matter in galaxies (e.g. the Milky Way) we need <span class="math-container">$\sim 10^{12} M_\odot$</span> within about 100 kpc, meaning a number density of neutrinos of <span class="math-container">$10^{14}$</span> per cubic metre.</p>
<p>These neutrinos are spin 1/2 fermions and thus would have a Fermi energy of about <span class="math-container">$5\times 10^{-3}$</span> eV. That would mean if they were any colder than 6 K, they would be degenerate and exert a degeneracy pressure. This would be sufficient to prevent the halos forming - <a href="https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.42.407" rel="nofollow noreferrer">Tremaine &amp; Gunn (1979)</a> showed that cold dark matter halos cannot be made from low mass leptons like standard neutrinos.</p>
<p>Edits:</p>
<p>A back of the envelope Tremaine-Gunn limit (see also <a href="https://arxiv.org/abs/0808.3902" rel="nofollow noreferrer">Boyarsky et al. 2009</a>) is to assume that the escape speed of the galaxy is <span class="math-container">$v$</span>, it's dark matter halos has radius <span class="math-container">$r$</span>, the total mass is <span class="math-container">$M$</span> and the neutrino mass is <span class="math-container">$m$</span>.</p>
<p>The number of available quantum states to spin half fermions in this volume, up to a momentum <span class="math-container">$mv$</span> is
<span class="math-container">$$ N = \left(\frac{4\pi r^3}{3}\right) \left(\frac{8\pi}{3}\right) \left(\frac{mv}{h}\right)^3$$</span>
We can write
<span class="math-container">$$ v = \left(\frac{2GM}{r}\right)^{1/2}.$$</span>
The mass contained in these particles cannot be greater than if every quantum state is filled by one fermion of mass <span class="math-container">$m$</span> and if this is to explain dark matter, then this mass must be <span class="math-container">$\sim M$</span>. Thus
<span class="math-container">$$M &lt; m\left(\frac{4\pi r^3}{3}\right) \left(\frac{8\pi}{3}\right) \left(\frac{m\sqrt{2GM/r}}{h}\right)^3$$</span>
and
<span class="math-container">$$mc^2 &gt; 8.9\left(\frac{r}{\rm 100 kpc}\right)^{-3/8} \left(\frac{M}{10^{12}M_\odot}\right)^{-1/8}\ {\rm eV}\ .$$</span>
Thus there are not enough quantum states to accommodate a halo of fermions unless their rest mass energies exceed about 10 eV. For neutrinos, there are 3 flavours and anti particles, which reduces this number by <span class="math-container">$6^{1/4}$</span>, but conversely it must be increased because particles in the halo cannot be uniformly distributed in velocity between 0 and <span class="math-container">$v$</span>.</p>
<p>10 ev is about two orders of magnitude larger than the likely rest masses of the known neutrinos.</p>
<p>The idea that neutrinos from stars can make any contribution to dark matter halos is untenable. The vast majority of solar neutrinos have energies above 0.1 MeV, and so for an assumed neutrino rest mass energy of <span class="math-container">$\sim 0.1$</span> eV, they have Lorentz factors that exceed <span class="math-container">$10^6$</span> - i.e. they travel exceedingly close to the speed of light and are not confined to galaxies. The neutrinos emitted during supernova explosions are even more energetic. Secondly, even if you invent a magical process that can produce neutrinos with kinetic energies less than 0.1 eV, you still have the Tremaine-Gunn limit to overcome <em>and</em> even if <em>all</em> the rest mass of all the stars in a galaxy was converted into neutrinos, that mass would still fall short by more than an order of magnitude of that required to explain dark matter in galaxies. You cannot imagine that the neutrinos would &quot;pile up&quot; over time because the vast majority of the mass that has ever been turned into stars is still in the form of stars today and the stars that have already lived and died are a tiny percentage of the required dark matter mass.</p>

CC BY-SA 4.0
2020-11-20T16:21:07.110Z
By cosmic neutrinos you mean neutrinos formed in the Big Bang. I was rather thinking about 'modern' neutrinos constantly spewed by stars. The ones going below galactic escape velocity will just pile up...forever..  and form a cloud.  "The flux of solar neutrinos at the earth's surface is on the order of 10\11 per square centimeter per second" http://www.sns.ias.edu/~jnb/Papers/Popular/Scientificamerican69/scientificamerican69.html
Mark Besser
CC BY-SA 4.0
2020-11-20T17:00:49.407Z
@MarkBesser But they would have to be really cold. How does their origin change that? The neutrinos emitted by stars are basically travelling at $c$. It is also fairly clear that the rest-mass energy in stellar neutrinos can't exceed the mass of the stars that produced them, and stars are a minor component of the matter density of the universe.
ProfRob
CC BY-SA 4.0
2020-11-20T19:08:11.507Z
Neutrinos emitted by stars would not have helped explain early structure formation either.
ProfRob
CC BY-SA 4.0
2020-11-21T01:27:38.850Z
I am assuming neutrinos are produced at all speeds, and those below galactic/cluster escape velocity will simply accumulate, indefinitely... and the path one would imagine for them somewhat resembles the dark matter halos. Early structure: yes, then the 'cosmic' (Big Bang) ones played a role. Not today, you nailed it - ll'be too cold.
Mark Besser
CC BY-SA 4.0
2020-11-23T12:37:13.273Z
~"The neutrinos emitted by stars are basically travelling at c"~ That's where the detection survivorship bias comes in. We don't know that they are not produced at all speeds. ~" It is also fairly clear that the rest-mass energy in stellar neutrinos can't exceed the mass of the stars that produced them, and stars are a minor component of the matter density of the universe."~ yes, but they accumulate, they pile up. Were I to risk a hunch I'd say maybe around 50% of cdm are slow modern (stellar) neutrinos emitted in the past, accumulating over time, and the other 50% something else.
Mark Besser
CC BY-SA 4.0
2020-11-23T12:41:53.717Z
@MarkBesser - besides ripping up nuclear physics and the Pauli Exclusion Principle - how do you propose that neutrinos emitted from stars can comprise about 20 times the masses of the stars themselves? Most of the stars that were ever born (containing the vast majority of the stellar mass) are still alive now.
ProfRob
CC BY-SA 4.0
2020-11-24T14:38:59.103Z
yes 50% is a tad high, 10-20% is more likely. on the other hand, the ultra-cold cosmic neutrinos you thought of... there is nothing wrong with them (unless they decay; we do not know yet). As to most stars being alive, first-generation / population III stars are certainly not and should have also made a sizable contribution - https://www.eso.org/public/news/eso1524/. There has to be several components to DM; I agree the widespread proportions of dark to visible matter - https://www.nature.com/articles/s41550-019-0930-9 - do suggest undiscovered particles or phenomena.
Mark Besser
CC BY-SA 4.0
2020-11-24T15:53:41.800Z
@MarkBesser there weren't enough of these massive stars. Even if they converted ALL their rest mass into neutrinos (which they don't) they would have to have a time-integrated mass that is equal to all the luminous matter that can be seen in the universe today in order to account for 10% of the dark matter, which is nowhere near true. Ultra-cold cosmic neutrinos produced by some other mechanism than the C$\nu$B wouldn't overcome the Tremain-Gunn phase-space argument. They would have to be massive as well. e.g.something like sterile neutrinos. Not the neutrinos we know about.
ProfRob
CC BY-SA 4.0
2020-11-25T13:22:56.250Z
i see. yet "20x visible mass" is only if dark energy is included. I am proposing slow (below local galactic / cluster escape velocity) neutrinos as a fraction (which you point out will be minor) of cold dm and 'fast', of hot, what percentages could we be talking about? Slightly off topic, would you happen to have any hunches of dm cold composition beyond 'some unknown particle or hypothetical brane superposition phenomena'? (and the multiple-component approach would seem self-evident given machos alone - would you agree?)
Mark Besser
CC BY-SA 4.0
2020-11-25T14:41:00.337Z
@MarkBesser Most baryonic matter is dark and most matter is non-baryonic. The fraction of matter seen as stars is about 1% of the critical density. Ergo, neutrinos pruduced by stars cannot even be 1% of the critical density, wher the total matter density is 30%.  Therefore no more than a very small fraction << 1 part in 20 of dark matter.
ProfRob
CC BY-SA 4.0
2020-11-30T14:25:40.967Z
of course, and thank you. we should really be looking at mapping the several components of dm rather than looking for a single solution. one last question - what happens to old neutrinos as they cool - do they expand in wavelength as photons or slow down as molecules? because if they slow down all relativistic neutrinos become "slow" eventually  (<local galactic/cluster escape velocity) and thus turn to a component of cold dm, no?
Mark Besser
CC BY-SA 4.0
2020-11-30T14:36:13.153Z
@MarkBesser cold DM refers to them being cold at the epoch when structures were formed. It is not a description of their current state. Neutrinos from the big bang are not currently ultrarelativistic and, depending on their exact rest masses, they will have started to "accumulate" or be focused by gravitational wells, but are still moving way to fast to be captured. The neutrinos have a frozen-in momentum distribution, but the momentum (with respect to the local co-moving volme) will decrease as the scale factor expands.
ProfRob
CC BY-SA 4.0
2020-11-30T14:42:51.547Z
@MarkBesser see https://physics.stackexchange.com/a/268348/43351
ProfRob
CC BY-SA 4.0
2021-06-03T06:23:56.020Z
finally some common sense https://www.scientificamerican.com/article/maybe-dark-matter-is-more-than-one-thing/
Mark Besser
CC BY-SA 4.0
2021-06-03T20:53:08.523Z
@MarkBesser unless I missed something, that opinion piece makes no mention of neutrinos at all.
ProfRob
CC BY-SA 4.0
2021-06-04T23:50:41.413Z
Certainly one can understand the spirit, not the letter of "Maybe Dark Matter Is More Than One Thing"; I was putting slow cold neutrinos at 5-15%, specifically in the shape and behavior of the galactic halos. I think DM is several things we still don't know about and each part of it - galactic rotation curve (old slow cold) fossil neutrinos, CMB ripple being whatever, intercluster cohesion being cold (10K) diffuse (1  atom m3) h2, the overexited cosmic constant something else altogether, and so forth - caused by a separate component.
Mark Besser
CC BY-SA 4.0
2021-06-05T04:43:25.717Z
We don't detect neutrinos unless they're energetic. We don't detect diffuse EGM unless it's at a million degrees. What dark matter is, is several sorts of detection bias limitations.
Mark Besser
CC BY-SA 4.0
2020-11-20T08:33:18.363Z
2020-11-23T13:10:31.557Z
2020-11-23T13:10:31.557Z
ProfRob
<p>Cold dark matter is the type of dark matter that is most eminently neutrino-free. But neutrinos themselves suffer a large survivorship detection bias (“all the neutrinos you can detect necessarily have to have relativistic speeds”) <a href="https://physics.stackexchange.com/questions/267035/where-are-all-the-slow-neutrinos">https://physics.stackexchange.com/questions/267035/where-are-all-the-slow-neutrinos</a></p>
<p>By the same principle that there are more pebbles than boulders, and more red dwarfs than blue giants, slow neutrinos should be more abundant than the fast, detectable ones.</p>
<p>Non-relativistic (slow) neutrinos - in particular those going at below the galactic escape velocity - could be a major competent of cold dark matter: slow neutrinos could be slow enough to orbit galaxies and galactic clusters and thus form a significant amount of cdm, which should be shaped as a galactic halo.</p>
<p>If neutrinos are produced at all speeds, those stellar (modern) neutrinos below galactic escape velocity will accumulate indefinitely. This should generate a halo-shaped cloud, and this could comprise a large part (of course 15% are MACHOs etc <a href="https://ned.ipac.caltech.edu/level5/Sept17/Freese/Freese4.html" rel="nofollow noreferrer">https://ned.ipac.caltech.edu/level5/Sept17/Freese/Freese4.html</a> - I am assuming here a multi-component DM) of cold dark matter.</p>

CC BY-SA 4.0
2020-11-23T15:19:20.120Z
Regarding MACHOS - a more modern limit (from EROS and OGLE) is <10% of the dark halo can be composed of objects between about $10^{-6}$ and 1 solar masses (e.g. planets, brown dwarfs, cold white dwarfs etc.).  https://arxiv.org/pdf/2002.12778.pdf
ProfRob
<dark-matter><neutrinos>
Could not slow neutrinos orbit galaxies and clusters, thus comprising a large component of even COLD dark matter?
Mark Besser
# Could not slow neutrinos orbit galaxies and clusters, thus comprising a large component of even COLD dark matter?

(Asked by: username_0 on 2020-11-19)

Cold dark matter is the type of dark matter that is most eminently neutrino-free. But neutrinos themselves suffer a large survivorship detection bias (“all the neutrinos you can detect necessarily have to have relativistic speeds”) <https://physics.stackexchange.com/questions/267035/where-are-all-the-slow-neutrinos>

By the same principle that there are more pebbles than boulders, and more red dwarfs than blue giants, slow neutrinos should be more abundant than the fast, detectable ones.

Non-relativistic (slow) neutrinos - in particular those going at below the galactic escape velocity - could be a major competent of cold dark matter: slow neutrinos could be slow enough to orbit galaxies and galactic clusters and thus form a significant amount of cdm, which should be shaped as a galactic halo.

If neutrinos are produced at all speeds, those stellar (modern) neutrinos below galactic escape velocity will accumulate indefinitely. This should generate a halo-shaped cloud, and this could comprise a large part (of course 15% are MACHOs etc <https://ned.ipac.caltech.edu/level5/Sept17/Freese/Freese4.html> - I am assuming here a multi-component DM) of cold dark matter.

**Tags:** dark-matter, neutrinos
> **Comments:**
> **username_1**: Regarding MACHOS - a more modern limit (from EROS and OGLE) is <10% of the dark halo can be composed of objects between about $10^{-6}$ and 1 solar masses (e.g. planets, brown dwarfs, cold white dwarfs etc.).  https://arxiv.org/pdf/2002.12778.pdf  

---

## 2 answers

### Answer by username_1 on 2020-11-20. Score: 11 | Accepted answer

These neutrinos would have to be really cold. The cosmic neutrino background is at 1.9K, and they are considered *hot* dark matter, because they would have been highly relativistic at the epoch of structure formation. To be considered cold dark matter, and also to be captured in orbits in galaxies, the neutrinos would have to be much colder - totally non-relativistic now.

Let's assume an average energy then of about 0.1 eV for each neutrino (similar to their likely rest mass energy). In order to account for $\Omega\_{\rm CDM}\sim 0.3$ there would need to be $5\times 10^{10}$ per cubic metre, or about $10^{10}$ per cubic metre per flavour, *on average* over the universe.

To account for dark matter in galaxies (e.g. the Milky Way) we need $\sim 10^{12} M\_\odot$ within about 100 kpc, meaning a number density of neutrinos of $10^{14}$ per cubic metre.

These neutrinos are spin 1/2 fermions and thus would have a Fermi energy of about $5\times 10^{-3}$ eV. That would mean if they were any colder than 6 K, they would be degenerate and exert a degeneracy pressure. This would be sufficient to prevent the halos forming - [Tremaine & Gunn (1979)](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.42.407) showed that cold dark matter halos cannot be made from low mass leptons like standard neutrinos.

Edits:

A back of the envelope Tremaine-Gunn limit (see also [Boyarsky et al. 2009](https://arxiv.org/abs/0808.3902)) is to assume that the escape speed of the galaxy is $v$, it's dark matter halos has radius $r$, the total mass is $M$ and the neutrino mass is $m$.

The number of available quantum states to spin half fermions in this volume, up to a momentum $mv$ is
$$ N = \left(\frac{4\pi r^3}{3}\right) \left(\frac{8\pi}{3}\right) \left(\frac{mv}{h}\right)^3$$
We can write
$$ v = \left(\frac{2GM}{r}\right)^{1/2}.$$
The mass contained in these particles cannot be greater than if every quantum state is filled by one fermion of mass $m$ and if this is to explain dark matter, then this mass must be $\sim M$. Thus
$$M < m\left(\frac{4\pi r^3}{3}\right) \left(\frac{8\pi}{3}\right) \left(\frac{m\sqrt{2GM/r}}{h}\right)^3$$
and
$$mc^2 > 8.9\left(\frac{r}{\rm 100 kpc}\right)^{-3/8} \left(\frac{M}{10^{12}M\_\odot}\right)^{-1/8}\ {\rm eV}\ .$$
Thus there are not enough quantum states to accommodate a halo of fermions unless their rest mass energies exceed about 10 eV. For neutrinos, there are 3 flavours and anti particles, which reduces this number by $6^{1/4}$, but conversely it must be increased because particles in the halo cannot be uniformly distributed in velocity between 0 and $v$.

10 ev is about two orders of magnitude larger than the likely rest masses of the known neutrinos.

The idea that neutrinos from stars can make any contribution to dark matter halos is untenable. The vast majority of solar neutrinos have energies above 0.1 MeV, and so for an assumed neutrino rest mass energy of $\sim 0.1$ eV, they have Lorentz factors that exceed $10^6$ - i.e. they travel exceedingly close to the speed of light and are not confined to galaxies. The neutrinos emitted during supernova explosions are even more energetic. Secondly, even if you invent a magical process that can produce neutrinos with kinetic energies less than 0.1 eV, you still have the Tremaine-Gunn limit to overcome *and* even if *all* the rest mass of all the stars in a galaxy was converted into neutrinos, that mass would still fall short by more than an order of magnitude of that required to explain dark matter in galaxies. You cannot imagine that the neutrinos would "pile up" over time because the vast majority of the mass that has ever been turned into stars is still in the form of stars today and the stars that have already lived and died are a tiny percentage of the required dark matter mass.

> **Comments:**
> **username_0**: By cosmic neutrinos you mean neutrinos formed in the Big Bang. I was rather thinking about 'modern' neutrinos constantly spewed by stars. The ones going below galactic escape velocity will just pile up...forever..  and form a cloud.  "The flux of solar neutrinos at the earth's surface is on the order of 10\11 per square centimeter per second" http://www.sns.ias.edu/~jnb/Papers/Popular/Scientificamerican69/scientificamerican69.html  
> **username_1**: @MarkBesser But they would have to be really cold. How does their origin change that? The neutrinos emitted by stars are basically travelling at $c$. It is also fairly clear that the rest-mass energy in stellar neutrinos can't exceed the mass of the stars that produced them, and stars are a minor component of the matter density of the universe.  
> **username_1**: Neutrinos emitted by stars would not have helped explain early structure formation either.  
> **username_0**: I am assuming neutrinos are produced at all speeds, and those below galactic/cluster escape velocity will simply accumulate, indefinitely... and the path one would imagine for them somewhat resembles the dark matter halos. Early structure: yes, then the 'cosmic' (Big Bang) ones played a role. Not today, you nailed it - ll'be too cold.  
> **username_0**: ~"The neutrinos emitted by stars are basically travelling at c"~ That's where the detection survivorship bias comes in. We don't know that they are not produced at all speeds. ~" It is also fairly clear that the rest-mass energy in stellar neutrinos can't exceed the mass of the stars that produced them, and stars are a minor component of the matter density of the universe."~ yes, but they accumulate, they pile up. Were I to risk a hunch I'd say maybe around 50% of cdm are slow modern (stellar) neutrinos emitted in the past, accumulating over time, and the other 50% something else.  
> **username_1**: @MarkBesser - besides ripping up nuclear physics and the Pauli Exclusion Principle - how do you propose that neutrinos emitted from stars can comprise about 20 times the masses of the stars themselves? Most of the stars that were ever born (containing the vast majority of the stellar mass) are still alive now.  
> **username_0**: yes 50% is a tad high, 10-20% is more likely. on the other hand, the ultra-cold cosmic neutrinos you thought of... there is nothing wrong with them (unless they decay; we do not know yet). As to most stars being alive, first-generation / population III stars are certainly not and should have also made a sizable contribution - https://www.eso.org/public/news/eso1524/. There has to be several components to DM; I agree the widespread proportions of dark to visible matter - https://www.nature.com/articles/s41550-019-0930-9 - do suggest undiscovered particles or phenomena.  
> **username_1**: @MarkBesser there weren't enough of these massive stars. Even if they converted ALL their rest mass into neutrinos (which they don't) they would have to have a time-integrated mass that is equal to all the luminous matter that can be seen in the universe today in order to account for 10% of the dark matter, which is nowhere near true. Ultra-cold cosmic neutrinos produced by some other mechanism than the C$\nu$B wouldn't overcome the Tremain-Gunn phase-space argument. They would have to be massive as well. e.g.something like sterile neutrinos. Not the neutrinos we know about.  
> **username_0**: i see. yet "20x visible mass" is only if dark energy is included. I am proposing slow (below local galactic / cluster escape velocity) neutrinos as a fraction (which you point out will be minor) of cold dm and 'fast', of hot, what percentages could we be talking about? Slightly off topic, would you happen to have any hunches of dm cold composition beyond 'some unknown particle or hypothetical brane superposition phenomena'? (and the multiple-component approach would seem self-evident given machos alone - would you agree?)  
> **username_1**: @MarkBesser Most baryonic matter is dark and most matter is non-baryonic. The fraction of matter seen as stars is about 1% of the critical density. Ergo, neutrinos pruduced by stars cannot even be 1% of the critical density, wher the total matter density is 30%.  Therefore no more than a very small fraction << 1 part in 20 of dark matter.  
> **username_0**: of course, and thank you. we should really be looking at mapping the several components of dm rather than looking for a single solution. one last question - what happens to old neutrinos as they cool - do they expand in wavelength as photons or slow down as molecules? because if they slow down all relativistic neutrinos become "slow" eventually  (<local galactic/cluster escape velocity) and thus turn to a component of cold dm, no?  
> **username_1**: @MarkBesser cold DM refers to them being cold at the epoch when structures were formed. It is not a description of their current state. Neutrinos from the big bang are not currently ultrarelativistic and, depending on their exact rest masses, they will have started to "accumulate" or be focused by gravitational wells, but are still moving way to fast to be captured. The neutrinos have a frozen-in momentum distribution, but the momentum (with respect to the local co-moving volme) will decrease as the scale factor expands.  
> **username_1**: @MarkBesser see https://physics.stackexchange.com/a/268348/43351  
> **username_0**: finally some common sense https://www.scientificamerican.com/article/maybe-dark-matter-is-more-than-one-thing/  
> **username_1**: @MarkBesser unless I missed something, that opinion piece makes no mention of neutrinos at all.  
> **username_0**: Certainly one can understand the spirit, not the letter of "Maybe Dark Matter Is More Than One Thing"; I was putting slow cold neutrinos at 5-15%, specifically in the shape and behavior of the galactic halos. I think DM is several things we still don't know about and each part of it - galactic rotation curve (old slow cold) fossil neutrinos, CMB ripple being whatever, intercluster cohesion being cold (10K) diffuse (1  atom m3) h2, the overexited cosmic constant something else altogether, and so forth - caused by a separate component.  
> **username_0**: We don't detect neutrinos unless they're energetic. We don't detect diffuse EGM unless it's at a million degrees. What dark matter is, is several sorts of detection bias limitations.  

---

### Answer by username_2 on 2020-11-19. Score: 4

It's an interesting but frustrating question. ;)

As you mentioned, we can't detect slow neutrinos. Direct detection of them may never be technically feasible. One answer of the linked question does mentions that there are some *possible* indirect detection techniques for neutrinos below current thresholds, but detecting the theoretically huge numbers of neutrinos & antineutrinos released & produced during a couple of phases of the Big Bang is a much harder proposition. Those neutrinos have experienced a far greater redshift than the cosmic microwave background. As another answer at that link mentions, the CNB (cosmic neutrino background) redshift is on the order of $10^{10}$, compared to the 1100 or so of the CMB.

We can estimate numbers of low energy neutrinos, but there could be some factor that our theories have overlooked, so the numbers *might* be way off. However, cold slow neutrinos don't have much energy, so even in astronomically huge quantities they don't have much impact on spacetime curvature, certainly not enough to account for all the dark matter that we've indirectly detected via its mass.

According to Wikipedia's article on the [Lambda CDM](https://en.wikipedia.org/wiki/Lambda-CDM_model) cosmological model, the relic neutrinos *could* account for as much as 0.5% of the universes energy content. OTOH, that's more than the 0.01% due to EM radiation, which is dominated by CMB photons.

Our current most sensitive [neutrino detection](https://en.wikipedia.org/wiki/Neutrino_detector) reaction, the Alsace-Lorraine technique (so-named because it uses a gallium → germanium → gallium sequence) has a threshold of 233 keV. That is, the kinetic energy of those neutrinos is over a quarter of a million times their (rest) mass energy. And our detectors are lucky to catch about 1 neutrino per billion that pass through them. Note that 233 keV is less than half the rest mass energy of an electron (511 keV).

Neutrinos need to be very cold / redshifted to orbit anything (apart from black holes & possibly neutron stars). Bear in mind that even neutrinos with an eV or so of kinetic energy are *still* relativistic. So they can be deflected by galaxies and even stars, but they can't get into a closed orbit.

As I said earlier, the CNB neutrinos are highly redshifted, and so (some of them) *can* be gravitationally bound to galaxies, and maybe even individual stars. So they are a component of dark matter, but a fairly small one.

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The bulk of the Big Bang neutrinos (and antineutrinos, the term "neutrino" can cover both types when the difference between them isn't relevant) in the CNB were released during neutrino decoupling, 1 second after the start of the big bang. From [Wikipedia](https://en.wikipedia.org/wiki/Neutrino_decoupling):

> In Big Bang cosmology, neutrino decoupling was the epoch at which neutrinos ceased interacting with other types of matter, and thereby ceased influencing the dynamics of the universe at early times. Prior to decoupling, neutrinos were in thermal equilibrium with protons, neutrons and electrons, which was maintained through the weak interaction.
>
> Decoupling occurred approximately at the time when the rate of those weak interactions was slower than the rate of expansion of the universe. Alternatively, it was the time when the time scale for weak interactions became greater than the age of the universe at that time. Neutrino decoupling took place approximately one second after the Big Bang, when the temperature of the universe was approximately 10 billion kelvin, or 1 MeV.

After decoupling, some neutrinos and antineutrinos were released as neutrons converted to protons and vice versa. Proton → neutron conversion normally requires a high energy environment, because neutrons have more mass than protons. Conversely free neutrons are unstable, with a half-life of a little over 10 minutes. There were also some neutrinos produced during [Big Bang nucleosynthesis](https://en.wikipedia.org/wiki/Big_Bang_nucleosynthesis) (which ended about 20 minutes after the Big Bang), as hydrogen was converted to helium. BB nucleosynthesis cleaned up most of the remaining free neutrons.

> **Comments:**
> **username_1**: The cosmic neutrino background is non-relativistic (or at least not highly relativistic).  

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