<p>For realistic values of the small, but non-zero, mass of at least some of the neutrino families, the vast numbers of cosmic background neutrinos (currently at a temperature of around 2.3 K) are not highly relativistic. As such, depending on their actual masses and hence speeds, they <em>will</em> &quot;clump&quot; around <em>pre-exisiting</em> concentrations of mass in the present-day universe - i.e. galaxy clusters and galaxies that have escape velocities in the regions of thousands to hundreds of km/s respectively. This clumping tendency will increase into the future as the neutrinos lose energy due to the cosmic expansion.</p>
<p>The average speed of the neutrinos is given by (see <a href="https://arxiv.org/abs/1404.0680" rel="nofollow noreferrer">Safdi et al. 2014</a>).
<span class="math-container">$$\left&lt;v\right&gt; = 160 \left(\frac{m_{\nu} c^2}{{\rm eV}}\right)^{-1} \ (1+z)\ \ \ {\rm km/s}$$</span></p>
<p>Neutrino masses are not fully constrained. At least two of the three flavours must have masses <span class="math-container">$0.05&lt;m_{\nu}c^2 &lt;2$</span> eV that make them non-relativistic at the current epoch. The total neutrino mass (all three flavours) is probably less than 2 eV from beta decay experiments; but some cosmological constraints using galaxy clustering data and the cosmic microwave background suggest this could be as low as <span class="math-container">$&lt;0.5$</span> eV (<a href="http://arxiv.org/abs/1306.5544" rel="nofollow noreferrer">Guisarma et al. 2013</a>).</p>
<p>Thus neutrino speeds are likely to be low enough (<span class="math-container">$m_{\nu}c^2 \sim 0.2$</span> eV; <span class="math-container">$\left&lt;v\right&gt; \sim 800$</span> km/s), that they are affected by the gravitational potentials of galaxies and galaxy clusters, and that some have low enough energies to become bound to those structures. Some simuations of how the cosmic neutrino background might become &quot;clumped&quot; are provided by <a href="https://arxiv.org/abs/hep-ph/0408241" rel="nofollow noreferrer">Ringwald &amp; Wong (2004)</a>.</p>
<p>Since the momentum distribution of the neutrinos is &quot;stretched&quot; by a factor of <span class="math-container">$(1+z)$</span> as the universe expands, then once the neutrinos are non-relativistic, their kinetic energies scale as <span class="math-container">$(1+z)^2$</span>. This means that the tendency of cosmic background neutrinos to clump around cosmic structures increases as the universe expands.</p>

CC BY-SA 4.0
2024-06-04T10:41:51.060Z
thanks. Do you have any references and papers talking about how neutrinos be gravitationally attracted this way? Do the papers that you already linked talk about this? Also, if baryonic matter making galaxies will disappear in the future (for example, through proton decay, if it occurs) will the neutrinos still be gravitationally bounded (since they have mass, couldn't they still be bounded by attracting each other)? @ProfRob
vengaq
CC BY-SA 4.0
2024-06-04T10:50:14.193Z
@vengaq you could look at the papers I've referenced. Why would proton decay lead to mass disappearing from the universe? I've added a reference to Ringwald & Wong (2004) who show some simulations.
ProfRob
CC BY-SA 4.0
2024-06-24T08:42:17.730Z
I mean, if the proton decays, wouldn't the resulting particles be ejected or create antiparticles that could annihilate with other particles? If the mass is dispersed or maybe transformed into energy this way, would neutrinos stay clumped? @ProfRob
vengaq
CC BY-SA 4.0
2024-05-30T12:48:55.597Z
2024-06-04T10:52:30.793Z
2024-06-04T10:52:30.793Z
ProfRob
<p>I was wondering whether (standard model) neutrinos could form clumped structures (like halos perhaps). The problem with this is that neutrinos have a very light mass, have a great speed and do not really have a way to radiate excess energy.</p>
<p>However, I found these works (<a href="https://academic.oup.com/mnras/article/434/3/2679/1046015" rel="noreferrer">https://academic.oup.com/mnras/article/434/3/2679/1046015</a> ; <a href="https://arxiv.org/pdf/astro-ph/9707285" rel="noreferrer">https://arxiv.org/pdf/astro-ph/9707285</a> ; <a href="https://franciscovillaescusa.github.io/neutrinos.html" rel="noreferrer">https://franciscovillaescusa.github.io/neutrinos.html</a>) where the authors seem to indicate that there could be halos of hot dark matter (or halos made by standard model neutrinos). But I have talked with some physicists about this possibility and they were very skeptical, saying that with the current age of the universe it is impossible for neutrinos to form bound structures (mainly because they are light and relativistic).</p>
<p>But I was thinking, could this happen in the future? I mean, once standard neutrinos lose enough kinetic energy with time and become non-relativistic, as they have non-zero mass, couldn't they clump together to form structures like halos? Are there any references discussing this?</p>

CC BY-SA 4.0
2024-05-30T11:59:42.830Z
https://www.nytimes.com/2020/07/07/science/neutrinos-snowball-randall-munroe.html
Mithoron
CC BY-SA 4.0
2024-05-30T12:05:33.603Z
And in Lem's "Solaris" there were *people* made of neutrinos! So, general idea isn't new, but what would slow them down is indeed the issue. Perhaps cold neutron stars and black dwarfs in the far future.
Mithoron
CC BY-SA 4.0
2024-05-30T12:13:46.890Z
Maybe. Most of the neutrinos are in the [cosmic neutrino background](https://en.wikipedia.org/wiki/Cosmic_neutrino_background) (CNB), and due to the expansion of space those neutrinos have now been redshifted to non-relativistic speeds. OTOH, all of our neutrino detection mechanisms require highly relativistic neutrinos. I have some info here: https://physics.stackexchange.com/a/795389/123208
PM 2Ring
CC BY-SA 4.0
2024-05-30T12:17:23.723Z
Related: https://astronomy.stackexchange.com/q/39945/16685
PM 2Ring
<astrophysics><cosmology><gas><neutrinos><galactic-halo>
References about neutrinos getting clumped in "structures" in the future?
vengaq
# References about neutrinos getting clumped in "structures" in the future?

(Asked by: username_0 on 2024-05-30)

I was wondering whether (standard model) neutrinos could form clumped structures (like halos perhaps). The problem with this is that neutrinos have a very light mass, have a great speed and do not really have a way to radiate excess energy.

However, I found these works (<https://academic.oup.com/mnras/article/434/3/2679/1046015> ; <https://arxiv.org/pdf/astro-ph/9707285> ; <https://franciscovillaescusa.github.io/neutrinos.html>) where the authors seem to indicate that there could be halos of hot dark matter (or halos made by standard model neutrinos). But I have talked with some physicists about this possibility and they were very skeptical, saying that with the current age of the universe it is impossible for neutrinos to form bound structures (mainly because they are light and relativistic).

But I was thinking, could this happen in the future? I mean, once standard neutrinos lose enough kinetic energy with time and become non-relativistic, as they have non-zero mass, couldn't they clump together to form structures like halos? Are there any references discussing this?

**Tags:** astrophysics, cosmology, gas, neutrinos, galactic-halo

> **Comments:**
> **username_1**: https://www.nytimes.com/2020/07/07/science/neutrinos-snowball-randall-munroe.html  
> **username_1**: And in Lem's "Solaris" there were *people* made of neutrinos! So, general idea isn't new, but what would slow them down is indeed the issue. Perhaps cold neutron stars and black dwarfs in the far future.  
> **username_2**: Maybe. Most of the neutrinos are in the [cosmic neutrino background](https://en.wikipedia.org/wiki/Cosmic_neutrino_background) (CNB), and due to the expansion of space those neutrinos have now been redshifted to non-relativistic speeds. OTOH, all of our neutrino detection mechanisms require highly relativistic neutrinos. I have some info here: https://physics.stackexchange.com/a/795389/123208  
> **username_2**: Related: https://astronomy.stackexchange.com/q/39945/16685  

---

## 1 answers

### Answer by username_3 on 2024-05-30. Score: 10

For realistic values of the small, but non-zero, mass of at least some of the neutrino families, the vast numbers of cosmic background neutrinos (currently at a temperature of around 2.3 K) are not highly relativistic. As such, depending on their actual masses and hence speeds, they *will* "clump" around *pre-exisiting* concentrations of mass in the present-day universe - i.e. galaxy clusters and galaxies that have escape velocities in the regions of thousands to hundreds of km/s respectively. This clumping tendency will increase into the future as the neutrinos lose energy due to the cosmic expansion.

The average speed of the neutrinos is given by (see [Safdi et al. 2014](https://arxiv.org/abs/1404.0680)).
$$\left<v\right> = 160 \left(\frac{m\_{\nu} c^2}{{\rm eV}}\right)^{-1} \ (1+z)\ \ \ {\rm km/s}$$

Neutrino masses are not fully constrained. At least two of the three flavours must have masses $0.05<m\_{\nu}c^2 <2$ eV that make them non-relativistic at the current epoch. The total neutrino mass (all three flavours) is probably less than 2 eV from beta decay experiments; but some cosmological constraints using galaxy clustering data and the cosmic microwave background suggest this could be as low as $<0.5$ eV ([Guisarma et al. 2013](http://arxiv.org/abs/1306.5544)).

Thus neutrino speeds are likely to be low enough ($m\_{\nu}c^2 \sim 0.2$ eV; $\left<v\right> \sim 800$ km/s), that they are affected by the gravitational potentials of galaxies and galaxy clusters, and that some have low enough energies to become bound to those structures. Some simuations of how the cosmic neutrino background might become "clumped" are provided by [Ringwald & Wong (2004)](https://arxiv.org/abs/hep-ph/0408241).

Since the momentum distribution of the neutrinos is "stretched" by a factor of $(1+z)$ as the universe expands, then once the neutrinos are non-relativistic, their kinetic energies scale as $(1+z)^2$. This means that the tendency of cosmic background neutrinos to clump around cosmic structures increases as the universe expands.

> **Comments:**
> **username_0**: thanks. Do you have any references and papers talking about how neutrinos be gravitationally attracted this way? Do the papers that you already linked talk about this? Also, if baryonic matter making galaxies will disappear in the future (for example, through proton decay, if it occurs) will the neutrinos still be gravitationally bounded (since they have mass, couldn't they still be bounded by attracting each other)? @username_3  
> **username_3**: @username_0 you could look at the papers I've referenced. Why would proton decay lead to mass disappearing from the universe? I've added a reference to Ringwald & Wong (2004) who show some simulations.  
> **username_0**: I mean, if the proton decays, wouldn't the resulting particles be ejected or create antiparticles that could annihilate with other particles? If the mass is dispersed or maybe transformed into energy this way, would neutrinos stay clumped? @username_3  

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