Question on halos of matter made from massive and stable particles?

[ohwilleke]

But as the universe aproaches heat death wouldn't there be less and less protons created as time passes if proton decay were true? I mean, less and less "useful" energy could be used to make new protons...

The minimum mean lifetime of a proton is 10²³ times the 13.8 billion year age of the universe (and this is as low as it is simply due to the limited of precision measurement by scientists).

This is 100,000,000,000,000,000,000,000 x 13.8 billion years!

This is actually a conservative estimate that is a bit out of date itself:

[M]inimum proton lifetimes from research (at or exceeding the 10³⁴~10³⁵ year range) have ruled out simpler GUTs and most non-SUSY models. The maximum upper limit on proton lifetime (if unstable), is calculated at 6×10³⁹ years for SUSY models and 1.4×10³⁶ years for minimal non-SUSY GUTs.

(Source citing this peer reviewed journal article from 2023 about minimum proton mean lifetimes, and this 2007 article about maximum proton lifetimes in GUT theories.). There is also no observational evidence supporting the existence of any form of supersymmetry (SUSY) so far.

In contrast, every radioactive isotope that experiences beta decay creates new protons "gillions" of times a year, and natural nuclear fusion in stars creates new radioactive isotopes that will beta decay in the future on a regular basis.

These is not a single example of baryon number non-conservation in the entire history of science.

In the Standard Model, baryon number non-conservation can only happen at extremely high sphaleron energies, which by assumption isn't possible during a "heat death of the universe" scenario.

There are no outstanding experimental anomalies meaningfully suggesting that discovery any beyond the Standard Model physics that would give rise to baryon number non-conservation is "around the corner".

Okay. I was pretty sure that massive particles travelling at some velocity were "redshifted" by the expansion of spacetime in a similar way to how photons have their frequency redshifted, so in the future we would have very low energetic photons and particles that would tend to be at rest. If this is the wrong picture then everything changes of course.

This is the wrong picture.

What is the right picture is that the density of neutrinos per cubic light-year in the universe is falling in proportion to the expansion of the universe, which makes it harder for neutrinos to clump in the future than it is today.

It's not that I'm not willing to listen. The thing is that you were saying that since neutrinos do not interact with each other through any forces and they travel so fast that they could not be gravitationally attracted then they will never clump. But I though that you were referring only to the present universe where neutrinos have relativistic velocities, so I was asking what would happen if they lose enough velocity in the future due to the "redshift" that I though they suffered as spacetime expands. I though this would slow them down so in the future they could be gravitationally attracted. But if this is wrong then of course there will be no compact neutrino structures.

This is wrong so there will be no compact neutrino structures.

So then, will neutrinos always have high velocities even in far future timescales (so that they will never really be slow enough to be gravitationally attracted and clumped into structures)?

Yes.

So, at most, neutrinos would aggregate or cluster into diffuse halos around galaxies instead of compact solid structures? Or this would also be impossible?

The density of neutrinos in the vicinity of galaxies (and galaxy clusters and closer to the "cosmic web") is somewhat higher than it is in the middle of cosmic voids.

Neutrinos will never form compact solid structures.

Neutrinos will not even segregate from ordinary matter to form a halo distinct from stars, interstellar gas, dust, and (if it exists) dark matter particles. Streams of high energy neutrinos in all directions are generated in supernova events that the ICE neutrino detector in Antarctica detects now and then.

 

[PeterDonis]

the density of neutrinos per cubic light-year in the universe is falling in proportion to the expansion of the universe

It is true, though, that for ultrarelativistic particles, the density decreases as the fourth power of the scale factor, instead of the cube. Which makes the effect you are describing even more pronounced for neutrinos as compared with cold matter.

 

[Orodruin]

This causes them to put neutrino mass in their four analyzed examples at 0.15 to 0.6 eV, when the average neutrino mass of the three neutrino mass eigenstates is probably closer to 0.02 eV, and the lightest neutrino mass eigenstate is probably on the order of 0.001 eV. This materially impacts clustering estimates, making clustering less likely and less strong.

Yes, this is obvious from the paper. It is not to the paper’s detriment in any way though. The effects are clearly illustrated for different neutrino masses and it is not a bygone conclusion how the overdensity will behave for smaller neutrino masses. I do not see a need for this to be pointed out.

The reason that someone would want to know about this difference in relic neutrino density is to figure out what kind of sensitivities you need to be targeting to build a neutrino detector that can detect relic neutrinos.

As you are well aware, this is my area of research. I have cited this paper for that very reason back in 2008. Yvonne coincided with me as a postdoc in Munich.

In the same vein, estimates of the local dark matter density and dark matter particle mean velocity in our part of the Milky Way are used to tune the design of, and to interpret the results from, dark matter detection experiments like the XENON100 experiment.

In the standard setting to obtain a benchmark, yes. It is kind of what you have to do. But over the last decade or so there has also been significant effort to work the other way, ie, to examine what could be said about the dark matter velocity distribution should direct detection experiments see a signal in the future. Most people assume a cutoff Maxwellian distribution but this is of course very much an assumption.

 

[Orodruin]

This is the wrong picture.

Well, half wrong. Both effects occur in an expanding spacetime. Dilution and redshift of particle momentum. Then it becomes a question of considering what effect will dominate the potential for clustering where I suspect dilution will doninate, but I have not looked into it further.

 

[Suekdccia]

Well, half wrong. Both effects occur in an expanding spacetime. Dilution and redshift of particle momentum. Then it becomes a question of considering what effect will dominate the potential for clustering where I suspect dilution will doninate, but I have not looked into it further.

mmmh, but @ohwilleke mentioned that redshift of particle momentum wouldn't mean that neutrinos would lose velocity with time (so they will always have some velocity, even in the far future, contrary to what. thought), so then how can my original picture be "half wrong" (or "half right")?

 

[PeterDonis]

Both effects occur in an expanding spacetime. Dilution and redshift of particle momentum.

The "redshift" appears as a change in the dilution as a function of the scale factor, as I said in post #37. Unless one is tracking the momentum of individual particles relative to comoving observers, I think that is the only effect of significance.

 

[Suekdccia]

Unless one is tracking the momentum of individual particles relative to comoving observers

What would happen if one did that? Would it change?

 

[ohwilleke]

As you are well aware, this is my area of research. I have cited this paper for that very reason back in 2008. Yvonne coincided with me as a postdoc in Munich.

For what it is worth, while I was aware that you were employed in a scientific field, I had no idea that this particular sub-field was your area of research (let alone that you would have been a postdoc in this time frame, you can't see how many gray hairs someone has on the Internet, to the extent I thought about it at all, I figured you were older than you are, I'm 53 years old).

But, of course, while my response was to your post, my primary audience was the OP.

 

[PeterDonis]

What would happen if one did that? Would it change?

Yes, the momentum of any freely moving object relative to comoving observers will decrease over time. But for an ultrarelativistic object like a neutrino, it can take a very, very long time for the decrease in momentum to produce an observable decrease in velocity.

 

[Suekdccia]

Yes, the momentum of any freely moving object relative to comoving observers will decrease over time. But for an ultrarelativistic object like a neutrino, it can take a very, very long time for the decrease in momentum to produce an observable decrease in velocity.

Then here I think it's where my confusion is rooted.

Okay so on the one hand we have that neutrino will decrease its velocity due to its momentum redshift by cosmological expansion. This is why I asked my question on neutrinos being able to clump in the future, once they have slowed down enough, whatever time it takes

But in the other hand in post #36 @ohwilleke said "yes" to my question "So then, will neutrinos always have high velocities even in far future timescales (so that they will never really be slow enough to be gravitationally attracted and clumped into structures)?"

Here I see a contradiction but I must be missing something.

Apart from that, then, the problem with my question is that neutrinos WILL lose velocity over time but when they will do that the universe will be so diluted that they could not form structures because there will be no other neutrinos to be gravitationally attracted to?

 

[PeterDonis]

neutrino will decrease its velocity due to its momentum redshift by cosmological expansion

Yes, but by how much? The answer is, for time periods on the order of the age of the universe (and even orders of magnitude longer), way, way, way too little to matter. The gamma factor of neutrinos is simply way too large.

in post #36 @ohwilleke said "yes" to my question "So then, will neutrinos always have high velocities even in far future timescales (so that they will never really be slow enough to be gravitationally attracted and clumped into structures)?"

Yes, and that's true, and is perfectly consistent with what I said. See above. He didn't say the neutrinos will always have the same velocities. He just said they will have high velocities even in the far future--and I just told you above why that is the case.

 

[Suekdccia]

Yes, but by how much? The answer is, for time periods on the order of the age of the universe (and even orders of magnitude longer), way, way, way too little to matter. The gamma factor of neutrinos is simply way too large.


Yes, and that's true, and is perfectly consistent with what I said. See above. He didn't say the neutrinos will always have the same velocities. He just said they will have high velocities even in the far future--and I just told you above why that is the case.

Well there's also post #29 where he said:

This isn't how it work. Cosmological redshift isn't friction. It doesn't slow down particles over any time scale, even "forever". You fundamentally have this concept wrong.

Note how he says that particles don't slow down over any time scale, even forever (i.e. they never slow down). So, again, I see a contradiction here

Apart from that, then, if they do indeed slow down, why can't they gravitationally attract to each other in the far future? Is it because they will be so diluted by the expansion that they won't be able to interact gravitationally with one another?

 

[PeterDonis]

Note how he says that particles don't slow down over any time scale, even forever

Yes, that's not quite correct.

if they do indeed slow down, why can't they gravitationally attract to each other in the far future? Is it because they will be so diluted by the expansion that they won't be able to interact gravitationally with one another?

Since "far future" here means time scales many orders of magnitude larger than the current age of the universe, yes, by that time dilution will have made any gravitational interactions between them negligible.

 

[Suekdccia]

Since "far future" here means time scales many orders of magnitude larger than the current age of the universe, yes, by that time dilution will have made any gravitational interactions between them negligible.

At last, thank you, now I'm beginning to really see where was my mistake


Alright, and concerning those neutrinos that are in halos around galaxies as @Orodruin mentioned in post #3

Technically, there is (most likely according to present theory) a minor neutrino halo consisting of cosmic background neutrinos around any galaxy. As Peter said though, the mass of this halo is much lower than that of the galaxy itself and therefore not very significant for the dynamics.

Are these neutrinos gravitationally bound to their host galaxies?

Yes, that's not quite correct

By the way, thanks for clarifying that, I was getting extremely confused

 

[PeterDonis]

Are these neutrinos gravitationally bound to their host galaxies?

I would think not since they are probably moving faster than the escape velocity from the galaxies. But the presence of the galaxies would mean that the density of cosmic background neutrinos would be higher around the galaxies than elsewhere.

 

[Orodruin]

The gamma factor of neutrinos is simply way too large.

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.

 

[Suekdccia]

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?

 

[Suekdccia]

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.

I'll try to summarize my questions as the previous post was a bit too large:

1. As you mentioned there can be diffuse halos of neutrinos around galaxies and the gamma factor for these could be close to 1. Then, would their speed be smaller than the escape velocity of a galaxy and therefore would be gravitationally bound to it?

2. If they can, can neutrinos also be gravitationally bound to larger structures that are still bound like clusters and superclusters of galaxies?

3. Yvonne Wang explained that considering the gravitational potential from baryonic matter and dark matter it seems that neutrinos would be gravitationally bounded to these galaxies+dark matter halos structures. She also said that even in the hypothetical scenario that dark matter and baryonic matter particles decayed into something else leaving only neutrinos, they would still be gravitationally bounded (given that this occurs in extremely far future scales, once neutrinos' momentum have been redshifted). Is this right?

I ask you specifically @Orodruin as you mentioned that this was your area of expertise

 

[Suekdccia]

I'll try to summarize my questions as the previous post was a bit too large:

1. As you mentioned there can be diffuse halos of neutrinos around galaxies and the gamma factor for these could be close to 1. Then, would their speed be smaller than the escape velocity of a galaxy and therefore would be gravitationally bound to it?

2. If they can, can neutrinos also be gravitationally bound to larger structures that are still bound like clusters and superclusters of galaxies?

3. Yvonne Wang explained that considering the gravitational potential from baryonic matter and dark matter it seems that neutrinos would be gravitationally bounded to these galaxies+dark matter halos structures. She also said that even in the hypothetical scenario that dark matter and baryonic matter particles decayed into something else leaving only neutrinos, they would still be gravitationally bounded (given that this occurs in extremely far future scales, once neutrinos' momentum have been redshifted). Is this right?

I ask you specifically @Orodruin as you mentioned that this was your area of expertise

Or @PeterDonis if you want to add anything to this, you are welcome to do so!