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

[Suekdccia]

TL;DR Summary

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

Consider a halo made up from massive and stable particles like neutrinos* (let's not consider protons which, although we don't have any experimental evidence showing that they are unstable and decaying, there are some GUTs proposing theoretical mechanisms where they could decay over extremely long timescales). Those neutrinos in the halo would collapse over time (for example due to the emission of gravitational waves as they orbit the central point of mass) and if the amount of neutrinos is enough this would form a black hole


But could there be some possibility in which, once it collapses, it does not end in a black hole?

For instance, what about if we had halo of neutrinos around a galaxy that when collapsing would not be enough to turn into a black hole (but near that limit)? And in that case, would the halo have a higher angular momentum than most of the galaxy components not due to its mass content but rather due to the distance from the galactic center?

And even if this could happen, are there any other ways in which a high amount of collapsing neutrinos would not end up in a black hole? Or is it unavoidable for larger masses?


*let's assume that neutrinos had a much smaller velocity than they generally do so they would easily get gravitationally bounded

 

[PeterDonis]

a halo

A halo around what? Something like a galaxy, from what you say later on in your post. Which means that just considering collapse of the halo in isolation is pointless, because the halo's mass is much, much smaller than whatever it's a halo around, and the latter's spacetime geometry is what will determine what happens.

are there any other ways in which a high amount of collapsing neutrinos would not end up in a black hole? Or is it unavoidable for larger masses?

Any system whose mass is over the maximum mass limit for a neutron star will have to collapse to a black hole.

 

[Orodruin]

Consider a halo made up from massive and stable particles like neutrinos* (let's not consider protons which, although we don't have any experimental evidence showing that they are unstable and decaying, there are some GUTs proposing theoretical mechanisms where they could decay over extremely long timescales). Those neutrinos in the halo would collapse over time (for example due to the emission of gravitational waves as they orbit the central point of mass) and if the amount of neutrinos is enough this would form a black hole

The time scales for anything like this to occur would be absolutely enormous. Most likely well beyond the heat death of the Universe. Another question would be how you would form such a structure in the first place.

But could there be some possibility in which, once it collapses, it does not end in a black hole?

I am not sure it would collapse to start with. At some point you will run into non-classical effects, in particular for relatively light particles such as neutrinos.

For instance, what about if we had halo of neutrinos around a galaxy that when collapsing would not be enough to turn into a black hole (but near that limit)? And in that case, would the halo have a higher angular momentum than most of the galaxy components not due to its mass content but rather due to the distance from the galactic center?

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.

And even if this could happen, are there any other ways in which a high amount of collapsing neutrinos would not end up in a black hole? Or is it unavoidable for larger masses?

Neutrinos are fermions. Just as electrons or neutrons, they would be subject to a degeneracy pressure. There will be a mass limit, just as for neutron stars.

because the halo's mass is much, much smaller than whatever it's a halo around, and the latter's spacetime geometry is what will determine what happens.

This is not necessarily true though. Dark matter halos are significantly more massive than the host galaxies. There are dark matter theories with very light particles where the dark matter is essentially a Bose-Einstein condensate of galactic size.

 

[PeterDonis]

Dark matter halos are significantly more massive than the host galaxies.

Hm, yes, good point. In that case, though, collapse of the halo by itself still is not a good model; one has to include the host galaxy since its mass, while it might be smaller than that of the halo, is not negligible.

 

[ohwilleke]

Consider a halo made up from massive and stable particles like neutrinos* . . . . Those neutrinos in the halo would collapse over time (for example due to the emission of gravitational waves as they orbit the central point of mass) and if the amount of neutrinos is enough this would form a black hole

The assumption in the quote above is not correct.

While it is possible for a halo neutrinos of a given average angular momentum to collapse, there are also ways that the particles in the halo could receive boosts, for example, from the gravity of particles further from the center than they are, and even from self-interactions between particles of the same type. You have to consider all possibilities and there is not a general trend towards collapsing in realistic scenarios.

Also, particles in a halo around a galaxy are also not necessarily in full equilibrium at the outset (which is what the OP analysis assumes). Indeed, in some circumstances, such as a collision of two galaxies within the past billion years or so, they are almost certain to be far out of equilibrium. And the LambdaCDM model of cosmology, which is the baseline assumption despite its known issues, assumes that the main way we get larger galaxies is from the collision and merger of smaller galaxies, in multiple rounds of collisions. Thus, a substantial percentage of the particles of all kinds in the universe, especially closer to the Big Bang, are not in equilibrium at any given time.

Whether a halo of particles around a galaxy is stable is a calculation that can be and is done. If it is stable, one can also reverse engineer how long it takes to become stable and in near equilibrium and how that will affect the angular momentum of the particles in the halo.

But this is a tricky calculation. And, as other responses have noted, it depends upon the distribution of mass-energy and momentum of everything within the galaxy, and not just the halo itself.

As a practical matter, light particles with a low cross-section of interaction, like neutrinos or hypothetical near collisionless dark matter particles, are not very likely to collapse into a black hole at all. There are no known examples of this happening and I'm not even aware of any systems where it is suspected that this has happened (even in cosmology simulations). To do that, you need not just a high enough total mass (the minimum is somewhere between 2 and 3 solar masses), but you need to have that mass to be extremely densely clumped in one place (a sphere of about 12 km radius for the smallest possible neutron star that tips over into becoming a black hole, and larger, as a function of mass, for larger masses).

Getting neutrinos or hypothetical collisionless or near collisionless dark matter particles to clump that densely is much harder than herding cats. And this lack of clumping prevents these kinds of particles from getting enough local density to form black holes in time frames such as the first 14 billion years of the universe.

This is why "hot dark matter" composed of neutrinos or other particles with masses comparable to neutrinos that are almost collisionless (like neutrinos) that have a high mean velocity, were among the first dark matter candidates to be ruled out. Hot dark matter, generically, leads to very little large scale structure in the universe (i.e. to very little matter clumping into galaxies, galaxy clusters, etc.) relative to what is observed.

Neutrinos observed in nature usually have relativistic mean velocities (i.e. mean velocities close to the speed of light). But dark matter candidates should have speeds on the order of a few hundred km/s.

The particles in the halo need to have low mean velocities to be consistent with what is observed, which in the case of low mass dark matter particle candidates (e.g. <<1 MeV) means that "thermal freeze out" scenarios for the appearance of these particles in the universe don't work due to the virial theorem https://en.wikipedia.org/wiki/Virial_theorem relationship between particle mass and velocity upon "thermal freeze out" of the particles. So, you need to come up with some cosmology that injects these particles into the universe at low energies relative to their masses in dark matter particle proposals involving low mass dark matter particles.

Stacy McGaugh outlines some of these issues in a June 27, 2023 post: https://tritonstation.com/2023/06/27/checking-in-on-troubles-with-dark-matter/ (under the headings the angular momentum challenge, the pure disk challenge, and the stability challenge).

 

[Orodruin]

viral

 

[ohwilleke]

Yeah. I let spell check lead me astray. I fixed it.

 

[Vanadium 50]

The famed "viral theorem" as it "I saw it on YouTube" along with "they wouldn't let it on the internet if it weren't true."

 

[Suekdccia]

At some point you will run into non-classical effects, in particular for relatively light particles such as neutrinos.

What kind of non-classical effects would appear?

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.

Would these halos orbit their "host" galaxies as well?

Neutrinos are fermions. Just as electrons or neutrons, they would be subject to a degeneracy pressure. There will be a mass limit, just as for neutron stars.

So there will be a moment where too much neutrinos will unavoidably end up in a black hole no matter the conditions and the situation right?

 

[Suekdccia]

Getting neutrinos or hypothetical collisionless or near collisionless dark matter particles to clump that densely is much harder than herding cats. And this lack of clumping prevents these kinds of particles from getting enough local density to form black holes in time frames such as the first 14 billion years of the universe.

And couldn't neutrinos get this so much clumped if we assume a sufficiently large mass? I mean, couldn't just the force of gravity be enough to clump a large mass of neutrinos to the point of forming a black hole? Or you would need something else?...

So, you need to come up with some cosmology that injects these particles into the universe at low energies relative to their masses in dark matter particle proposals involving low mass dark matter particles.

Although this is not relevant to our present models and observation, could neutrinos in the future make halos (or at least part of halos) once they have lost enough velocity (due to interactions with other particles or even by getting their velocity "redshifted" by the expansion of the universe itself)?

 

[Orodruin]

What kind of non-classical effects would appear?

Bose-Einstein condensation for bosons and degeneracy pressure for fermions.

Would these halos orbit their "host" galaxies as well?

By definition, a halo does not orbit a host galaxy as much as exist around it.

So there will be a moment where too much neutrinos will unavoidably end up in a black hole no matter the conditions and the situation right?

For any realistic scenarios, probably not.

 

[ohwilleke]

And couldn't neutrinos get this so much clumped if we assume a sufficiently large mass? I mean, couldn't just the force of gravity be enough to clump a large mass of neutrinos to the point of forming a black hole? Or you would need something else?...

You need more than that.

The well studied example is interstellar hydrogen gas, which does continue to clump to form gas giants and stars, but at a much lower rate than in the early universe, and mostly without sinking towards the center of a galaxy. But neutrinos or collisionless dark matter is ghost-like compared to interstellar hydrogen gas.

When two hydrogen atoms get very close to each other, they form a molecule which is a bigger thing to clump with that has a higher cross-section of interaction than a bare atom.

In contrast, when neutrinos get similarly close to each other they tend to breeze right by each other without stopping or interacting with each other, because the cross-section of interaction is so much lower and the relative speed is so much greater.

Another way to think about it is in terms of escape velocity. The definition of a black hole is a system in which the speed of light is not a sufficient escape velocity.

Neutrinos almost always travel at very close to the speed of light, since they have so little mass. The average of the three neutrino mass eigenvalues is probably <0.04 eV. This is more than 10 million times less massive than an electron, and roughly 20 billion times less massive than a hydrogen atom. And all common means for neutrino creation impart relativistic momentum to a neutrino. So, almost nothing short of a black hole can tie a neutrino down into being part of a gravitationally bound clump.

You also can't ignore non-neutrino matter (as the OP seems to want to, to a great extent) because less than 0.62% of the mass-energy of the universe is made up of neutrinos so neutrinos are almost always a tiny minority of the mass-energy of any gravitationally bound system.

The main way that neutrinos end up in black holes is that a black hole already exists and the neutrino is racing through empty space at almost the speed of light minding its own business when "wham" it ends up on a collision course with that black hole as a matter of random chance.

Although this is not relevant to our present models and observation, could neutrinos in the future make halos (or at least part of halos) once they have lost enough velocity (due to interactions with other particles or even by getting their velocity "redshifted" by the expansion of the universe itself)?

Neutrinos don't lose any meaningful amount of velocity in empty space over very long time periods (not infinitely long perhaps, but many, many billions of years). Any loss of velocity due to gravitational radiation is more or less in equilibrium with gains in velocity due to gravitational radiation encountered. The ratio can change depending on the exact circumstances, but that's pretty much the baseline.

The neutrinos aren't interacting with photons or gluons or the Higgs field, and the weak force is a very short range force (since its mediators have masses of 80-90 GeV) in an environment where the average distance between particles in space is much larger than the range of the weak force.

Also, don't forget that for particles traveling at relativistic speeds, the relationship between momentum and velocity is non-linear due to special relativity. A 1% drop in momentum will reduce its velocity (which is just slightly less than the speed of light) by less than 1%.

Further, keep in mind that the expansion of the universe (let alone the accelerated expansion of the universe) is constantly reducing the mass density of neutrinos in the universe because the 3D volume of the observable universe gets larger over time, but the quantity of ordinary matter stays more or less constant. The further in the future you get, the less likely it is for neutrinos to clump into any kind of structure because there are fewer neutrinos per cubic meter.

 

[Suekdccia]

By definition, a halo does not orbit a host galaxy as much as exist around it

And would these halos have a fiven amount of angular momentum as they "float" around their galaxies?

 

[Suekdccia]

The main way that neutrinos end up in black holes is that a black hole already exists and the neutrino is racing through empty space at almost the speed of light minding its own business when "wham" it ends up on a collision course with that black hole as a matter of random chance.

I understand. But I'm trying to see what would happen, even in the hypothetical scenario where neutrinos would have sufficiently low velocities to be significantly clumped. If there are enough neutrinos, would they collapse into a black hole? Or would there be some effects (like quantum effects) that would make this difficult particularly for neutrinos? For example, in post #3 and #11 @Orodruin mentioned that the collapse could be avoided by non-classical effects (degeneracy pressure for fermions). Would this be one example why neutrinos would not be likely collpase into a black hole if they enough of them clumping?

I mean, I understand that this would be difficult because neutrinos don't interact with each other most of the time and they travel at great speeds, but if they were slowed down enough, would it still be difficult? Or they would certainly form a black hole if there was enough mass, just as if we have enough protons they can easily collapse into a black hole?

Neutrinos don't lose any meaningful amount of velocity in empty space over very long time periods (not infinitely long perhaps, but many, many billions of years). Any loss of velocity due to gravitational radiation is more or less in equilibrium with gains in velocity due to gravitational radiation encountered. The ratio can change depending on the exact circumstances, but that's pretty much the baseline.

So they could form halos in the future but they would be very rare (they would form them if the right conditions are met, like for instance, if they are in an isolated region of the universe, so they do not gain gravitational radiation from other sources)?

The neutrinos aren't interacting with photons or gluons or the Higgs field, and the weak force is a very short range force (since its mediators have masses of 80-90 GeV) in an environment where the average distance between particles in space is much larger than the range of the weak force.

I was considering that they would form halos purely based on gravotational attraction, not other forces

Further, keep in mind that the expansion of the universe (let alone the accelerated expansion of the universe) is constantly reducing the mass density of neutrinos in the universe because the 3D volume of the observable universe gets larger over time, but the quantity of ordinary matter stays more or less constant. The further in the future you get, the less likely it is for neutrinos to clump into any kind of structure because there are fewer neutrinos per cubic meter.

But if they get gravitationally bounded (around an initial galaxy like @Orodruin commented in post #3) then spacetime expansion shouldn't affect them (at that local level) right?

 

[PeterDonis]

in post #3 and #11 @Orodruin mentioned that the collapse could be avoided by non-classical effects (degeneracy pressure for fermions)

That only works up to the maximum mass limit for neutron stars, as I pointed out in post #2. And even that assumes that the neutrinos would turn into neutrons under sufficient compression. Otherwise the maximum mass limit would probably be smaller, something more like the white dwarf limit, since that is due to lepton (electron) degeneracy pressure.

 

[ohwilleke]

I understand. But I'm trying to see what would happen, even in the hypothetical scenario where neutrinos would have sufficiently low velocities to be significantly clumped. If there are enough neutrinos, would they collapse into a black hole? Or would there be some effects (like quantum effects) that would make this difficult particularly for neutrinos? For example, in post #3 and #11 @Orodruin mentioned that the collapse could be avoided by non-classical effects (degeneracy pressure for fermions). Would this be one example why neutrinos would not be likely collpase into a black hole if they enough of them clumping?

I mean, I understand that this would be difficult because neutrinos don't interact with each other most of the time and they travel at great speeds, but if they were slowed down enough, would it still be difficult? Or they would certainly form a black hole if there was enough mass, just as if we have enough protons they can easily collapse into a black hole?



So they could form halos in the future but they would be very rare (they would form them if the right conditions are met, like for instance, if they are in an isolated region of the universe, so they do not gain gravitational radiation from other sources)?

I was considering that they would form halos purely based on gravotational attraction, not other forces

But if they get gravitationally bounded (around an initial galaxy like @Orodruin commented in post #3) then spacetime expansion shouldn't affect them (at that local level) right?

I honestly can't think of any circumstance where this could every happen in neutrinos. There is no mechanism by which you could segregate neutrinos from other matter on that scale. There is no way to slow down neutrinos sufficiently. There is no mechanism by which you could squeeze neutrinos into a sufficiently tight space.

Existing experimental fusion reactors squeeze atoms into a tight enough space for nuclear fusion (which is much less dense than necessary to form a black hole) using magnets. But you can't squeeze neutrinos with magnets.

Also, the lower the mass of the system, the more density you need to get it to form a black hole. Suppose that you tried to form a black hole from 0.3 solar masses of neutrinos (it has never happened, but it is theoretically possible to form a 0.3 solar mass black hole if you can get the density high enough considering GR alone without considering the properties of neutrinos). This would require a density an order of magnitude higher than the density of a neutron star. And there is no conceivable way of doing that.

In a tangentially related point, there are theoretical physics papers that argue convincingly that it is (when you go beyond considering only GR and also consider the properties of photons) theoretically impossible to form a black hole from pure photons, even though they too gravitate.

Now, getting away from neutrinos, to hypothetical dark matter particles, which could have a lower velocity and a higher mass per particle, which are invented to fit a halo possibility, you get away from some of the problems specific to neutrinos. But the fundamental problem is still low density and a low cross-section of interaction.

 

[Vanadium 50]

Otherwise the maximum mass limit would probably be smaller, something more like the white dwarf limit, since that is due to lepton (electron) degeneracy pressure.

I don't think you ever get neutrino degeneracy pressure.

Think about neutrino-antineutrino atoms. Neutrinos are a million times lighter than electrons so the Bohr radius is a million times bigger. But the range of the weak force is a million times smaller than atoms. So you are off by a factor of a trillion. So they never "clump".

If you put a bunch of neutrinos and/or antineutrinos in a small volume, they feel no net force, and therefore just leak out/fly away. There's nothing to hold them together.

 

[PeterDonis]

If you put a bunch of neutrinos and/or antineutrinos in a small volume, they feel no net force, and therefore just leak out/fly away. There's nothing to hold them together.

The OP's scenario assumed that there was a large enough number of neutrinos for gravity to be significant. Gravity could in principle hold such a system together even in the absence of any binding forces between individual particles. (Indeed, in white dwarf models such forces can be ignored and a reasonably good estimate of the structure can still be obtained. In neutron star models the details are sensitive to the actual behavior of the strong interaction so inter-particle interactions can't be ignored, but it is known that gravity could still bind the object together even if the strong force didn't exist--that was the initial model that Oppenheimer investigated as part of the work that led to his classic paper with Tolman and Volkoff.)

Whether any of this could actually happen with neutrinos given their other properties (in particular the fact that we have no evidence of any neutrinos that are not ultra-relativistic) is a separate question. But I don't think it can be ruled out simply on the grounds of "no binding forces between neutrinos".

 

[Vanadium 50]

The OP's scenario assumed that there was a large enough number of neutrinos for gravity to be significant. Gravity could in principle hold such a system together even in the absence of any binding forces between individual particles

But that won't work either.

The MW's escape velocity is around 300 km/s. That's 0.001c. Neutrinos travel at 0.999+ c.

If you want neutrinos to be bound gravitationally, you need to increase the MW mass by a factor of millions. (Without increasing the radius)

 

[Orodruin]

Neutrinos travel at 0.999+ c.

This is not entirely correct. While correct for the typical neutrinos produced nowadays, the cosmic neutrino background is essentially guaranteed not to be ultrarelativistic just from the minimal masses required from neutrino oscillations. Studies focusing on obtaining the CNB density indeed find that they will have higher densities in large gravitational wells, such as those created by galaxies and the accompanying dark matter halos.

 

[PeterDonis]

Neutrinos travel at 0.999+ c.

All the ones we know of directly do, yes. (The "directly" is to take into account the indirect evidence @Orodruin described.) That's why I explicitly addressed that point in the last paragraph of my post. And why I also said that this is a separate question from the question of what would happen if hypothetically we found neutrinos that were not ultra-relativistic and could be bound gravitationally.

 

[PeterDonis]

If you want neutrinos to be bound gravitationally, you need to increase the MW mass by a factor of millions.

No, that won't help, because it is impossible to have a bound system with an escape velocity at its surface of 0.999+ c. Buchdahl's Theorem says that no bound system (i.e., one made of matter, not a black hole) can have a radius less than 9/8 of the Schwarzschild radius for its mass. The corresponding surface escape velocity is just the square root of $8/9$, or $2 \sqrt{2} / 3$, or about $0.943$ c.

 

[Vanadium 50]

Agreed. It can't be done. There is no place in the universe with the right conditions.

As far as neutrino speeds, CMB neutrinos have T ~ 1/6000 eV (1.95K). In the worst case, you have three semi-degenerate species at 0.3 eV each. That's 0.033c or ~35x escape velocity. The argument still stands, and only becomes stronger with less stringent assumptions.

 

[Orodruin]

CMB neutrinos have T ~ 1/6000 eV (1.95K)

That's not how cosmological redshift of massive particles works though. What is scaled with the inverse of the scale factor is the particle momentum. For a massless particle that doesn't really matter since momentum and energy are proportional. For a massive particle however, you need to consider that it is momentum that is scaled, not kinetic energy.

For the case in point, this would work out to p = 1/6000 eV and, since p << m, $v \simeq p/m = 0.3/6000 = 5\cdot 10^{-5}$. This is about 15000 m/s or 15 km/s if you will.

 

[Suekdccia]

There is no mechanism by which you could segregate neutrinos from other matter on that scale

Consider proton decay (if it's true). After long timescales, they will decay and all that would be left would be fundamental particles like neutrinos.

There is no way to slow down neutrinos sufficiently

Also after very long timescales neutrinos would be slowed down due to the expansion of spacetime

There is no mechanism by which you could squeeze neutrinos into a sufficiently tight space.

That's essentially my question. I mean, imagine an initial central point of mass: gravity could cluster neutrinos (simply because they have mass) around it. If they begin to orbit that central point of mass they will emit gravitational waves, which overtime this would cause them to clump into a central point.

By the way, I'm not saying that this scenario will necessarily happen, I'm just trying to see (theoretically) what would happen if these conditions would be met.

So, if we had a universe where neutrinos have been slowed down sufficiently, would gravity be enough to clump them into a black hole if we had a large mass of neutrinos? Or because of their light mass gravity won't be enough (unless we had a ridiculously large amount of neutrinos)?

This would require a density an order of magnitude higher than the density of a neutron star. And there is no conceivable way of doing that.

Then there is no conceivable way of doing that because the force of gravity wouldn't be enough to clump them into such high densities? So we would need a much higher mass of neutrinos to be clumped into such high densities?

 

[Suekdccia]

That only works up to the maximum mass limit for neutron stars, as I pointed out in post #2. And even that assumes that the neutrinos would turn into neutrons under sufficient compression. Otherwise the maximum mass limit would probably be smaller, something more like the white dwarf limit, since that is due to lepton (electron) degeneracy pressure.

So it would be "easier" to have a gravitational collapse with neutrinos than with neutrons?

 

[Suekdccia]

Agreed. It can't be done. There is no place in the universe with the right conditions.

As far as neutrino speeds, CMB neutrinos have T ~ 1/6000 eV (1.95K). In the worst case, you have three semi-degenerate species at 0.3 eV each. That's 0.033c or ~35x escape velocity. The argument still stands, and only becomes stronger with less stringent assumptions.

Also, in the far future there will be a moment where neutrinos would have lost enough speed to be gravitationally bounded to other structures due to cosmological redshift acting on massive particles' speed

This is a related paper on the topic: https://arxiv.org/abs/hep-ph/0408241

 

[ohwilleke]

Consider proton decay (if it's true). After long timescales, they will decay and all that would be left would be fundamental particles like neutrinos.

Proton decay is not real. Even if it were, we know, at a minimum, that it would be insignificant: less than one proton decay per gram of protons over the entire lifetime of the universe.

Processes that create new protons would outnumber it. You should banish the idea of proton decay from your mind.

Also after very long timescales neutrinos would be slowed down due to the expansion of spacetime

No. This isn't how it works. You are mistaken.

That's essentially my question. I mean, imagine an initial central point of mass: gravity could cluster neutrinos (simply because they have mass) around it. If they begin to orbit that central point of mass they will emit gravitational waves, which overtime this would cause them to clump into a central point.

Your basic mental model is so deeply wrong that it you should throw it in the trash bin like a bag of broccoli so molded that it has turned to a smelly green liquid. We've told you again and again in detail that this doesn't happen. Don't waste our time sticking to your flawed model any longer if you aren't willing to listen.

By the way, I'm not saying that this scenario will necessarily happen, I'm just trying to see (theoretically) what would happen if these conditions would be met.

Asking questions about things that can't happen even theoretically confounds, it doesn't enlighten.

So, if we had a universe where neutrinos have been slowed down sufficiently, would gravity be enough to clump them into a black hole if we had a large mass of neutrinos?

No.

Or because of their light mass gravity won't be enough (unless we had a ridiculously large amount of neutrinos)?

Even if you had all the neutrinos in the universe it wouldn't happen.

Then there is no conceivable way of doing that because the force of gravity wouldn't be enough to clump them into such high densities?

Yes.

So we would need a much higher mass of neutrinos to be clumped into such high densities?

Hello! Have you read anything in this thread? This is not the issue. The problem isn't the mass. It is the neutrinos don't clump.

 

[ohwilleke]

Also, in the far future there will be a moment where neutrinos would have lost enough speed to be gravitationally bounded to other structures due to cosmological redshift acting on massive particles' speed

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.

 

[ohwilleke]

This is a related paper on the topic: https://arxiv.org/abs/hep-ph/0408241

This 2004 paper is out of date. Among other things, it assumes that 20% of the mass in the universe is made up of neutrinos (with the same total number of neutrinos). We now know that neutrinos are less than 0.7% of the mass in the universe.

Also, the clustering they are talking about is moderately higher or lower relic densities on scales of parsecs, not compact, gravitationally bound objects.

 

[PeterDonis]

So it would be "easier" to have a gravitational collapse with neutrinos than with neutrons?

I don't know what you mean by "easier". I am not aware of any actual analysis in the literature of neutrino degeneracy so we have no basis for making any actual predictions. I was simply pointing out that the general analysis that says there must be a maximum mass limit for any object supported by degeneracy pressure works for any type of fermion, and neutrinos are fermions.

 

[Orodruin]

a bag of broccoli so molded that it has turned to a smelly green liquid

So … regular broccoli soup?

Among other things, it assumes that 20% of the mass in the universe is made up of neutrinos (with the same total number of neutrinos).

This is an incorrect representation of what the paper states. They quote the then current result that $\rho_\nu < 0.2\rho_m$, but this is not an assumption that is going into the analysis. In fact, what they say is that they work in the limit where the clustering is dominated by the CDM background.

 

[Suekdccia]

Processes that create new protons would outnumber it. You should banish the idea of proton decay from your mind.

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...

No. This isn't how it works. You are mistaken.

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.

Your basic mental model is so deeply wrong that it you should throw it in the trash bin like a bag of broccoli so molded that it has turned to a smelly green liquid. We've told you again and again in detail that this doesn't happen. Don't waste our time sticking to your flawed model any longer if you aren't willing to listen.

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.

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)?

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.

So again if this is what I got wrong then yes you are right, I apologize for misunderstanding concepts!

Also, the clustering they are talking about is moderately higher or lower relic densities on scales of parsecs, not compact, gravitationally bound objects.

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

 

[Suekdccia]

This is an incorrect representation of what the paper states. They quote the then current result that ρν<0.2ρm, but this is not an assumption that is going into the analysis. In fact, what they say is that they work in the limit where the clustering is dominated by the CDM background.

Mmmmh but then it's not clear to me whether neutrinos can cluster in diffuse halos or not (as I think you said in post #3). Can they?

 

[ohwilleke]

This is an incorrect representation of what the paper states. They quote the then current result that $\rho_\nu < 0.2\rho_m$, but this is not an assumption that is going into the analysis. In fact, what they say is that they work in the limit where the clustering is dominated by the CDM background.

The paper says:

Ων/Ωm is at most ∼ 0.2

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.

But the more fundamental point is that the clustering the papers is not talking about the formation of compact objects made of gravitationally bound neutrinos. It is talking about regions (in parsec sized chunks) of somewhat higher densities of still very diffuse relic neutrino backgrounds, relative to regions of somewhat lower densities of diffuse relic neutrino backgrounds.

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.

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.

 

[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.