How would dark matter aggregate?

[haruspex]

I'm a mathematician, not a physicist, so I apologise in advance if I'm just showing my ignorance here.
My only source of information on dark matter is popular science texts, like New Scientist. One thing that is never explained is how it gets to aggregate around galaxies. Lacking the ability to shed energy by radiation, it seems it should just fly straight past and through, never even getting trapped into an orbit.
I can think of two possible explanations, neither very convincing.

1. Chaotic gravitational interactions catapulting much of it away.
Just as planets can get ejected from solar systems, carrying off a lot of the system's KE, a large portion of the original dark matter flying through could leave with increased energy, allowing its kin to become trapped. If so, there must be constantly a great stream of dark matter coursing everywhere at greater than escape velocity.
A problem with this is that it ought also to lead to normal matter constantly being flung out.

2. Thermodynamic cooling
The normal matter in a galaxy, having shed energy as radiation, is thermodynamically cooler (i.e. less KE) than the dark matter zipping past it. That should lead to some transfer of energy through the gravitational interaction.
A problem with this is that it would slow the cooling of the normal matter, delaying galaxy formation. As I understand it, it is already a challenge to explain how galaxies formed so swiftly.
​

 

[phinds]

dark matter interacts via gravity, so it "clumps" on very large scales, but not small scales (planets, suns) the way normal matter does

 

[Ken G]

1. Chaotic gravitational interactions catapulting much of it away.​

I don't think this could explain aggregation, because you already need aggregation before this will happen.

2. Thermodynamic cooling
The normal matter in a galaxy, having shed energy as radiation, is thermodynamically cooler (i.e. less KE) than the dark matter zipping past it.

Believe it or not, when gas in a gravitational well that has negligible pressure outside it (so has already clumped) loses heat, it goes to higher temperature, not lower temperature. This is the virial theorem, and is responsible for the reason that stars get hot, for example. It's an interesting question how gravity could transfer heat from the baryonic gas to the dark matter as the baryonic gas gets hotter.

But that's not really relevant to aggregation either, because to be able to neglect the external pressure, you already have to have an aggregation to use the virial theorem. So the situation needed to understand aggregation is when there is an important external pressure, and you give some self-gravitating gas a little random overdensity. If you assume this happens under isothermal conditions, so the gas is able to freely exchange heat with its surroundings, you get what is called the Jeans instability, whereby if the slightly overdense region has a mass above the Jeans mass, the overdensity will increase due to itself gravity (if it's below the Jeans mass, it re-expands like any normal overdense isothermal gas would).

So I think your question basically boils down to, does dark matter aggregate due to the Jeans instability? That instability requires that the gas be able to exchange heat with its surroundings very easily, so it is held at the same temperature as the gas around it (the gas around it is crucial to the instability, as it is that external pressure that is helping the contraction along). The instability ends when the gas decouples from its surrounding temperature and starts to go to higher temperature as it contracts, which eventually leads to stabilization by the internal pressure. We do need dark matter to aggregate, because that's what creates the galaxies, but we don't want it to keep aggregating, or we'd have the dark matter equivalent of stars (called MACHOS, and we don't seem to get that). So apparently, dark matter loses the ability to exchange heat with its surroundings earlier in the contraction than baryonic matter does, presumably because dark matter doesn't have light to use to exchange heat. I don't know what dark matter uses to exchange heat in the early phases of its gravitational instability, but it has to be something or it wouldn't contract and make galaxies.

 

[haruspex]

dark matter interacts via gravity, so it "clumps" on very large scales, but not small scales (planets, suns) the way normal matter does

That doesn't explain the loss of energy. If the dark matter started (roughly) uniformly spread over the vastness of space, the KE when trapped in orbit in a galaxy is only half the lost PE. Where did the rest go?
Writing that made me aware of a third possibility, that the dark matter started clumped for some reason, so created the galaxies.

 

[Orodruin]

ESA has a short and relatively accessible description of structure formation that should be quite suitable for the layman http://www.esa.int/Our_Activities/Space_Science/Planck/History_of_cosmic_structure_formation

 

[haruspex]

interesting question how gravity could transfer heat from the baryonic gas to the dark matter as the baryonic gas gets hotter.

I was suggesting the other way around... that some normal matter has managed to clump, shedding excess KE as radiation. Then along comes fast moving dark matter. Chaotic gravitational interactions should tend to even out the KE, transferring energy to the normal matter, which then radiates...

 

[haruspex]

ESA has a short and relatively accessible description of structure formation that should be quite suitable for the layman http://www.esa.int/Our_Activities/Space_Science/Planck/History_of_cosmic_structure_formation

Thanks for that link, it certainly gets me a lot closer.
The critical paras are:

"fluctuations in the distribution of cold dark matter can grow denser and more massive even before the release of the cosmic microwave background."
"Since dark matter particles had already created a network of dense and empty structure, ordinary matter particles could feel the gravitational attraction from the densest concentrations of dark matter and fall toward them."

Still doesn't quite seem to explain my energy difficulty though. How do the fluctuations grow denser without losing energy?​

 

[Ken G]

I was suggesting the other way around... that some normal matter has managed to clump, shedding excess KE as radiation.

I was correcting you-- it doesn't happen the other way around, as baryonic gas in a gravity well loses heat to radiation, its temperature rises, not falls. As a mathematician, you would like the virial theorem, give it a look.

The rest of my post attempts to explain what the ESA site does not-- how the dark matter clumps into the "cosmic web" in the first place. Simulations can give something that looks reasonable, so they must have some idea what the physics is, but given that dark matter's attributes are barely understood, it's possible that it is not yet known how the aggregation occurs.

 

[Chronos]

The cosmic web of dark matter strands and knots had already formed before matter structures [galaxies] formed. Simulations have shown matter distribution is strongly correlated with dark matter distribution. For discussion, see: http://arxiv.org/abs/1608.01763, "ELUCID - Exploring the Local Universe with reConstructed Initial Density field III: Constrained Simulation in the SDSS Volume", and, https://arxiv.org/abs/0906.4340, "The structure and evolution of cold dark matter halos".

 

[haruspex]

I was correcting you-- it doesn't happen the other way around, as baryonic gas in a gravity well loses heat to radiation, its temperature rises, not falls. As a mathematician, you would like the virial theorem, give it a look.

No, I do understand the virial theorem, and that as the ball of dark matter contracts the average KE increases.
The situation I am describing is that at any given radius and given time you would have a mix of normal matter with, on average, approximately the "right" KE for that radius (GMm/2r), and dark matter with a greater energy. Yes, both kinds will tend to have greater KE at less radius, but that is not what I'm considering here.
I believe the interactions between nearby dark matter and normal matter, though it be purely gravitational, and can sometimes result in the more energetic particle gaining energy, will overall tend to transfer KE from the faster particles to the slower.

 

[haruspex]

The cosmic web of dark matter strands and knots had already formed before matter structures [galaxies] formed. Simulations have shown matter distribution is strongly correlated with dark matter distribution. For discussion, see: http://arxiv.org/abs/1608.01763, "ELUCID - Exploring the Local Universe with reConstructed Initial Density field III: Constrained Simulation in the SDSS Volume", and, https://arxiv.org/abs/0906.4340, "The structure and evolution of cold dark matter halos".

Ok, thanks for those links. From the synopses, I get the impression that they present simulations that demonstrate the large scale structuring, but maybe not the qualitative description I was after of how the energy balance works out. I'll take a more detailed look.

 

[Ken G]

No, I do understand the virial theorem, and that as the ball of dark matter contracts the average KE increases.
The situation I am describing is that at any given radius and given time you would have a mix of normal matter with, on average, approximately the "right" KE for that radius (GMm/2r), and dark matter with a greater energy.

But it would never obey the virial theorem to maintain that baryonic gas can cause ten times that amount of dark matter to contract by robbing kinetic energy from it. You have to have the dark matter aggregate before you even can get the baryonic gas to fall into the gravity wells, because there is much more dark matter mass.

I believe the interactions between nearby dark matter and normal matter, though it be purely gravitational, and can sometimes result in the more energetic particle gaining energy, will overall tend to transfer KE from the faster particles to the slower.

Actually, I think the opposite would happen. If we look even before any galaxies have formed, then if dark matter particles share energy with baryons due to gravitational scattering (which I'm not sure they would-- two-particle gravitational interactions are spectacularly weak!), then the presence of baryons will make the dark matter temperature drop more slowly than would occur without baryons. That's because the baryons cool the way radiation energy density does (their kinetic energy is coupled to the radiation temperature prior to release of the CMB), and so their temperature scales with the inverse of the scale parameter (that's how a relativistic gas adiabatically cools as it expands), whereas uncoupled (cold) dark matter would cool to have its temperature drop like the inverse square of the scale parameter (the way nonrelativistic gas adiabatically cools as it expands). So without coupling, the dark matter gets much cooler than the baryonic gas, though maybe some of that heat comes back from the baryons to the dark matter by gravitational interactions. The modern temperature of the dark matter is not known-- it would be proportional to the unknown particle mass.

 

[haruspex]

uncoupled (cold) dark matter would cool to have its temperature drop like the inverse square of the scale parameter

This is exactly what I am not getting. How does dark matter aggregate and cool (lose KE)? What happens to the lost PE?
From links others have provided, I now understand that it has nothing to do with interactions with baryonic matter, so we can set that discussion aside.

 

[Ken G]

The cooling is basic adiabatic cooling. Any time a nonrelativistic gas is placed in a volume that is increasing, its random (thermal) kinetic energy U will drop with volume V according to the rule that dU/U = -2/3 dV/V, which is sometimes called "PdV work." That ignores gravity, but gravity doesn't appear in the energy equation because it is the same everywhere. Of course, the scale parameter "a" will obey da/a = 1/3 dV/V, so we get dU/U = -2 da/a. But relativistic gas (like photons) obey dU/U = -1/3 dV/V, so dU/U = - da/a. Thus the dark matter cools faster than the photons, and the baryon temperature follows the photons.

Still, this only tells us about the global temperature of the dark matter prior to aggregation. It doesn't tell us what processes keep the dark matter at a constant temperature spatially, which is a requirement of the Jeans gravitational instability. In the opposite limit, where the perturbations are adiabatic, there can never be a gravitational instability in nonrelativistic gas, so you'd never get clumping that way.

 

[Chalnoth]

I'm a mathematician, not a physicist, so I apologise in advance if I'm just showing my ignorance here.
My only source of information on dark matter is popular science texts, like New Scientist. One thing that is never explained is how it gets to aggregate around galaxies. Lacking the ability to shed energy by radiation, it seems it should just fly straight past and through, never even getting trapped into an orbit.
I can think of two possible explanations, neither very convincing.

1. Chaotic gravitational interactions catapulting much of it away.
Just as planets can get ejected from solar systems, carrying off a lot of the system's KE, a large portion of the original dark matter flying through could leave with increased energy, allowing its kin to become trapped. If so, there must be constantly a great stream of dark matter coursing everywhere at greater than escape velocity.
A problem with this is that it ought also to lead to normal matter constantly being flung out.

2. Thermodynamic cooling
The normal matter in a galaxy, having shed energy as radiation, is thermodynamically cooler (i.e. less KE) than the dark matter zipping past it. That should lead to some transfer of energy through the gravitational interaction.
A problem with this is that it would slow the cooling of the normal matter, delaying galaxy formation. As I understand it, it is already a challenge to explain how galaxies formed so swiftly.
​

The first definitely does happen, but it's a very slow process. I'm not sure it's even measurable. It's probably a little bit faster for dark matter because dark matter is still a diffuse gas, rather than collected into clumps like normal matter. But it's still very slow.

The second is largely just a different way of describing the first, as dark matter's only long-range interactions are through gravity.

So to a first approximation, dark matter doesn't aggregate at all: overdense regions stay in more-or-less the same configuration as they were in the early universe. They'll get a little bit more dense at their centers due to the gravity of normal matter that collects near the centers of dark matter halos, and will collapse slowly due to thermal exchange mentioned above. I think the better picture for visualizing how this works is to imagine an expanding universe where the expansion rate is slowing down. As the expansion rate slows, objects that are less dense are able to stop expanding, so they just stay more or less stationary as the expansion continues around them.

One issue that can muddy the waters here is if you look at some of the N-body simulations, they usually show the evolution of the density of the universe in terms of co-moving coordinates. This is done largely because it makes the animation appear more stable, but it also means that an object that has a constant size will appear to shrink as the universe expands overall.

 

[haruspex]

nonrelativistic gas is placed in a volume that is increasing

As the expansion rate slows, objects that are less dense are able to stop expanding,

I thought the expansion was supposed to be accelerating...
But that aside, I think what you are both telling me is that if the distribution of dark matter had stayed uniform in an expanding universe then its PE would have increased, so the aggregation does not represent a loss of PE, merely a constant PE.
If so, that says the total PE of the dark matter indicates the point in the expansion at which it formed?

 

[Ken G]

Potential energy is not a well defined notion in the context of a uniform gas in an expanding universe. It only comes into play once you start getting aggregation of the dark matter, so that aggregation would indeed represent a drop in PE, and that's why there would be a rise in KE. But in the Jeans instability, which is the normal way you get spherical clumping, there is efficient heat transfer so the temperature stays fixed and the KE does not rise as the PE falls (the PE is getting larger negatively). But the gas pressure does rise, so that's why the Jeans instability only happens on large enough scales such that the PE is larger than the KE, it needs to overcome internal pressure. That would never happen unless there was heat transfer-- adiabatic gas wouldn't fall into itself spherically. But dark matter shouldn't be very good at heat transfer, so it must find some other way to clump. Not much is said about how that works, though I have seen some reference to Jeans instability, so I don't know how the heat transfer is being handled.

 

[Chronos]

No. DM density is not unaffected by expansion, but, the effect is too small to be significant at galactic distances. DE is only noticeable at distances beyond galactic cluster scales.

 

[Orodruin]

I thought the expansion was supposed to be accelerating...

The expansion is accelerating in the sense that the second derivative of the scale factor is positive. The Hubble parameter, which is the actual rate of expansion (logarithmic derivative) is monotonically decreasing to a constant value in a Lambda-CDM universe.

 

[haruspex]

No. DM density is not unaffected by expansion, but, the effect is too small to be significant at galactic distances

If there is a roughly constant total of dark matter in an expanding region of space, the average density must be reducing, no? And if that was in response to post #16, the scale is that of the vast voids and their membranous walls.

 

[Chronos]

Expansion is too feeble to affect gravitationally bound structures, like galaxies or galactic clusters. This means a DM halo would not suffer dilution due to expansion.

 

[Chalnoth]

I thought the expansion was supposed to be accelerating...

Not quite. The language is confusing here.

The expansion of our universe is accelerated in the sense that individual objects are moving away from one another at an accelerated pace.

However, the rate of expansion is still dropping. It's just dropping more slowly. If the cosmological constant is accurate, then the expansion will level out at a constant rate in the far future, which will lead to exponential increase in distances between objects.

But that aside, I think what you are both telling me is that if the distribution of dark matter had stayed uniform in an expanding universe then its PE would have increased, so the aggregation does not represent a loss of PE, merely a constant PE.
If so, that says the total PE of the dark matter indicates the point in the expansion at which it formed?

I think that's more or less accurate.

Bear in mind that what is changing as the universe expands is that objects in the galaxy are getting further apart. So one (nearly) static dark matter halo around one galaxy is moving away from another (nearly) static dark matter halo around another far-away galaxy. But the halos themselves don't change very much due to the expansion (they definitely change some, just not much).

 

[phinds]

If there is a roughly constant total of dark matter in an expanding region of space, the average density must be reducing, no?

Well, it would except that it seems that most dark matter is within bound systems, so it experiences no expansion.

And if that was in response to post #16, the scale is that of the vast voids and their membranous walls.

EDIT: I see Chalnoth beat me to it.

 

[Ken G]

Well, the average density of dark matter is certainly dropping, and its gravitational influence on the universal expansion is responding to that drop in density. Though it is certainly true that bound dark-matter systems don't expand.

 

[haruspex]

most dark matter is within bound systems, so it experiences no expansion.

That makes it sound as though there is some magic cut-off; if it's gravitationally bound then it ignores the expansion going on around it, but if it's not bound then it happily goes with the expansion in lock step. I'm sure that's not what you mean. Rather, the expansion and gravitational collapse act oppositely, and within some radius gravitation wins, yes? But I struggle to understand how conservation of energy applies in an expanding universe. Maybe that is at the root of my puzzlement.
Anyway, I think I now am closer to understanding, and for that I thank you all for your contributions.

 

[Orodruin]

That makes it sound as though there is some magic cut-off; if it's gravitationally bound then it ignores the expansion going on around it, but if it's not bound then it happily goes with the expansion in lock step.

Well, there is a cutoff but it is neither magic or a step function. It is just how GR works. The point is that within the bound structure itself, you do not have any expansion. The universal homogeneous expansion is based on the assumption of a FLRW universe. Gravitationally bound structures clearly break this assumption so looking at those scales FLRW will no longer be a good description.

 

[haruspex]

Well, there is a cutoff but it is neither magic or a step function. It is just how GR works. The point is that within the bound structure itself, you do not have any expansion. The universal homogeneous expansion is based on the assumption of a FLRW universe. Gravitationally bound structures clearly break this assumption so looking at those scales FLRW will no longer be a good description.

Ok.

 

[phinds]

That makes it sound as though there is some magic cut-off; if it's gravitationally bound then it ignores the expansion going on around it, but if it's not bound then it happily goes with the expansion in lock step. I'm sure that's not what you mean. Rather, the expansion and gravitational collapse act oppositely, and within some radius gravitation wins, yes? But I struggle to understand how conservation of energy applies in an expanding universe. Maybe that is at the root of my puzzlement.
Anyway, I think I now am closer to understanding, and for that I thank you all for your contributions.

There is no such thing as conservation of energy on cosmological scales.

 

[Ken G]

But I struggle to understand how conservation of energy applies in an expanding universe. Maybe that is at the root of my puzzlement.

One way to reconcile the problems with thinking in terms of conservation of energy in cosmology is that conservation of energy is designed to be applied in a single reference frame-- what the energy is doing always looks like it is changing all over the place if you start changing reference frames. But that is in fact what you are constantly doing in cosmology, when we compare the situation at one age (one "reference frame" if you will) to a different age. General relativity gives us ways to cobble together these reference frames into a consistent narrative, but conservation of energy is a casualty of that cobbled-together narrative.

That said, I do think some people like to think in terms of conservation of energy even in cosmology, and they simply attribute the apparent loss of energy in things like the redshifting of the cosmic microwave background to an increase in some type of gravitational potential energy. In fact, using this perspective Hawking has said one can think of the total energy as being always zero, which helps reconcile the appearance of a zero-energy universe. But it gets very technical if one tries to ram conservation of energy down the throat of general relativity! It's probably easier just to keep that principle only in local regions that can be regarded all from the same reference frame, like bound systems.

 

[Khashishi]

I'm guessing here. Assume dark matter was initially spread evenly across the universe as a hot gas. The universe is expanding, so the kinetic energy of dark matter is redshifted. Eventually, the energy is low enough that they form gravitationally-bound clumps. In the clumps the kinetic energy is no longer controlled by the expansion of the universe, but by the virial theorem.

 

[Chalnoth]

I'm guessing here. Assume dark matter was initially spread evenly across the universe as a hot gas. The universe is expanding, so the kinetic energy of dark matter is redshifted. Eventually, the energy is low enough that they form gravitationally-bound clumps. In the clumps the kinetic energy is no longer controlled by the expansion of the universe, but by the virial theorem.

It can't start out spread perfectly evenly. If it was spread out evenly at the start, then it would still be spread out evenly. Instead, there needs to be very small differences in density from place to place in the early universe.

 

[Chronos]

Since it appears likely dark matter has primordial origins [was around before ordinary matter], you are forced to concede it was never uniformly dense, ostensibly due to quantum fluctuations prior to inflation. These density variations show up as tiny anisotrophies in the CMB that are widely believed to have seeded large scale matter structures in the universe today. While dark matter is virtually undetectable in the EM spectrum, researchers assure us it's there. Virtually every galaxy and galactic cluster hints at being embedded in a massive cloud of dark matter. The DM is distributed in a gigantic network called the cosmic web as illustrated here http://www.illustris-project.org/.

 

[Orodruin]

due to quantum fluctuations prior to inflation.

Technically during inflation. Anything from before inflation is diluted into nothing. This is the point of inflation.

 

[Davephaelon]

Here's an interesting new (19 Sept. 16) correlation discovered between radial acceleration curves in galaxies and baryonic matter distribution in galaxies deduced from near-infrared data.

https://arxiv.org/abs/1609.05917

 

[mrspeedybob]

The universe is expanding, so the kinetic energy of dark matter is redshifted. Eventually, the energy is low enough that they form gravitationally-bound clumps.

You beat me to it.

The other thing that I was going to ask is, how do we know dark matter does not radiate? We know it doesn't radiate EM because we can't see it, but what's wrong with the idea of another force or type of radiation that interacts with dark matter and not normal matter. DM had to come from somewhere. If I understand correctly, normal matter condensed out of primordial EM radiation, so it makes sense that there has to be some interactivity between the 2. DM could not have condensed out of EM because EM does not interact with it. Soo, isn't it at least plausible (if not likely) that there's another form of energy that DM does interact with?