Gravitational Collapse of Dark Matter Halos

[DrMars]

It is a well accepted theory that the gravitational collapse of 'ordinary' (baryonic) matter into galaxies and stars is related to the radiative energy loss following the collisional excitation of atoms/molecules.
I just wonder what the corresponding energy loss processes for non-baryionic dark matter are supposed to be, and why the energy loss processes do not lead to a further gravitational collapse of the dark matter halos surrounding galaxies (assuming that the dark matter is indeed non-baryonic).

[Fortunate]

Hi DrMars,
Here (http://www.bautforum.com/showthread.php?t=36144) is some discussion of a somewhat related question.

Now, it seems, some of the dark matter may be tepid (http://news.bbc.co.uk/1/hi/sci/tech/4679220.stm), moving too fast to collapse.

[DrMars]

I had a look at the links above, but they don't really answer my question. The point is that if the dark matter is collisionless, this would explain the fact that the halos don't collapse any further into smaller structures (like the collisional 'normal' matter does), but this poses then the question how they were formed in the first place (the temperature issue doesn't really change anything about this argument (which merely depends on the matter being collisional or non-collisional)).

[Fr. Wayne]

How they were formed? In the Big Bang the power unleashed was exponentially greater than any to-date particle accelerator we have in the laboratories. Yet even our experiments have created these particles. Are non-b's left-overs from Big Bang? Possibly, but there remains the chance that there are powerful forces still in the Universe capable of naturally making these non-b's more efficiently than us such as supernova's (discretely) and pulsars (continuously) and who know's what else. Only the Shadow knows!

[Ken G]

Welcome to the forum DrMars. I too have this same question, and don't know the answer. I think the theories do account for mechanisms that can cause contraction without radiation, but it can't be all that simple. And here's a related question I have-- how do we know dark matter doesn't radiate dark light?

[Ken G]

How they were formed?
DrMars means how did the dark-matter clumps form, not how did the dark matter itself form. The theory is that at some early point, there were overdensities in the dark matter just by chance. These overdensities then underwent a gravitational instability which caused them to clump more, eventually on galactic scales. The galactic clumps then draws in the normal matter and makes galaxies. But the question is, what is this gravitational instability in the dark matter, and why did it stop on scales of the haloes, while the normal matter in galaxies (which is able to radiate light) managed to filter down deeper and deeper into the dark-matter potential wells.

[korjik]

It is a well accepted theory that the gravitational collapse of 'ordinary' (baryonic) matter into galaxies and stars is related to the radiative energy loss following the collisional excitation of atoms/molecules.
I just wonder what the corresponding energy loss processes for non-baryionic dark matter are supposed to be, and why the energy loss processes do not lead to a further gravitational collapse of the dark matter halos surrounding galaxies (assuming that the dark matter is indeed non-baryonic).

We would have to have the slightest clue what dark matter is before we could try to figure its dynamics.

There is also that the dark matter is still a halo, implying that it dosent collapse. At least not in the same time scale as baryonic matter does.

[Ken G]

Actually, the gravitational dynamics of objects don't depend on their masses except in terms of whether they are "hot" (relativistic) or "cold" (nonrelativistic). So "cold dark matter" is already a dynamical model. DrMars is asking about how that model works, and it's a good question that is probably explained somewhere under the heading of "cold dark matter haloes".

[Fr. Wayne]

gamma rays do increase the creation of ions, so sufficient energy from magnastar outbursts can also contribute to dark matter's "Quantity?"
http://www.space.com/scienceastronomy/bright_flash_050218.html

[Ken G]

Not in any significant way. Remember, there is already much more energy in dark matter than in baryonic matter, so the creation of the former from the latter would not be important. Another problem is, I don't think you can make dark matter from photons, they might not couple well enough to do that. Perhaps you can, I don't know!

[Fr. Wayne]

I wasn't implying that ions made dark matter. I was pondering that gamma rays hitting a dark matter reservoir would effect its expansion and/or quantity.

[Fortunate]

It's tough to say much because we don't know much.

[DrMars]

DrMars means how did the dark-matter clumps form, not how did the dark matter itself form. The theory is that at some early point, there were overdensities in the dark matter just by chance. These overdensities then underwent a gravitational instability which caused them to clump more, eventually on galactic scales. The galactic clumps then draws in the normal matter and makes galaxies. But the question is, what is this gravitational instability in the dark matter, and why did it stop on scales of the haloes, while the normal matter in galaxies (which is able to radiate light) managed to filter down deeper and deeper into the dark-matter potential wells.
Yes, that's exactly the point I wanted to make: if the dark matter would be strictly non-collisional, it could not lose any energy and hence would not be able to form galactic halos by means of gravitational contraction; on the other hand, if it is collisional, the contraction should not suddenly stop at a certain size. In fact, as the density gets higher as the cloud contracts, the effects of collisions should even become more important and the contraction be accelerated. The only way to have a halo that stops contracting at a certain point would be that the dark matter condenses, like the visible matter, into 'stars'. This would reduce any collisions practically to zero and hence the halo would be almost indefinitely stable (like the 'normal' galaxy). I wonder if there are any observational data that would allow to determine whether the dark matter is actually homogeneously distributed or maybe indeed concentrated in dark matter 'stars'.
In any case, a gravitational contraction should not be possible without some degree of collisional energy loss, and it is the question whether non-baryonic dark matter could provide this.

[ngc3314]

Yes, that's exactly the point I wanted to make: if the dark matter would be strictly non-collisional, it could not lose any energy and hence would not be able to form galactic halos by means of gravitational contraction; on the other hand, if it is collisional, the contraction should not suddenly stop at a certain size. In fact, as the density gets higher as the cloud contracts, the effects of collisions should even become more important and the contraction be accelerated. The only way to have a halo that stops contracting at a certain point would be that the dark matter condenses, like the visible matter, into 'stars'. This would reduce any collisions practically to zero and hence the halo would be almost indefinitely stable (like the 'normal' galaxy). I wonder if there are any observational data that would allow to determine whether the dark matter is actually homogeneously distributed or maybe indeed concentrated in dark matter 'stars'.
In any case, a gravitational contraction should not be possible without some degree of collisional energy loss, and it is the question whether non-baryonic dark matter could provide this.

Even a collisionless gravitating system (that is, one consisting of particles which interact ony gravitationally, the one thing dark matter shows evidence of doing) can collapse, more or less by evaporative cooling. In this sense what happens is like we see in simulations of dense star clusters. Multibody interactions will give some particles much more than the average energy at their location, making them unbound (escaping the system) or at least less tightly bound, and the remainder, conserving energy, more tightly bound (shrinking). Any constraints due to particle properties may set limits on this (for example, low-mass weakly interacring particles could become degenerate in the central parts of galaxies, as in one recent suggestion). Any other cooling mechanisms would naturally make such a collapse more effective, but are not needed for collapse to happen (although the collapse slows down a great deal as time goes on).

Gravitational microlensing statistics make it pretty clear that the dark-matter halo of the Milky Way is not dominated by condensed starlike objects, which is why we're back to talking about elementary-particle (or indeed modified-physics) solutions.

[Relmuis]

If the Dark Matter consisted of Fermions, no cloud of these particles with a certain total energy could collapse past the size where all low energy states are filled. Just like the degeneracy pressure of electrons keeps a white dwarf buoyed up, and the degeneracy pressure of neutrons does the same for a neutron star.

For such a degenerate Fermi gas to fill a galactic halo, the mass of the individual particles would have to be extremely small, but as it is unknown what Dark Matter is, that doesn't seem to be a problem.

[Ken G]

Actually, the mass of cold dark matter (which is the behavior that ngc3314 was talking about) particles could not be too small or it would not clump on galactic scales at all (they'd be relativistic, like the neutrinos). So there are some things that are expected to hold for the dynamics of the dark matter, and they seem to work out pretty well-- for example, spiral galaxy rotation curves favor a spherical distributon of dark matter in which the density falls like 1/r^2, and that is apparently just what a cold dark matter model would predict. I'm not sure exactly why that is, perhaps a mechanism like what ngc3314 leads to that naturally. But I did have a question about this:

In this sense what happens is like we see in simulations of dense star clusters.

It seems to me that star clusters are effectively not collisionless, because although stars don't formally collide, they do suffer two-body interactions due to their gravity, and that would look just like collisions. Perhaps multibody (more than two at a time, that is) interactions play a role too, but this is still different than collisionless dark matter particles, which should only interact with the overall gravitational field with no stochastic component. I'm not clear that evaporation could happen to such particles-- maybe they do need some kind of weak interactions to make this work.

[ngc3314]

It seems to me that star clusters are effectively not collisionless, because although stars don't formally collide, they do suffer two-body interactions due to their gravity, and that would look just like collisions. Perhaps multibody (more than two at a time, that is) interactions play a role too, but this is still different than collisionless dark matter particles, which should only interact with the overall gravitational field with no stochastic component. I'm not clear that evaporation could happen to such particles-- maybe they do need some kind of weak interactions to make this work.

You can get evaporative effects even without close two-body encounters (for example, using test particles moving in an overall potenential). Early simulations of galaxy interactions did this, and demonstrated the exchange of internal and orbital energy. I take your point with respect to dark-matter particles - they ought to interact with each other gravitationally, but low-mass particles would take a very long time for this to affect their distribution. There are odd-seeming mechanisms that exchange lots of energy by exciting large-scale dynamical modes, which have been implicated in the "violent relaxation" of stellar sstems, but I'd be in over my head to go further without some reading.

[Ricimer]

I'll see if I can't get a friend to post here (no promises), he's actually working on simulations about collapsing and coelescing of dark matter sub halos.

[Fortunate]

I'll see if I can't get a friend to post here (no promises), he's actually working on simulations about collapsing and coelescing of dark matter sub halos.

Would it help to beg?

[Ken G]

There are odd-seeming mechanisms that exchange lots of energy by exciting large-scale dynamical modes, which have been implicated in the "violent relaxation" of stellar sstems, but I'd be in over my head to go further without some reading.
I was wondering about that kind of thing, if that plays a role. Another point to consider is that if you have a collisionless gas at a constant temperature in a spherical distribution where the density falls off like 1/r^2, then the pressure gradient balances gravity. Thus, the static configuration of a spherical isothermal self-gravitating gas is to be centrally compressed to the tune of a 1/r^2 density. That has to be trying to tell us that you'll get contraction even without collisions, i.e., spherical perturbations will grow in density toward the center.

[DrMars]

Even a collisionless gravitating system (that is, one consisting of particles which interact ony gravitationally, the one thing dark matter shows evidence of doing) can collapse, more or less by evaporative cooling. In this sense what happens is like we see in simulations of dense star clusters. Multibody interactions will give some particles much more than the average energy at their location, making them unbound (escaping the system) or at least less tightly bound, and the remainder, conserving energy, more tightly bound (shrinking). Any constraints due to particle properties may set limits on this (for example, low-mass weakly interacring particles could become degenerate in the central parts of galaxies, as in one recent suggestion). Any other cooling mechanisms would naturally make such a collapse more effective, but are not needed for collapse to happen (although the collapse slows down a great deal as time goes on).
Just for clarification: with collisions I was primarily referring to inelastic collisions that can lead to radiative energy losses. Of course, as you mentioned, there can also be an energy loss due to elastic collisions if high energy particles escape the system.
However, it is not clear to me how you can have a cooling without any collisions at all (as you seem to be suggesting).

[DrMars]

If the Dark Matter consisted of Fermions, no cloud of these particles with a certain total energy could collapse past the size where all low energy states are filled. Just like the degeneracy pressure of electrons keeps a white dwarf buoyed up, and the degeneracy pressure of neutrons does the same for a neutron star.

For such a degenerate Fermi gas to fill a galactic halo, the mass of the individual particles would have to be extremely small, but as it is unknown what Dark Matter is, that doesn't seem to be a problem.
Shouldn't degenerate matter imply that its density is constant throughout? This would then not be consistent with galactic rotation curves (which require a density dependence ~1/r^2 ).

[DrMars]

It seems to me that star clusters are effectively not collisionless, because although stars don't formally collide, they do suffer two-body interactions due to their gravity, and that would look just like collisions.
Yes, but the point is that a) these distant two body interactions are not associated with inelastic atomic collisions that could cause radiative energy loss and b) distant 'collisions' of two stars are very unlikely to double the kinetic energy of one of them (which would be required for a system in virial equilibrium if one of the stars should be able to escape). If there would be a significant energy loss due to stellar encounters in galaxies, then the latter could hardly be stable over the course of many galactic rotations.

[DrMars]

I was wondering about that kind of thing, if that plays a role. Another point to consider is that if you have a collisionless gas at a constant temperature in a spherical distribution where the density falls off like 1/r^2, then the pressure gradient balances gravity. Thus, the static configuration of a spherical isothermal self-gravitating gas is to be centrally compressed to the tune of a 1/r^2 density.
But a 1/r^2 density distribution requires a collisional energy loss. Otherwise the gas could not become centrally compressed.

[Ken G]

But a 1/r^2 density distribution requires a collisional energy loss. Otherwise the gas could not become centrally compressed.
There are really two questions here, one is why do you expect the 1/r^2 density, and the other is why do you expect dark matter to clump at all.
The second issue relates to the question of how does a population of stars, like a globular cluster, get even more centrally compressed after forming from gas that was somewhat centrally compressed. In other words, note that the motion of stars does not couple into any kind of radiative energy, you can't radiate that energy away. ngc3314 mentioned a mechanism whereby you can lose energy, where ejected stars take over the role of radiation. The bottom line, as you know, is that the collection of stars or dark matter must obey the virial theorem, which means that to contract, a lot of energy must be removed from the system somehow. In the case of dark matter, this must occur due to binary interactions of some kind, i.e., collisions in effect, but not ones that generate any appreciable amount of light.

The first question, why 1/r^2, is very different because you can ask what would happen to a gravitationally bound spherical distribution of constant dark matter density out to some given radius. This configuration would not be in force balance, and in the absence of any interactions at all, it will have to oscillate forever, but if there are even very weak interactions (and there is certainly gravity, though I don't know if that would really be enough), then after a while you'll reach a steady state which follows the 1/r^2 density. You'll probably also eject some matter and end up a bit more centrally compressed, as per the answer to the first question. So I think the answer to DrMars' question must be that the cold dark matter model does account for some weak interactions between the dark matter particles, i.e., elastic collisions.

[Relmuis]

Shouldn't degenerate matter imply that its density is constant throughout? This would then not be consistent with galactic rotation curves (which require a density dependence ~1/r^2 ).

I was under the impression that galaxies were found to rotate almost like rigid wheels, with orbital speeds increasing from hub to rim. That would require equal background density throughout.

Anyway, a degenerate gas with a swarm of gravitating stars inside would densify somewhat around these stars, because inside the stars' gravity wells there would be more states to be filled than elsewhere. This would have the effect of enhancing the stars' own gravity fields, which might explain the Pioneer anomalies.

But the argument about very small particles being likely to have high energies is rather compelling. Yet, if there were no thermal contact at all with ordinary matter, the dark matter might have been created at a small fraction of the then-existing temperature of ordinary matter, and the ratio between the two temperatures would (I think) have remained the same throughout history. I.E. the dark matter might now be cold enough to be beneath the Fermi temperature even for very small particles.

Of course, there is thermal contact, through the gravitational interaction. But this might be negligible. (Or it might not; I don't know how to calculate it.)