How do concentrations of dark matter arise?

[Eise]

Normal matter clumps under the influence of gravity, but this is only because of other interactions: normal matter particles collide, loose energy and so get closer to each other. And because of the conservation of angular momentum, structures made of normal matter tend to concentrate in more or less disk-like structures (planetary systems, galaxies).

Now we learn that most galaxies are supposed to be embedded in a sphere of dark matter. These are spheres, not disks, because dark matter particles, interacting through gravity only, cannot average out their angular momentum, and so do not form a disk-like structure. So far so good.

But if we suppose that dark matter also came into existence during the big bang, and was more or less evenly distributed as normal matter, how did concentrations of dark matter arise? Because dark matter particles do not interact, except by their gravity, should these particles not be more or less evenly distributed through the universe, instead of being concentrated around galaxies and galaxy clusters? I would say that the influence of normal matter can play no role either, because dark matter also does not interact with normal matter, except again gravity. 

So one of my assumptions must be wrong. Which one? How did concentrations of dark matter arise?
 

[Strange]

My understanding is that dark matter particles can lose/exchange momentum via gravitational interactions (think gravitational slingshots, for example) it just takes a lot longer. 

Dark matter has an essential role in creating the large scale structures in the universe (including galaxies) so I suppose it is inevitable that it would be more concentrated around (not just in) those structures. 

[Eise]

After billions of years, wouldn't these average out? Or does a equilibrium arise, where part of dark matter is concentrated in/around galaxies, and another part is moving too fast to be 'captured' and moves more or less freely through the universe?

 

[Strange]

3 minutes ago, Eise said:

After billions of years, wouldn't these average out? Or does a equilibrium arise, where part of dark matter is concentrated in/around galaxies, and another part is moving too fast to be 'captured' and moves more or less freely through the universe?

I think that's basically right: there is dark matter everywhere but more concentrated around the large scale structures. I haven't seen a more detailed analysis of this, though.

[Eise]

So it would be interesting to compare the percentage of dark matter concluded from the CMBR, with an estimate how much dark matter is concentrated in and around galaxies and galaxy clusters. There should be more dark matter than 'observed' by galaxy rotations, their movements in clusters, and gravity lensing.

[Sensei]

If dark matter reacts only to gravity, the largest concentration of it should be inside of black holes, stars, and planets. In the core center...

 

[Strange]

18 minutes ago, Sensei said:

If dark matter reacts only to gravity, the largest concentration of it should be inside of black holes, stars, and planets. In the core center...

No. For exactly the reason pointed out in the first post: that requires particles to interact (bump into each other) to efficiently transfer momentum and allow matter to condense into clumps. 

[Sensei]

33 minutes ago, Strange said:

No. For exactly the reason pointed out in the first post: that requires particles to interact (bump into each other) to efficiently transfer momentum and allow matter to condense into clumps. 

These "clumps of matter" are made of ordinary matter i.e. black holes, stars and planets.. Already..

i.e. they are source of gravity which should attract whatever else what reacts only to gravity..

You described situation in which DM is alone (and does not interact even with itself), without any ordinary matter around.

Edited October 1, 2019 by Sensei

[Strange]

57 minutes ago, Sensei said:

You described situation in which DM is alone (and does not interact even with itself), without any ordinary matter around.

No I didn't.

Here is an explanation of why dark matter doesn't form structures: https://medium.com/starts-with-a-bang/ask-ethan-100-why-doesn-t-dark-matter-form-black-holes-c5b6d90b1883

[Mordred]

Good link it's nice and accurate.

[Eise]

It is a good article, and it exactly explains where my problem lies. But it does not give the answer. So can 'slingshots' explain the local concentrations of dark matter: slowing down one particle, accelerating the other, and the slow ones in the end form the dark matter halos around galaxies?

[Strange]

1 hour ago, Eise said:

So can 'slingshots' explain the local concentrations of dark matter: slowing down one particle, accelerating the other, and the slow ones in the end form the dark matter halos around galaxies?

That is pretty much my understanding. I have seen mention of this being modelled, but not any direct articles or papers on the subject. It would be included (implicitly, at least) in the simulations of large scale structure formation, such as:

https://wwwmpa.mpa-garching.mpg.de/galform/virgo/millennium/

http://www.illustris-project.org/about/

http://cosmicweb.uchicago.edu/sims.html

[Janus]

5 hours ago, Sensei said:

These "clumps of matter" are made of ordinary matter i.e. black holes, stars and planets.. Already..

i.e. they are source of gravity which should attract whatever else what reacts only to gravity..

You described situation in which DM is alone (and does not interact even with itself), without any ordinary matter around.

While dark matter is gravitationally attracted to these bodies, and will fall in towards them, there is no mechanism equivalent to electromagnetic interaction to keep it there.  If you imagine a dark matter particle falling towards Earth, it will pick up speed as it gets closer and closer.  It will reach the Earth moving at some great speed, pass through it, and climb away out the other side with the same velocity as it had coming in, climbing back out into space. (It pretty much behaves as visible matter would if it were falling through a tunnel bored through the Earth)

Put another way, if an asteroid is moving at escape velocity with respect to the Earth, as long as its trajectory doesn't intersect the Earth itself, it will fall in towards the Earth, swing around it and head back into space never to return.  On the other hand, if it hits the surface,  thus converting a great deal of its velocity into heat it can be left with too little KE to climb back out of the Earth's gravity well.  Dark matter will just pass through the Earth, even if on a surface intersecting trajectory, without shedding energy in this way.

So, no, you would not expect to find dark matter in great quantities inside planets or stars.

The only mechanisms available to Dark matter for shedding energy is the aforementioned slingshot ( which involves a third body. So for example in our last example, while the entry and exit velocities for the DM particle remain the same relative to the Earth, the Earth-dark matter interaction could reduce the dark matter's velocity with respect to the Sun, or increase it at the expense of some the Earth's orbital energy.

The other mechanism is gravitational radiation emission.  The acceleration of the dark matter particle due to it gravitational interaction with the Earth can cause it to produce gravitational waves which come at the expense of the KE of the particle. However, gravitational radiation is very weak, and we are talking about a minimal loss via this mechanism.

 

[mistermack]

It's only ASSUMED that dark matter doesn't interact at all, because no evidence has been seen so far. Might it be that very high speed high energy particles can on occasions collide with dark matter? Over billions of years, it might be enough to cause a bit of clumping around a galaxy. 

[Strange]

30 minutes ago, mistermack said:

It's only ASSUMED that dark matter doesn't interact at all, because no evidence has been seen so far.

That is not quite right. There are a number of different dark matter searches underway, based on different models of the nature of dark matter particles. These all assume there will be some interaction otherwise they would not be able to detect anything!

However, we know it hardly interacts because of its properties - in other words, we know it doesn’t interact because of its non-clumpy distribution.

 

[Sensei]

1 hour ago, Janus said:

If you imagine a dark matter particle falling towards Earth,

...that is why in my previous response, not with a reason, I imagined black hole... i.e. escape velocity from black hole is >= speed of light..

 

[swansont]

14 minutes ago, Sensei said:

...that is why in my previous response, not with a reason, I imagined black hole... i.e. escape velocity from black hole is >= speed of light..

But absent any significant loss mechanisms, it has to directly hit the black hole to be lost to it. 

[Danijel Gorupec]

6 hours ago, Eise said:

It is a good article, and it exactly explains where my problem lies. But it does not give the answer. So can 'slingshots' explain the local concentrations of dark matter: slowing down one particle, accelerating the other, and the slow ones in the end form the dark matter halos around galaxies?

How you described those 'slingshots' reminds me on evaporative cooling - is that how you imagine it? Or you thinking about slingshots caused by massive ordinary-mater objects?

(I like to think about DM as gas... I guess, DM particles may still obey Bolltzman distribution of their energies, unless maybe the gas is so cold that quantum effect could prevail... If I suppose Boltzman distribution, then some particles should obtain escape velocity... I wonder if we know the upper limit for the mass of one DM particle?)

[Janus]

2 hours ago, Sensei said:

...that is why in my previous response, not with a reason, I imagined black hole... i.e. escape velocity from black hole is >= speed of light..

 

In order to be captured by the black hole, the dark matter would already have to be on an initital trajectory that crosses the event horizon.  escape velocity is c for objects that originate at the event horizon.   At any point further out, the escape velocity is less. So it is quite possible to have something fall in towards the black hole and skim by it outside of the event horizon.

Visible matter doing this runs the risk of colliding with other matter surrounding the black hole (the accretion disk,.  for example), losing orbital energy, and finding itself with an event horizon crossing trajectory even if it didn't start with one.

[mistermack]

This might be of interest :

Over at another thread, the one about "Planet 9" if you read the link provided in the original post, Scholz and Unwin say that if Planet 9 turned out to be a small primordial black hole, they would expect it to be surrounded by a halo of dark matter. 

At the bottom of the page :    https://www.technologyreview.com/s/614441/is-planet-9-actually-a-primordial-black-hole/    

[Strange]

9 minutes ago, mistermack said:

This might be of interest :

Over at another thread, the one about "Planet 9" if you read the link provided in the original post, Scholz and Unwin say that if Planet 9 turned out to be a small primordial black hole, they would expect it to be surrounded by a halo of dark matter. 

At the bottom of the page :    https://www.technologyreview.com/s/614441/is-planet-9-actually-a-primordial-black-hole/    

Although they don't discuss that in their paper, the various papers they reference on that might answer the original questions in more detail.

[MigL]

I suppose a lot depends on the mass of DM particles and the 'curvature' of the geodesics they are constrained to follow.
Even if massless ( moving at c ), any contact with an event horizon ( actually even larger ) will constrain them along inescapable geodesics ( as Sensei/Janus mention ).
But DM particle motion at sub-light speed will allow them to be captured by sufficiently massive objects, as evidenced by the concentrations about galaxies. Not necessarily interacting with anything, just following curved trajectories which keep them localized.

This may be a way to determine a lower bound on the mass of DM particles, as they need to be captured in considerable quantities by galaxies.

Edited October 1, 2019 by MigL

[Strange]

5 minutes ago, MigL said:

This may be a way to determine a lower bound on the mass of DM particles, as they need to be captured in considerable quantities by galaxies.

I think that is basically how we moved from hot dark matter to cold dark matter: analysis of the distribution observed by gravitational lensing and from the simulations of large scale structures put limits on possible velocity and mass. 

[Mordred]

5 hours ago, Strange said:

I think that is basically how we moved from hot dark matter to cold dark matter: analysis of the distribution observed by gravitational lensing and from the simulations of large scale structures put limits on possible velocity and mass. 

Actually it's more complicated than this but in a sense does relate.

The primary difference between hot warm and cold DM involves a term called the free streaming length. In essence this is the average length a DM particle can travel before it falls into a gravitational potential well.

 The main evidence for Cold DM is the CMB background. As a weakly interactive particle we have to employ a combination of two fundamental equations. Jeans equations which correlates to the rate of infalling matter for structure formation and the thermodynamic collisionless Boltzmann equations. Baryons would employ the collision Boltzmann. This combination leads to the Baryon accoustic oscillations. However the collisionless Boltzmann leads to the free streaming length rather than accoustic oscillations.( Commonly referred to as free streaming or Landau damping) this involves the velocity dispersion factors given as a velocity dispersion tensor ( employs a Fourier transform in six dimensional phase space and how they correlate to velocity space) now there is a mouthful (the Jeans equation is in essence the six dimensional collisionless Boltzmann equation)

 These factors affect when the various DM species would drop out of thermal equilibrium and commence their contribution to Structure formation. The CMB data originally done by COBE provided the first evidence for the CDM version coupled with Lambda. Subsequent datasets placed further bounds in favor of the CDM. 

 The equations involved are rather lengthy so I will leave it to the above explanation it would take to long to explain Jeans equations. The topic itself can encompass entire textbooks. 

In essence it boils down to the best fit for early galaxy formation.

Side note the Jeans equations are also used to estimate DM around BH's. So your both right but as mentioned it's a bit complex in how it's correlated.

Edited October 2, 2019 by Mordred

[MigL]

I remember reading about the collisionless Boltzmann equation and the Jeans analysis in some MIT lecture notes a while back

https://ocw.mit.edu/courses/physics/8-902-astrophysics-ii-fall-2004/lecture-notes/

Unfortunately only the first 11 lectures are available, and the omitted ones probably contain the 'good stuff'.

Maybe you can recommend some 'light' reading Mordred.