How do concentrations of dark matter arise?

[Eise]

9 hours ago, Danijel Gorupec said:

How you described those 'slingshots' reminds me on evaporative cooling - is that how you imagine it?

Yes, more or less. If slingshots are the mechanism, then the KE won by a DM particle that flies away is lost by another one, and this one might then be bound to the local gravitation. But still... As Janus remarks, for slingshots at least 3 particles are needed. At least one of them should be much more heavier than the others for the slingshot mechanism to work effectively. Of course this must not be one single particle: a concentration of DM particles would do, but this presupposes already what I want to understand. How do DM particles concentrate if they do not interact by anything but gravity?

There is of course a huge difference with evaporate cooling: there particles collide (electromagnetic interaction), which DM particles would not do. 

6 hours ago, MigL said:

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.

But this is exactly what I would like an explanation for. DM particles would just 'fall through' massive objects and stick to their Newtonian orbits. One could even defend that close to gravitational centres DM is diluted, because at Newtonian orbits particles (any object inf fact) are less time close to the centre of gravity than farther away. But as the simulations seem to prove, DM concentrates too, just less than baryonic matter. And I assume these simulations are made on the basis of 'gravitational interaction only' for DM particles. 

[Danijel Gorupec]

12 minutes ago, Eise said:

There is of course a huge difference with evaporate cooling: there particles collide (electromagnetic interaction), which DM particles would not do.

Hmm... But if they are fermions, they should be, in a way, colliding, no? On the other hand, if they are bosons, they should be lumping toghether, no? I mean, they should be interacting by some mean... unless you believe they are so much different that are beyond wave mechanics?

[Danijel Gorupec]

In fact... I am not sure electromagnetic interaction is responsible for collisions in a (fermionic) gas.

[Eise]

1 hour ago, Danijel Gorupec said:

if they are bosons, they should be lumping toghether, no? 

Why? That bosons can be at the same place as other bosons does not mean they tend to take the same place. And are bosons not always force carrying particles? If so, from what force? Not gravity, that would be gravitons.

33 minutes ago, Danijel Gorupec said:

In fact... I am not sure electromagnetic interaction is responsible for collisions in a (fermionic) gas.

I do not think so: neutron stars are made of degenerate neutrons, which are of course electrically neutral. But it is a good question: how does a neutron 'recognise' that a place is already occupied? Because of their magnetic moments? Can some real physicist shine some light on this?

 

[swansont]

10 hours ago, Danijel Gorupec said:

On the other hand, if they are bosons, they should be lumping toghether, no? I mean, they should be interacting by some mean... unless you believe they are so much different that are beyond wave mechanics?

Via what interaction? 

9 hours ago, Danijel Gorupec said:

In fact... I am not sure electromagnetic interaction is responsible for collisions in a (fermionic) gas.

Pretty sure it is, for fermions that can interact that way. 

A common method in fermi gas experiments is tuning the scattering length (a measure of the interaction strength) via an external magnetic field.

[Sensei]

Charged fermions react to external electric and/or magnetic fields. Uncharged fermions i.e. neutrinos interact via weak-force (and gravity)..

 

[swansont]

7 minutes ago, Sensei said:

Charged fermions react to external electric and/or magnetic fields. Uncharged fermions i.e. neutrinos interact via weak-force (and gravity)..

 

Uncharged composite fermions such as neutrons and atoms will interact electromagnetically.

[Mordred]

23 hours ago, MigL said:

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.
 

Unfortunately I haven't found any decent light reading material outside of textbooks.

 One of the better books I have on the topic is Elements of Atrophysics.

[mistermack]

I wonder if its possible that DM can interact at very high velocities. 

As was mentioned earlier, DM has to score a direct hit on the event horizon of a black hole to get trapped. But what happens to the DM that only just misses ? Presumably, it will be travelling at a significant fraction of the speed of light as it skirts the black hole, and could be encountering both matter and dark matter, coming in the opposite direction at high speed, as it skims the event horizon and flies off on it's next ellipse. 

If there are any conditions in which it could possibly interact, I'm guessing it's probably there, just outside the event horizon. 

On the page I'm linking below, a UK team have found that matter falling in from the accretion disk was travelling at 30% of light speed, so if dark matter was meeting it head on ( not being caught by the disk ) they would be meeting at very high speed. 

https://ras.ac.uk/news-and-press/research-highlights/matter-falling-black-hole-30-percent-speed-light  

 

[swansont]

If dark matter has difficulty in shedding angular momentum, there won't be much around to be near the BH. Highly elliptical orbits have minimal angular momentum (L = r x p); maximum angular momentum is a circular orbit (for a given energy).  

[Eise]

Wikipedia also has something to say about this topic:

Quote

 

Dark matter aggregation and dense dark matter objects
If dark matter is composed of weakly-interacting particles, an obvious question is whether it can form objects equivalent to planets, stars, or black holes. Historically, the answer has been it cannot, because of two factors:

It lacks an efficient means to lose energy
Ordinary matter forms dense objects because it has numerous ways to lose energy. Losing energy would be essential for object formation, because a particle that gains energy during compaction or falling "inward" under gravity, and cannot lose it any other way, will heat up and increase velocity and momentum. Dark matter appears to lack means to lose energy, simply because it is not capable of interacting strongly in other ways except through gravity. The virial theorem suggests that such a particle would not stay bound to the gradually forming object – as the object began to form and compact, the dark matter particles within it would speed up and tend to escape.
It lacks a range of interactions needed to form structures
Ordinary matter interacts in many different ways. This allows the matter to form more complex structures. For example, stars form through gravity, but the particles within them interact and can emit energy in the form of neutrinos and electromagnetic radiation through fusion when they become energetic enough. Protons and neutrons can bind via the strong interaction and then form atoms with electrons largely through electromagnetic interaction. But there is no evidence that dark matter is capable of such a wide variety of interactions, since it seems to only interact through gravity (and possibly through some means no stronger than the weak interaction, although until dark matter is better understood, this is only hopeful speculation).

 

But no answer to my question... So, slingshots it be?

[swansont]

There is a mechanism of gravitational radiation, which will arise from certain accelerations, so over a very long time you can dissipate some energy. Because that should be proportional to the acceleration experienced, I think that might tend to circularize orbits, which would lend itself to halo-like formations.

[Eise]

Yes, Janus mentioned it too, but with some hesitation:

On 10/1/2019 at 6:14 PM, Janus said:

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.

Would the energy loss due to gravitational radiation really explain this? E.g. do you think gravitational radiation was included in universe simulations? I doubt it.

[swansont]

Highly elliptical paths will radiate more strongly when the acceleration and speeds are larger.  A close pass by a large mass (black hole) will radiate a much larger fraction of an objects energy than something in e.g. an earth-like orbit.

 

[Sensei]

On 10/1/2019 at 6:14 PM, Janus said:

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.

Escape velocity equation (from surface and further) is:

[math]v=\sqrt{\frac{2 G M}{r}}[/math]

for any M, we can find any such so small r, after reaching it, escape velocity is equal or exceeding c.

So, for the Sun, it'll be:

[math]r=\frac{2 * 6.67*10^{-11} * 2*10^{30}}{299792458^2}[/math]

approximately 2968 meters.

Multiply by millions and billions of years sucking in any (hypothetical) DM, and these M_sun and M_earth must already have it included..

 

I think so escape velocity equation has sense only from object's surface and further. If (electric neutral) particle is inside (passing through) of e.g. star or planet or other object, it's attracted from the all directions, and calculation which is just toward center of it, is at least "imprecise"..

On 10/1/2019 at 6:14 PM, Janus said:

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

I said concentration, not quantity. Concentration requires both quantity and volume.

 

Edited October 6, 2019 by Sensei

[Janus]

6 hours ago, Sensei said:

Escape velocity equation (from surface and further) is:

v=2GMr−−−−√

for any M, we can find any such so small r, after reaching it, escape velocity is equal or exceeding c.

So, for the Sun, it'll be:

r=2∗6.67∗10−11∗2∗10302997924582

approximately 2968 meters.

Multiply by millions and billions of years sucking in any (hypothetical) DM, and these M_sun and M_earth must already have it included..

 

I think so escape velocity equation has sense only from object's surface and further. If (electric neutral) particle is inside (passing through) of e.g. star or planet or other object, it's attracted from the all directions, and calculation which is just toward center of it, is at least "imprecise"..

I said concentration, not quantity. Concentration requires both quantity and volume.

 

The escape velocity equation given only holds if all the mass concerned it contained within that radius.  To get an escape velocity of c from one solar mass, you would first have to squeeze all of the Sun's mass inside that 2968 meter radius. 

Escape velocity is dependent on gravitational potential.  It basically works out that you are at escape velocity when KE +GPE = 0   KE = mv²/2 and outside of a mass, GPE = -GMm/r

ergo  escape velocity is when:

mv²/2= GMm/r

v²/2= GM/r

v²= 2GM/r

Once you pass inside of a body like the Sun, the GPE equation changes to

GPE = -GMm[(3R² - r²)/2R³] (to be fair, this is not exact for the Sun, as this assumes a constant density, and the Sun's density increases as you move inward which would need to be accounted for)

where R is the radius of the body, (r is your distance from the center)

If r=0, (you are at the center) is reduces to

GPE = - 3GMm/2R, which makes the escape velocity

v² = 3GM/R

In other words, the escape velocity from the center of a uniformly dense object is just 22.5% greater than that at the surface. 

Thus, if the Sun where of uniform density, the escape velocity from its center would be ~757 km/sec, compared to the 617.5 km/sec it is from the surface.   Even after  you factor in the the increasing density with depth, you get nowhere close to c or the formation of a event horizon.

 

 

 

[Sensei]

4 hours ago, Janus said:

Once you pass inside of a body like the Sun, the GPE equation changes to

GPE = -GMm[(3R² - r²)/2R³] (to be fair, this is not exact for the Sun, as this assumes a constant density, and the Sun's density increases as you move inward which would need to be accounted for)

where R is the radius of the body, (r is your distance from the center)

If r=0, (you are at the center) is reduces to

GPE = - 3GMm/2R, which makes the escape velocity

v² = 3GM/R

In other words, the escape velocity from the center of a uniformly dense object is just 22.5% greater than that at the surface. 

Thus, if the Sun where of uniform density, the escape velocity from its center would be ~757 km/sec, compared to the 617.5 km/sec it is from the surface.   Even after  you factor in the the increasing density with depth, you get nowhere close to c or the formation of a event horizon.

I think so, in our deliberations, we can safely exclude outermost layers of the Sun (where the density is less than water on Earth), and concentrate just on the solar core.

Mass of the core is 34% of M_sun = 0.34 *  1.9885×10³⁰ kg = 6.761*10^29 kg

Radius of the core is ~20% of R_sun = 0.2 * 696,342,000 m = 139,268,400 m

So, using your above escape velocity from the center of object, we are getting:

v² = 3 * 6.67*10^-11 * 6.761*10^29 / 139,268,400 = ~9.714*10^11

v=sqrt( 9.714*10^11 ) = ~ 985,600 m/s = ~1 million m/s = ~1000 km/s

 

[Janus]

44 minutes ago, Sensei said:

I think so, in our deliberations, we can safely exclude outermost layers of the Sun (where the density is less than water on Earth), and concentrate just on the solar core.

Mass of the core is 34% of M_sun = 0.34 *  1.9885×10³⁰ kg = 6.761*10^29 kg

Radius of the core is ~20% of R_sun = 0.2 * 696,342,000 m = 139,268,400 m

So, using your above escape velocity from the center of object, we are getting:

v² = 3 * 6.67*10^-11 * 6.761*10^29 / 139,268,400 = ~9.714*10^11

v=sqrt( 9.714*10^11 ) = ~ 985,600 m/s = ~1 million m/s = ~1000 km/s

 

Still well short of c.  And remember that escape velocity is also the velocity something dropped at rest from an infinite distance would be moving at the center of the Sun as long it was able to fall unimpeded.  In other words, any dark matter that starts at or above escape velocity at any distance will be moving at or above escape velocity when it reaches the center.

[swansont]

If an object is not gravitationally bound, it will always have greater than escape velocity. It speeds up as it gets closer to the sun (or other celestial body). Unless it’s a BH (so that it can’t escape)

edit: xpost with Janus

[Airbrush]

How do concentrations of dark matter arise?  By gravity.

[swansont]

2 hours ago, Airbrush said:

How do concentrations of dark matter arise?  By gravity.

Now how about reading the OP to see why this doesn’t answer the question.

[Airbrush]

"...So even though we think of gravity as the only force that matters on the largest scales, the truth is when we think about the structures that we see — the ones that give off light, that house atoms and molecules, that collapse into black holes — it’s the other forces, in concert with gravity, that allow them to exist at all. Dark matter can’t make these structures, sadly, because gravity alone simply isn’t good enough to do the job."

https://medium.com/starts-with-a-bang/ask-ethan-100-why-doesn-t-dark-matter-form-black-holes-c5b6d90b1883

This is from the link that Strange provided near the beginning of the discussion.

So after the big bang there was ordinary matter and 5 or 6 (?) times that much dark matter.  If it wasn't for the dark matter the universe would be merely particles scattered evenly through space.  The dark matter gravity brought large-scale clumps of dark matter, on the size of galaxies and galaxy clusters. 

The dark matter attracted ordinary matter.  The electrostatic force of the ordinary matter caused ordinary matter to form small clumps that grew in size.  When these clumps of ordinary matter became large enough, then gravity assisted in forming large sized objects, without any help needed from DM.

 

[Eise]

OK, Ethan Siegel has given the answer now in his blog 'Starts with a Bang'.

In short:

Quote

... because the Universe expands, reducing the kinetic energy of particles traveling through it, and because structures also gravitationally grow over time, meaning that a particle that falls in has a tougher time getting back out again, dark matter particles wind up gravitationally bound inside these structures. 

That makes more sense to me than slingshots. I assume he got it right.

[swansont]

5 hours ago, Eise said:

OK, Ethan Siegel has given the answer now in his blog 'Starts with a Bang'.

In short:

That makes more sense to me than slingshots. I assume he got it right.

That’s good. I pointed out elsewhere recently that dark matter doesn’t readily dissipate energy, and you need KE to drop below |PE| to become bound. So this answer is that expansion can make KE drop, and structure growth makes PE increase in magnitude. So you can now have a bound system.