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Can someone please answer how dark matter theory resolves/eliminates these two possible problems

  1. Dark matter, per my understanding, due to gravity, keeps moving, and due to its non-interactive nature, does not stick to itself or normal matter. Therefore, it is in continuous (and may be somewhat random) movement. Wouldn't this make the speed curve of spiral galaxies pretty unstable, or unpredictable?

  2. Dark matter, due to gravity, keeps moving, (usually most dense at the center of the galaxy). Whenever some of it enters the event horizon of the central black hole, it should not be able to come out ever again. Over million/billions of years, all of it, little by little, should eventually end up inside the central black hole, making it impossible to maintain the uniform speed curve. Even though it is non-interactive, is it correct that it still could not escape the event horizon? If so, how it is still possible to maintain the uniform speed curve of galaxies for billions of years?

I am thinking due to non-interactive, non-sticking nature, movement/rotation of dark matter should not be uniform, and it should be crossing in and out passing the central black hole, thereby some of it being consumed for ever. Once this process starts, the central black hole would begin to become heavier making the process even faster.

Also, I am thinking that to cause uniform speed curve, dark matter has to be distributed over the galaxy in certain way. All or most of it in the central black hole would not support the uniform speed curve.

Do the dark matter simulations take these two problems into account? How they are resolved/avoided?

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what do you mean by "does not stick to itself or other matter"? – Jaywalker Feb 15 at 9:13
    
Does not stick, means it does not form rigid structures like planets etc. It passes right through normal, and dark matter without interacting, Only thing known to work on it is gravity, and it also causes gravity just like normal matter does. – kpv Feb 15 at 9:15
    
Gravitation is an interaction, the virial theorem applies, angular momentum conservation applies, the fluctuation-dissipation theorem applies etc.. I do agree, though, that one could have the false intuition that all constituents of a gravitating system have to be able to shed energy trough radiation directly to collapse. That's simply not so. Dark matter can transfer angular momentum and energy to ordinary matter which can then collapse and dissipate trough radiation. This will effectively cool the dark matter, as well. – CuriousOne Feb 15 at 9:21
    
Would it be more appropriate to say it interacts with normal matter only through gravity, and no other way? But my main question is why all of it does not fall into the central black hole over million/billions of years. – kpv Feb 15 at 9:25
    
The answer to that is simply angular momentum conservation... it can't. To fall into the sun from Earth's orbit would require a delta v of something like 30km/s! I am not sure we even have a rocket that could propel even a small payload into the sun. The only way we could manage that would probably be with several Earth, Venus and Mercury fly-bys and/or a very long thrusting phase with an ion engine. In terms of energetics the sun is the most expensive target in the solar system and to get from here to the center of the galaxy would require a delta v of over 200km/s! – CuriousOne Feb 15 at 9:35
up vote 6 down vote accepted

The properties you attribute to dark matter (non-interacting, affected only by gravity) are alo properties of a large fraction of the visible matter in our Galaxy. i.e. Stars orbit in the Galactic potential without directly interacting with other stars and their trajectories are only influenced by gravitational forces.

Far from being "random", dark matter is expected to orbit the Galaxy in a similar way to stars. The main difference being that most of the dark matter is on much larger orbits and the orbital axes are distributed more uniformly in space.

In the same way that stars on circular or even quite elliptical orbits never come anywhere near the BH at the centre of the galaxy, nor does most dark matter. Some dark matter will have been captured in the past, but only that which had almost perfectly radial orbits. The rest continues to orbit in the same way that the Earth continues to orbit the Sun, with nothing to dissipate its orbital kinetic energy. To extend the analogy between non-interacting stars and dark matter - there is a class of stars formed very early on in the Milky Way's history called population II or halo stars. These have been orbiting the Milky Way in pseudo-spherical orbits since they first formed more than 10 billion years ago - like dark matter.

Yes, the dark matter density is higher near the centre of the galaxy but the mass of dark matter is dominated by that which occupies the enormous volume at large distances from the centre.

To summarise, neither of the problems you have invented are problems.

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There is no confusion in the question between mass and density, I read it again to be sure. The uniform rotation of dark matter does answer the question though. Non-interactive was in the context when it comes in physical contact/vicinity. – kpv Feb 15 at 9:38
    
Rob Jeffries: How are the proposed orbits of dark matter? Are they exactly as those of baryonic matter (i.e. spiral), or different? – kpv Feb 16 at 17:44

To answer the question about falling into the central black hole.

If we start off with most of the dark matter having some significant angular momentum (ie it is on some kind of elliptical orbit) then for Newtonian gravity it can't fall into the black hole since it can't shed the angular momentum.

In fact it can shed angular momentum by interacting gravitationally with other matter -- dark and light -- in the galaxy, but the system as a whole can't. So neither dark nor light matter somehow gets sucked into the black hole, because to do so requires dumping angular momentum somewhere.

Well, this isn't quite true: GR does allow some systems to spin down. But the time-constants for this to happen for something like a galaxy would be absolutely enormous since the fields are very weak.

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The answer by Rob disentangles some of the similarities with dark matter and ordinary matter, but forgets to point out an important difference between them (apart from dark matter being dark).

Because Dark matter does not interact electromagnetically it will not "collide" with other matter. This is important since it prevents the dark matter from losing excess kinetic energy through collisions. The process I'm describing is one of the main reasons galaxies tend to be flat. Anything not orbiting in the plane of the galactic disc will need to pass through that disc as it orbits. This passage is prone to collisions, causing the orbit to get caught in the galactic disc.

Since dark matter does not collide in this way, it does not get accreted in the disc. As a consequence the dark matter forms a halo instead of a disc.

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The reason that disc galaxies are discs is not because stars interact with matter as they pass through the plane. It is because the gas from which they formed was dissipational and settled into a plane. That is why I stressed the similarities between the motion of stars and dark matter. Indeed halo stars have been orbiting the Milky Way for >11 billion years without becoming part of the disc. or being swallowed by a central black hole. – Rob Jeffries Feb 15 at 16:10
    
@Rob I agree that the question was geared toward the stable motion of start and/or DM. I was merely adding a point so that one would not go away from the question thinking all the DM was also in the disc. – Mikael Fremling Feb 15 at 17:21

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