According to this and this answer, and as far as I understand these answers, dark matter halos cannot collapse to a black hole because, due to uncoupling from the EM field, they are unable to radiate their kinetic energy, and hence, getting closer to some gravitational center point also means that they get faster and so they resist further "collapse".

But what about the motion perpendicular to the galactic plane? I would naively expect the dark matter to gravitationally fall down on the galactic plane on both its sides, until it concentrates there. Depending on whatever the type of dark matter may be, this may cause other forces (e.g. weak interaction) to take over (possibly at nuclear distances) or it may oscillate until it becomes spherical again.

One way I imagine that this might happen is a small-scale alternating velocity variation in the dark matter field, so that dark matter is alternately falling to/moving away from the mid plane from location to location, and these regions simply pass by one another infinitely. If this alternating pattern in the velocity field exactly balances, the dark matter halo is able to maintain a spherical shape. But even the slightest imbalance might result in a global oscillatory motion between spherical and disc-like.

Have the available observations been investigated with respect to these possible oscillations of the dark matter halos? And isn't it likely that such oscillatory motion (if it existed) would eventually stop due to second order dissipation (dark-matter to ordinary matter to radiation).

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  • $\begingroup$ How would the DM halo become a disc? Why would DM particles undergo compression (assuming all of their non-gravitational interactions are negligible)? $\endgroup$
    – PM 2Ring
    Commented May 14, 2023 at 10:42
  • $\begingroup$ If a sphere with angular momentum internally accelerates due to gravitation, then it must become oblate at one time or another. And if there is no force to withstand that motion, it must become even more oblate. Whether other forces than EM (e.g. weak interaction) might eventually stop this accelerated motion, is an open question, at least so I thought. So it is in my opinion logical that the question if the oblate shape returns to spherical in an oscillatory way, or if it ends up as a disc, is also open. $\endgroup$
    – oliver
    Commented May 14, 2023 at 12:08
  • 1
    $\begingroup$ Please don't completely change the title and nature of your question after it has been answered and upvoted. If you have another question that follows on from this then you can ask that as another question. $\endgroup$
    – ProfRob
    Commented May 14, 2023 at 12:58
  • $\begingroup$ @ProfRob: Please feel free to change the title of my question whenever you think you know better than me what I wanted to ask... I had the reference to the velocity field in the original question, and I left it there, but I changed the title because I noticed that your answer ignored what I felt was my main focus. $\endgroup$
    – oliver
    Commented May 14, 2023 at 13:06

2 Answers 2


The dark matter is (approximately) dissipationless. How can it collapse into a disk unless it has a means to rid itself of its kinetic energy? Any collapse would increase the kinetic energy at the expense of gravitational potential energy - without any dissipation then this process is then reversed.

The dark matter forms an approximately spheroidal distribution around a galaxy. The dark matter bodies will orbit in the galactic potential, just like other bodies that experience gravity - those orbits are non Keplerian but can be highly eccentric and would usually involve components that oscillate in both the radial and "vertical" directions along with any azimuthal component. If you randomly orient such orbits then you end up with a spherical distribution of density.

A disk is what you get when the orbiting bodies (could be particles, might be primordial black holes) are capable of losing their kinetic energy in some way, but without significant loss of angular momentum. Ordinary gas is capable of doing this because it radiates away energy when it is compressed and heated. Dark matter is (by definition) unable to do this. A better comparison for dark matter is the halo of very old stars that were thought to have formed very early in the history of our Galaxy, when the gas was distributed more spheroidally. These "halo stars" are now unable to lose their kinetic energy because stars basically behave like collisionless particles in the galaxy and so they maintain their spheroidal distribution.

In fact you can turn this answer entirely around. We know that dark matter is weakly dissipative and non-interacting because we observe (via its gravitational influence, e.g. an oblateness $q \simeq 0.8$, Piffl et al. 2014, but maybe even prolate with $q \sim 1.2$ in the inner 20 kpc, Dodd et al. 2021) that it forms a large, roughly spherical halo around the Galaxy and is not concentrated into a plane.

Edit: To address the possible long-term dissipation of energy.

In terms of whether the vertical component of dark matter orbital motion will ever be damped, then we are forced to make assumptions about what dark matter is and just how weakly interacting it is.

The inferred dark matter density at the solar galactocentric radius is about $0.013$ solar masses per cubic parsec and that of "normal matter" about $0.084$ solar masses per cubic parsec (McKee et al. 2015). If we assume the dark matter is in the form of WIMPS of mass 100 GeV the current experimental constraints appear to put an upper limit on the WIMP-nucleon cross-section of around $\sigma < 10^{-46}$ cm$^2$. The mean free path of a WIMP would be of order $(n \sigma)^{-1} = 10^{27}$ parsecs, where $n$ would be the average baryon number density of roughly $3 \times 10^6$ m$^{-3}$ (most of which is in stars).

The Galactic disc is of order 1000 pc thick, so a WIMP could oscillate back and forward through it about $10^{24}$ times before interacting. Given that the timescale of Galactic orbits are $\sim 10^8$ years, then it would take $10^{32}$ years to dissipate significant energy in this way.

  • $\begingroup$ First of all, I already accepted that it's (almost) dissipationless. I assumed, possibly wrongly, that there is some dissipation due to strong or weak interaction at nuclear distances, which might end up in a disc. You: "without any dissipation then this process is then reversed" How can a static spheroidal distribution be reversed? Maybe "collapse" is the wrong word, maybe I should have asked about "oscillations". But then an oscillation contradicts the static assumption, doesn't it? Should I rather have asked about the non-zero velocity field that we expect to exist in the dark matter halo? $\endgroup$
    – oliver
    Commented May 14, 2023 at 11:58
  • $\begingroup$ @oliver The spheroid is not "static" - the dark matter is orbiting. Indeed orbits within the Galactic potential (like the Sun's for instance) can oscillate through the plane of the Galaxy. But neither stars nor dark matter accumulate there through that process. The stars are concentrated towards the plane because they were born there. $\endgroup$
    – ProfRob
    Commented May 14, 2023 at 12:06
  • $\begingroup$ Okay, so the boundary conditions I have indicated are actually one possible scenario, but I guess you would argue that it need not be that regular. $\endgroup$
    – oliver
    Commented May 14, 2023 at 12:11
  • $\begingroup$ But another question arises as to your use of the term "bodies"... how can dark matter form bodies?. The bodies of the ordinary matter gain their structure from electromagnetic forces. Shouldn't we suppose that dark matter has a very diffuse density distribution? And what kind of velocity field do we expect then (already thinking of the equation of continuity and density variations)? $\endgroup$
    – oliver
    Commented May 14, 2023 at 12:20
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    $\begingroup$ @oliver I used the word "bodies" because we don't know what dark matter is. It could be in the form of particles. It could be primordial black holes. What we know is that it is very weakly interacting other than by gravity. One consequence of that is that it doesn't form flattened discs! $\endgroup$
    – ProfRob
    Commented May 14, 2023 at 12:23

Your idea of small scale alternating velocity variation is on the right track. The model that captures the properties of dark matter is a gas of particles with a temperature hot enough that the individual particles are moving a a few hundred km/s. In a gas, the motions of the individual particles are random, so a particle will generally have a substantial velocity out of the plane.

  • $\begingroup$ So this "temperature" is defined purely kinematically (via the DM particle velocities), I guess. But what about the black body aspect of temperature? Since DM doesn't radiate directly, shouldn't we at least be able to observe dark matter temperature by the gravitational coupling between the dark matter reservoir and the ordinary matter reservoir? Or is the relaxation time so huge due to the weakness of gravity, that a typical galaxy hasn't reached equilibrium and we always observe the temperature of ordinary matter? $\endgroup$
    – oliver
    Commented May 14, 2023 at 12:51
  • $\begingroup$ @oliver We do observe it that way. The velocity dispersion of things like stars on the scales where dark matter dominates gravity (a few kpc to a few Mpc) is a few hundred km/sec. But it's not Boltzmann thermal equilibrium: when the "collisions" are gravitational, the system tends to fall into a state where the velocities are the same on the average rather than the energies. $\endgroup$
    – John Doty
    Commented May 14, 2023 at 13:03

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