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If dark matter has gravity just like normal matter, does that mean it can also form planets, solar systems and so on? Any answer will be appreciated.

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I would think, at least within visible galaxies, that it would be unlikely for dark matter to accumulate without also attracting ordinary matter. Also, such accumulations would not be recognizable objects since dark matter does not interact the same way ordinary matter does. – called2voyage Apr 5 at 20:21
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No, not at all because dark matter doesn't exist, it is a figment of the imagination to solve the denial that the universe is plasma based and not gravity based. – Tim Netherwood Apr 6 at 8:22
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Similar questions have been asked & answered on Physics.SE as well: physics.stackexchange.com/questions/61223 and physics.stackexchange.com/questions/52877 – Kyle Kanos Apr 6 at 10:23
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@TimNetherwood According to plasma cosmology, yes. But not mainstream cosmology, which is what the site generally goes by. – Sir Cumference Apr 6 at 20:49
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@TimNetherwood Hopefully, we should not have to come up with a rule about this. The post assumes the existence of dark matter, and thus invokes mainstream cosmology. This is not the place to debate which cosmology to use. A question asking about what dark matter is might be a more appropriate place to make reference to plasma cosmology as one possible option, though the most even-handed approach should address the criticism of plasma cosmology raised by other cosmologists. – called2voyage Apr 7 at 14:05
up vote 16 down vote accepted

Planets and stars, no. Globular clusters and galaxies, yes.

Small scales

To condense into such relatively compact objects as planets, stars, and even the more diffuse star-forming clouds, particles need to be able to dissipate their energy. If they don't do this, their velocities prohibit them from forming anything.

"Normal" particles, i.e. atoms, do this by colliding. When atoms collide, they're excited, and when they de-excite, they emit radiation which leaves the system, carrying away energy. In this way, an ensemble of particles can relax into a less energetic system, eventually condensing into e.g. a star. Additionally, the collisions cause more energetic particles to donate energy to the less energetic ones, making the ensemble reach thermodynamic equilibrium, i.e. all particles have the same energy on average.

Dark matter is, by definition, unable to collide and radiate, and hence, on such small scales as stars and planets, particles that enters a potential well with a given energy will maintain that energy. They will thus accelerate toward the center, then decelerate after its closest approach to the center, and finally leave the system with the same energy as before (if it was unbound to begin with). This makes it impossible for collisionless matter to form such small objects.

Large scales

On the scale of galaxies, however, various relaxation mechanisms allows dark matter to form structure. This is the reason that in pure N-body simulations of the Universe, such as the Millennium Simulation, you will see galaxies. The sizes of these structures depend on the resolution, but are measured in millions of Solar masses.

The relaxation mechanisms include:

Phase mixing

This is sort of like galaxy arms winding up, but in phase space rather than real space.

Chaotic mixing

This happens when particles come so close that their trajectories diverge exponentially.

Violent relaxation

The two mechanisms listed above assume a constant gravitational potential $\Phi$, but as the systems relaxes, $\Phi$ changes, giving rise to an additional relaxation process. For instance, more massive particles tend to transfer more energy to their lighter neighbors and so become more tightly bound, sinking towards the center of the gravitational potential. This effect is known as mass segregation and is particularly important in the evolution of globular star clusters.

Landau damping

For a perturbation/wave with velocity $v_p$, if a particle comes with $v\gg v_p$, it will overtake the wave, first gaining energy as it falls into the potential, but later losing the same amount of energy as it climb up again. The same holds for particles with $v\ll v_p$ which are overtaken by the wave. However, particles with $v\sim v_p$ (i.e. that are near resonance with the wave) may experience a net gain or loss in energy. Consider a particle with $v$ slightly larger than $v_p$. Depending on its phase when interacting with the wave, it will be either accelerated and move away from resonance, or decelerated and move closer to resonance. The latter interact more effectively with the wave (i.e. be decelerated for a longer time), and on average there will thus be a net transfer of energy from particles with $v \gtrsim v_p$ to the wave. The opposite is true for particles with $v$ slightly smaller than $v_p$

You can read more about these mechanisms in Mo, Bosch, & White's Galaxy Formation and Evolution.

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NB: This assumes dark matter is WIMPs instead of the alternative hypothesis of MACHOs. In the latter case, planets and stars could be yes instead. – Kyle Kanos Apr 6 at 10:20
    
@KyleKanos: True, I'm assuming some sort of WIMP, more particularly cold dark matter, since this is in my, and most others', opinion by far the most likely candidate for DM. MACHOs are baryons, so by definition, planets and stars are MACHOs. As a candidate for the "missing" DM, however, MACHO can be ruled out using e.g. microlensing. – pela Apr 6 at 12:11

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