3.2 Superfluid Dark Matter

summary

What is a Superfluid?

The main example of superfluidity is found in the case of extremely cold liquid helium.
When liquid helium-3 or helium-4 is cooled to an extremely low temperature (~3K), near absolute zero, it does not freeze. Quantum jitter prevents the supercooled helium fluid from forming a solid–instead it becomes superfluid.
Superfluidity is notable because superfluids have zero viscosity. This means that it experiences no internal friction as it flows, allowing it to flow without losing any kinetic energy.

Conditions for Superfluidity

It is possible that dark matter actually exists in the superfluid phase throughout much of the universe. However, for this to be true, two conditions would need to be met.
The first condition is that dark matter would need to aggregate at high densities. The total mass of dark matter needed to make sense of current observations is enormous, so individual dark matter particles would need to be quite light to be able to aggregate at densities high enough for superfluidity.
The mass of a dark matter particle would need to be about 0.1% of the mass of a proton to meet the above criteria. This is much lighter than the common theorized candidate for dark matter, the weakly-interacting massive particle (WIMP).
The second condition is that the dark matter must be cold enough to enter the superfluid phase. The critical temperature for dark matter to transition to the superfluid state is about 1mK.

Superfluidity in Galactic Dark Matter

Calculations show that the motion of dark matter within galaxies would give it an average temperature of about 0.1mK, well below the threshold for superfluidity.
This means that within galaxies, most of the dark matter would be in the superfluid phase.
At a higher structural level, the critical dark matter responsible for the structure of galaxy clusters would move faster due to the large gravity. This dark matter would have an average temperature of about 10mK, putting it above the threshold for superfluidity.
This is the critical distinction between galaxies and galaxy clusters–galaxies contain superfluid dark matter, while only ordinary dark matter exists on the cluster level.

MOND and Superfluid Dark Matter

One critical feature of superfluids is that that the individual atoms in a superfluid do not behave independently. They are coupled at the quantum level and the bulk becomes coherent.
Each individual particle can no longer undergo excitations on their own. Instead, they must all move together, experiencing excitations as waves through the bulk superfluid.
The excitations of a superfluid are called phonons, which are just essentially sound waves through the dark matter. They are called sound waves because, just like actual pressure waves through the air, the excitations in a superfluid are longitudinal waves.
It is possible that dark matter phonons, propagating only through the superfluid dark matter found within galaxies, mediates a MOND force. This force is in addition to traditional Newtonian gravity and causes the phenomena discussed previously (like galaxy rotation curves).
Because dark matter at the galaxy cluster level is too hot to enter the superfluid phase, it does not exhibit MOND properties.
Professor Khoury came to this possibility because the mathematical model necessary to account for MOND phenomena is very similar to known superfluidic systems.