Superfluid Dark Matter

A new paper proposes that dark matter may be a quantum fluid that has condensed in puddles to seed galaxies.

If Superfluid was a superhero, it would creep through the tiniest door slits and flow up the walls to then freeze the evil villain to death. Few things are cooler than superfluids, an utterly fascinating state that some materials, such as Helium, reach at temperatures close to absolute zero. Superfluid’s superpower is its small viscosity, which measures how the medium sticks to itself and can resist flowing. Honey has a larger viscosity than oil, which has a lager viscosity than water. And at the very end of this line, at almost vanishing viscosity, you find superfluids.

There are few places on Earth cold enough for superfluids to exist, and most of them are beleaguered by physicists. But outer space is cold and plenty. It is also full with dark matter whose microscopic nature has so far remained mysterious. In a recent paper (arXiv:1507.01019), two researchers from the University of Pennsylvania propose that dark matter might be puddles of a superfluid that has condensed in the first moments of the universe, and then caught the matter we readily see by its gravitational pull.

This research reflects how much our understanding of quantum mechanics has changed in the century that has passed since its inception. Contrary to what our experience tells us, quantum mechanics is not a theory of the microscopic realm. We do not witness quantum effects with our own senses, but the reason is not that human anatomy is coarse and clumsy compared to the teensy configurations of electron orbits. The reason is that our planet is a dense and noisy place, warm and thriving with thermal motion. It is a place where particles constantly collide with each other, interact with each other, and disturb each other. We do not witness quantum effects not because they are microscopic, but because they are fragile and get easily destroyed. But at low temperatures, quantum effects can enter the macroscopic range. They could, in fact, span whole galaxies.

The idea that dark matter may be a superfluid has been proposed before, but it had some shortcomings that the new model addresses; it does so by combining the successes of existing theories which cures several problems these theories have when looked at separately. The major question about the nature of dark matter is whether it is a type of matter, or whether it is instead a modification of gravity, or MOG for short. Most of the physics community presently favors the idea that dark matter is matter, probably some kind of as-yet-unknown particle, and they leave gravity untouched. But a stubborn few have insisted pursuing the idea that we can amend general relativity to explain our observations.

MOG, an improved version of the earlier MOdified Newtonian Dynamics (MOND), has some things going for it; it captures some universal relations that are difficult to obtain with dark matter. The velocities of stars orbiting the center of galaxies – the galactic rotation curves – cannot be explained by visible matter alone but can be accounted for by adding dark matter. And yet, many of these curves can also be explained by stunningly simple modifications of the gravitational law. On the other hand, the simple modification of MOND fails for clusters of galaxies, where dark matter still has to be added, and requires some fudging to get the solar system right. It has been claimed that MOG fits the bill on all accounts but on the expense of introducing more additional fields, which makes it look more and more like some type of dark matter.

Another example of an observationally found but unexplained connection is the Tully-Fisher relation between galaxies’ brightness and the velocity of the stars farthest away from the galactic center. This relation can be obtained with modifications of gravity, but it is hard to come by with dark matter. On the other hand, it is difficult to reproduce the separation of visible matter from dark matter, as seen for example in the Bullet Cluster, by modifying gravity. The bottom line is, sometimes it works, sometimes it doesn’t.

It adds to this that modifications of gravity employ dynamical equations that look rather peculiar and hand-made. For most particle physicists, these equations appear unfamiliar and ugly, which is probably one of the main reasons they have stayed away from it. So far.

In their new paper, Berezhiani and Khoury demonstrate that the modifications of gravity and dark matter might actually point to the same origin, which is a type of superfluid. The equations determining the laws of condensates like superfluids at lowest temperatures take forms that are very unusual in particle physics (they often contain fractional powers of the kinetic terms). And yet these are exactly the strange equations that appear in modified gravity. So Berezhiani and Khoury use a superfluid with an equation that reproduces the behavior of modified gravity, and end up with the benefits of both, particle dark matter and modified gravity.

Superfluids aren’t usually purely super, instead they generally are a mixture between a normally flowing component, and a superfluid component. The ratio between these components depends on the temperature – the higher the temperature the more dominant the normal component. In the new theory of superfluid dark matter the temperatures can be determined from the observed spread of velocities in the dark matter puddles, putting galaxies at lower temperatures than clusters of galaxies. And so, while the dark matter in galaxies like our Milky Way is dominantly in the superfluid phase, the dark matter in galactic clusters is mostly in the normal phase. This model thus naturally explains why modified gravity works only on a galactic scales, and should not be applied to clusters.

Moreover, on scales like that of our solar system, gravity is strong compared to the galactic average, which causes the superfluid to lose its quantum properties. This explains why we do not measure any deviations from general relativity in our own vicinity, another fact that is difficult to explain with the existing models of modified gravity. And since the superfluid is matter after all, it can be separated from the visible matter, and so it is not in conflict with the observables from colliding clusters of galaxies. In fact, it might fit the data better than single-particle dark matter because the strength of the fluid dark matter’s self-interaction depends on the fraction of normal matter and so depends on the size of the clusters.

Superfluids have another stunning property which is that they don’t like to rotate. If you try to make a superfluid rotate by spinning a bucket full of it, it just won’t. Instead it will start to form vortices that carry the angular momentum. The dark matter superfluid in our galaxy should contain some of these vortices, and finding them might be the way to test this new theory. But to do this, the researchers first have to calculate how the vortices would affect normal matter.

I find this a very interesting idea that has a lot of potential. Of course it leaves many open questions, for example how the matter formed in the early universe, so as the scientists always say: more work is needed. But if dark matter was a superfluid that would be amazingly cool – a few milli Kelvin to be precise.

When it comes to superpowers, I’ll chose science over fiction anytime.