Strong lensing with superfluid dark matter

Sabine Hossenfelder, Tobias Mistele

arXiv:1809.00840 [astro-ph.GA]

Physicists still haven’t figured out what dark matter is made of, if anything. The idea that it’s made of particles that interact so weakly we haven’t yet measured them works well to explain some of the observational evidence. Notably the motions of galaxies bound to clusters and the features of the cosmic microwave background fit with theories of particle dark matter straight-forwardly. The galaxies themselves, not so much.Astronomers have found that galaxies have regularities that are difficult to accommodate in theories of particle dark matter, for example the Tully-Fisher relation and the Radial Acceleration Relation. These observed patterns in the measurements don’t follow all that easily from the simple models of particle dark matter. Thrifty theorists have to invoke additional effects that are assigned to various astrophysical processes, notably stellar feedback. While these processes arguably exist, it isn’t clear that they actually act in galaxies in amounts necessary to explain the observations.In the past 20 years or so, astrophysicists have improved computer simulations for galaxy formation until everything fit with the data, sometimes adapting the models to new observations. These computer simulations now contain about a dozen or so parameters (there are various simulations and not all of them list the parameters, so it’s hard to tell exactly) and the results agree well with observation.But I find it somewhat hard to swallow that regularities that seem to be generic in galaxies follow from the theory only after much fiddling. Indeed, the very fact that it took astrophysicists so long to get galaxies right tells me that the patters in our observations are not generic to particle dark matter. It signals that the theories are missing something important.One of the proposals for the missing piece has long been that gravity must be modified. But I, as many theorists, have not been particularly convinced by this idea, the reason being that it’s hard to change anything about Einstein’s theory of general relativity without running into conflict with the many high precision measurements that are in excellent agreement with the theory. On the other hand, modified gravity works dramatically well for galaxies and explains the observed regularities.For a long time I’ve been rather agnostic about the whole issue. Then, three years ago, I read a paper in which Berezhiani and Khoury proposed that dark matter is a superfluid . The reason I even paid attention to this had nothing to do with dark matter; at the time I was working on superfluid condensates that can mimic gravitational effects and I was looking for inspiration. But I have since become a big fan of superfluid dark matter – because it makes so much sense!You see, the superfluid that Berezhiani and Khoury proposed at isn’t just any superfluid. It has an interaction with normal matter and this interaction creates a force. This force looks like modified gravity. Indeed, I think, it is justified to call it modified gravity because the pull acting on galaxies it now no longer that of general relativity alone.However, to get the stuff to condense, you need sufficient pressure, and the pressure comes from the gravitational attraction of the matter itself. Only if you have matter sufficiently clumped together will the fluid become a superfluid and generate the additional force. If the matter isn’t sufficiently clumped, or is just too warm, it’ll not condense.This simple idea works remarkably well to explain why the observations that we assign to dark matter seem to fall into two categories: Those that fit better to particle dark matter and those that fit better to modified gravity. It’s because the dark matter is a fluid with two phases. In galaxies it’s condensed. In galaxy clusters, most of it isn’t condensed because the average potential isn’t deep enough. And in the early universe it’s too warm for condensation. On scales of the solar system, finally, it doesn’t make sense to even speak of the superfluid’s force, it would be like talking about van der Waals forces inside a proton. The theory just isn’t applicable there.I was pretty excited about this until it occurred to me there’s a problem with this idea. The problem is that we know at least since the 170817 gravitational wave event with an optical counterpart that gravitational waves travel to good precision at the same speed as light. This by itself is easy to explain with the superfluid idea: Light just doesn’t interact with the superfluid. There could be various reason for this, but regardless of what the reason, it’s simple to accommodate this in the model.This has the consequence however that light which travels through the superfluid region of galaxies will not respond to the bulk of what we usually refer to as dark matter. The superfluid does have mass and therefore also has a gravitational pull. Light notices that and will bend around it. But most of the dark matter that we infer from the motion of normal matter is a “phantom matter” or an “impostor field”. It’s really due to the additional force from the superfluid. And light will not respond to this.As a result, the amount of dark matter inferred from lensing on galaxies should not match the amount of dark matter inferred from the motion of stars. My student, Tobias Mistele, and I hence sent out to have a look at strong gravitational lensing. We just completed our paper on this and it’s now available on the arXiv.It turns out that the observations from strong gravitational lenses are not hard to accommodate with superfluid dark matter. The reason is, loosely speaking, that the amount of superfluid can be adjusted or, somewhat more technically, that the additional fields require additional initial conditions and those allow us to always find solutions that fit the data.This finding hence exemplifies why criticisms on modified gravity that insist on there only being one way to fit a galaxy are ill-founded. If you modify gravity by introducing additional fields – and that’s how almost all modifications of gravity work – the additional fields will have additional degrees of freedom and generally require additional initial conditions. There will hence usually be several solutions for galaxies. Indeed, some galaxies may by some statistical fluke not have attracted enough of the fluid for it to condense to begin with, though we have found no evidence of that.We have been able to fit all lenses in our sample – 65 in total – except for one. The one outlier is a near-miss. It could be off for a variety of reasons, either because the measurement is imprecise, or because our model is overly simplistic. We assume, for example, that the distribution of the superfluid is spherically symmetric and time-independent, which almost certainly isn’t the case. Actually it’s remarkable it works at all.Of course that doesn’t mean that the model is off the hook; it could still run into conflict with data that we haven’t checked so far. That observations based on the passage of light should show an apparent lack of dark matter might have other observable consequences, for example for gravitational redshift. Also, we have only looked at one particular sample of galaxies and those have no detailed data on the motion of stars. Galaxies for which there is more data will be more of a challenge to fit.In summary: So far so good. Suggestions for what data to look at next are highly welcome.