There’s been a lot of press revolving around dark matter this year, coming from a lot of different directions, so before I dive into any of it I thought it’d be useful to review why we think dark matter exists in the first place. As with anything in science, a lot of the evidence for dark matter is interconnected, and it can be tough to understand why such an overwhelming majority of the physics community believes dark matter exists without wading through confusing webs of complementary astronomical and cosmological evidence. All of this makes examples that can be understood on their own particularly valuable for scientists — particularly for trying to decide among several different explanations for observations. Luckily, just such an example exists for dark matter – the so-called “Bullet Cluster”.

If you ask a typical physics student why we believe in dark matter, the answer you’re most likely to get is rotational velocity curves – not without good reason. Rotational velocity curves were some of the first evidence for dark matter (dating back to Babcock’s measurements in 1939). The basic idea is that in a spiral galaxy, most of the mass orbits the center in a disk-like shape, and knowing the amount of mass within a given radius determines the rotational velocity of the stars at that radius based on Newton’s ordinary inverse-square law you learn in high school. So if you look in a telescope and see all the stars in the galaxy, estimate their masses and observe their rotational velocities, you should be able to plot rotational velocity as a function of radius and see a characteristic shape predicted by Newtonian mechanics. A similar idea applies to elliptical galaxies and clusters of galaxies except that they aren’t in a perfect disk shape, so it’s the averages that are determined rather than the absolute rotational velocities – this goes by the name of the “Virial Theorem”, and it was first applied to galaxies and clusters by Zwicky in 1937.

So what do we see? As you might have heard, when these curves are created, the velocity doesn’t drop off past a certain distance – instead it seems to continue to increase, as though the mass within a given radius continues to increase linearly with a function of distance. Very few stars are seen at such large distances from the center of galaxies, and while clusters of galaxies contain large clouds of x-ray emitting ionized gas, it’s not nearly enough to account for the “missing mass”. This leaves us with two (obvious) possibilities: either there’s some unseen form of matter making up a substantial fraction of the masses of galaxies, or our laws of gravity are incorrect on large scales. The evidence of something being missing is overwhelming, but much of our evidence for there being some form of dark matter relies on the assumption that General Relativity is the correct description of gravity – if we throw out that assumption, it becomes very hard to distinguish between extra mass and so-called “Modified Orbital Newtonian Dynamics” (or just “MOND”).

This is where the “Bullet Cluster” comes in — the Bullet Cluster actually refers to the smaller of two clusters of galaxies that have just recently passed through each other. Galaxy clusters in general have two “baryonic” (ordinary matter) components – the luminous galaxies we can see as ordinary light and a dense gas of ionized hydrogen – in other words, free protons and electrons. This ionized hydrogen gas emits thermal X-ray radiation, but we have satellites that can see this gas just by looking at a different part of the light spectrum. The important difference between the galaxies and the gas is that the galaxies are essentially collision-less – while there are a lot of galaxies in a cluster, when two clusters collide there’s so much space in between the galaxies that to good approximation they pass right through each other. The galaxies are also largely composed of neutral matter, so they don’t interact electromagnetically. The ionized gas on the other hand is dense and because it consists of charged particles (electrons and protons), when two clusters pass through each other there’s a significant amount of “drag” on the plasma: the galaxy and plasma components of the clusters are separated. This is relatively easy to see in images of the Bullet Cluster, where false coloring is added to show the X-ray radiation in pink.

The Bullet Cluster – courtesy NASA

But why is all of this important for dark matter? The punchline is that the plasma is known to contribute substantially more mass to a cluster than the individual galaxies – roughly 5 to 10 times as much. Therefore, regardless of whether you believe in the “normal” gravitational force or some variant of MOND, you would expect that in the absence of dark matter the gravitational field should be strongest near the dense plasma, shown in pink, and not centered around the visible galaxies. If on the other hand, the dark matter is also collision-less (or at least very weakly self-interacting), it should behave similar to the galaxies in the clusters, and pass straight through the other clusters. In this case, we’d expect the gravitational field to be strongest in the vicinity of the galaxies, and not near the clusters. Thus the Bullet Cluster gives us a unique opportunity to test the hypothesis of dark matter against modified gravity — all that’s needed is to trace the gravitational field.

This mapping can be done by using what’s called “Weak Gravitational Lensing”. The idea is that gravity curves spacetime, which bends the path of light, so a large mass can distort the image of objects lying behind it along our line of sight. In extreme cases, we can see the images of galaxies become flattened and curved, or even spread out in what’s called an “Einstein ring”, by having the light bend around the mass on all sides. These extreme cases are called “Strong Lensing” – in weak lensing, there is still a distortion, but it might not be easily visible to the naked eye. Instead, we look at a large number of galaxy images behind the mass we’re interested in, and statistically analyze their orientation and distortion. The idea is that if we had no mass between us, a random sample of galaxies should have a totally random set of orientations, but the presence of a large mass will distort the images in such a way as to make all the images curved slightly in a circular pattern. You can see a somewhat strong example below.

Strong Gravitational Lensing – Courtesy NASA/ESA

In the mid 2000’s, Clowe et al. applied this statistical technique to the Bullet Cluster, and constructed a map of the gravitational field in the bullet cluster. Their results are actually shown in the above image of the bullet cluster – the inferred mass from the gravitational field is shown in blue, and you can see clearly that the gravitational field traces the collision-less galaxies and is entirely separated from the hot plasma. The evidence here at the time was thought to be the nail in the coffin for modified gravity explanations of older results — the authors appropriately named this paper “A Direct Empirical Proof of the Existence of Dark Matter”.

As a last thought, we should note that this result doesn’t necessary preclude modified gravity – the lensing results show a clear separation between the bulk of the visible mass and the gravitational field, which necessitates some form of dark matter, but the lensing results can’t actually test whether general relativity or some more exotic theory is responsible for the lensing. That being said, existence of dark matter does remove some of the primary motivations of considering modified gravity. Some attempts have been made to reproduce these lensing results using MOND without dark matter, but doing so has proven to be extremely difficult, and the results are unconvincing. All of these results make the recent results from McGaugh et al even more compelling: if we accept that dark matter is a major component of galaxies, we’re forced to assume the dark matter has some extra interaction properties in order to reproduce their results without using modified gravity. In the end, we’ll likely have to find another independent method to distinguish between these two possibilities.

Update (Jan. 16, 2017): Sabine Hossenfelder recently provided an alternative viewpoint on the bullet cluster in her own blog. As she says in the comments, her viewpoint is certainly not the popular one (my understanding is that the best attempts at reproducing the observed separation between the gravitational field and the visible matter require neutrinos with masses in tension with the CMB, but perhaps that’s not the end of the story). In any case, the issues with many dark matter models she’s alluding to are certainly important ones to keep in mind.

References:
[1] D. Clowe, et al, “A Direct Empirical Proof of the Existence of Dark Matter”, The Astrophysical Journal Letters, Volume 648, Number 2 (2006). ArXiv:astro-ph/0608407v1.
[2] S. McGaugh, et al., “The Radial Acceleration Relation in Rotationally Supported Galaxies”, ArXiv:astro-ph/1609.05917v1.