Why Don’t Dark Matter Simulations And Observations Match Up?

Could this finally be the clue we’ve hoped for in uncovering the truth about dark matter?

In the physical sciences, theory and observation are supposed to work hand-in-hand. Theorists work out the details of various ideas, yielding predictions for what the Universe should deliver under a variety of circumstances. Measurements and observations yield useful data about the Universe as it actually is, and those results can then be compared with various theoretical predictions. Ideally, one theory will emerge as successful, fitting the full suite of data available, while the alternatives fall away, disfavored by what the Universe tells us about itself.

For the past 40+ years, this has been the story of dark matter. By adding just one new ingredient to the Universe — a new species of cold, collisionless, massive particle — a whole suite of predictions could be extracted. Dark matter has implications for the Universe from small, irregular galaxies up to the enormous scales of the cosmic web or even the all-sky view of the cosmic microwave background. But a brand new study on the scales of galaxy clusters, where dark matter had previously been extremely successful, shows that simulations and observations don’t match up in an important way. Here’s the science of what’s really going on.

The dark matter structures which form in the Universe (left) and the visible galactic structures that result (right) are shown from top-down in a cold, warm, and hot dark matter Universe. From the observations we have, at least 98%+ of the dark matter must be either cold or warm; hot is ruled out. (ITP, UNIVERSITY OF ZURICH)

On the theory side, understanding what should happen in a galaxy cluster is a relatively simple concept. You start out with the Universe as we know it must have been early on: hot, dense, mostly uniform but with tiny imperfections (overdense and underdense regions), and filled with radiation, normal matter, and dark matter. As time goes on, the dark matter will gravitate but not collide with itself, normal matter, or radiation, while radiation and normal matter interact not only gravitationally but also through the other forces of the Universe.

Over time, a great cosmic web forms, with dense clumps of matter leading to galaxies forming along filamentary lines and rich galaxy clusters building up at the intersectional nexus of multiple filaments. While, on average, dark matter is expected to form an enormous, diffuse halo surrounding the normal matter, there will also be smaller “clumps” of dark matter that persist within the larger halo. The nature of dark matter determines the distribution of the various sizes, masses, and numbers of clumps within each halo.

In theory, the majority of dark matter in any galaxy exists in a vast halo engulfing the normal matter, but occupying a much larger volume. While large galaxies, clusters of galaxies, and even larger structures can have their dark matter content determined indirectly, it’s challenging to trace out the dark matter distribution accurately, particularly on small scales and for dark matter substructure. (ESO / L. CALÇADA)

Because dark matter only interacts gravitationally, it neither absorbs nor emits any light of its own. Technically, it doesn’t behave like something that we conventionally think of as dark; instead, dark matter acts as though it’s invisible. That might seem like it poses an insurmountable challenge to astronomers who are looking for its effects. After all, how can you hope to see something that’s invisible and doesn’t interact with matter or radiation directly?

The answer, perhaps surprisingly, is that you don’t need to be able to see dark matter in order to know its there. If we can predict what it’s distribution is — how much of it is located along any particular line-of-sight we look in — then we can calculate what its effects will be on all the light that passes through the region of space that it occupies. This is, perhaps, the most exciting feature of Einstein’s theory of gravity, General Relativity: matter and energy curve the fabric of space, and that curved space determines how matter and energy move.

Gravitational lenses, magnifying and distorting a background source, allow us to see fainter, more distant objects than ever before. Similarly, observing the light that experiences a gravitational lensing effect enables us to reconstruct properties of the lens itself, potentially shedding light on the nature of dark matter. (ALMA (ESO/NRAO/NAOJ), L. CALÇADA (ESO), Y. HEZAVEH ET AL.)

Therefore, if we want to study dark matter, one of the most powerful things we can do is to look at very massive systems that require large amounts of dark matter to hold them together. Historically, some of the strongest observational evidence of dark matter has come from these rich galaxy clusters, as an additional gravitational effect well beyond what normal matter can account for is required to explain all that we observe.

This goes all the way back to the 1930s, when Fritz Zwicky was using the world’s largest telescope at the time, the 100-inch telescope atop Mt. Wilson — the same telescope Hubble used to discover the expanding Universe — to measure individual galaxies in the Coma Cluster. Because these galaxies are clustered together and we know how the law of gravity works, the speeds of the individual galaxies can be used to infer how massive the cluster must be.

The two bright, large galaxies at the center of the Coma Cluster, NGC 4889 (left) and the slightly smaller NGC 4874 (right), each exceed a million light years in size. But the galaxies on the outskirts, zipping around so rapidly, point to the existence of a large halo of dark matter throughout the entire cluster. The mass of the normal matter alone is insufficient to explain this bound structure. (ADAM BLOCK/MOUNT LEMMON SKYCENTER/UNIVERSITY OF ARIZONA)

Zwicky’s observations indicated that there wasn’t nearly enough normal matter present to keep the cluster bound together; if normal matter was all there was, these galaxies would be traveling far faster than “escape velocity,” meaning they’d fly off into space and the cluster would dissociate. Although his results weren’t taken seriously, they remain robust today. Without dark matter, the Coma Cluster (and many other galaxy clusters) wouldn’t have enough mass to hold their components together.

Over the years, many other cluster measurements support the existence of dark matter. Many clusters contain hot gas, which emits X-rays: we can measure how much “normal matter” is there and it’s only 11–15% of the required mass, leaving a need for dark matter beyond stars, gas and plasma. But the most important measurements are based on gravitational lensing, where the amount that light is curved, bent, magnified, and distorted reveals the total amount of mass present. In particular, when two galaxy clusters collide, we can literally see that the inferred mass and the observed location of the normal matter don’t match up.

This collage shows images of six different galaxy clusters taken with the NASA/ESA Hubble Space Telescope and NASA’s Chandra X-ray Observatory. The clusters were observed in a study of how dark matter in clusters of galaxies behaves when the clusters collide. The mismatch between X-ray data (in pink) and gravitational lensing mass reconstruction (in blue) showcases the need for dark matter that isn’t normal matter. (ASTROMATIC.NET)

Measurements like this have been around for a long time, indicating the overwhelming need for dark matter from a variety of independent observations. The Bullet Cluster, the first example of a colliding pair of galaxy clusters demonstrating the mismatch between the location of mass and the location of normal matter, is already 15 years old. But the decade-and-a-half that’s passed since then has given us more than just many examples of different systems that unambiguously illustrate these effects; they’ve also brought with them an increase in computing power, simulation capabilities, and observing technology.

Combined, this allows us to go farther than before. Instead of simply simulating the overall shape and mass of the galactic halo, we can simulate what both the dark matter and the normal matter distribution should look like for the substructures inside the halo as well. This includes individual galaxies, their halos, gas clouds, satellite galaxies, and even small clumps of dark matter.

A galaxy cluster can have its mass reconstructed from the gravitational lensing data available. Most of the mass is found not inside the individual galaxies, shown as peaks here, but from the intergalactic medium within the cluster, where dark matter appears to reside. More granular simulations and observations can reveal dark matter substructure as well. (A. E. EVRARD. NATURE 394, 122–123 (09 JULY 1998))

These theoretical predictions would also yield different observational signatures. Dark matter will form structures on different scales — substructures of different masses, sizes, and numbers within a large halo — dependent on its mass, temperature, and any potential self-interactions it may have. In January of 2020, a study came out constraining these properties of dark matter based on a sample of strong gravitational lenses that all produced quadruple images.

However, the most massive systems don’t generally have those serendipitous configurations. Instead, we have to rely on mass reconstructions based on more general features produced by these gravitational lenses: arcs, rings, galaxy shape distortion, etc. The simulations will predict, based on what we think we know about dark matter, what types of distortions should be present (and at what level), while the observations allow us to directly infer what the physical dark matter distribution is.

According to models and simulations, all galaxies should be embedded in dark matter halos, whose densities peak at the galactic centers. On long enough timescales, of perhaps a billion years, a single dark matter particle from the outskirts of the halo will complete one orbit. The effects of gas, feedback, star formation, supernovae, and radiation all complicate this environment, making it extremely difficult to extract universal dark matter predictions, but the biggest problem may be that the cuspy centers predicted by simulations are nothing more than numerical artifacts. (NASA, ESA, AND T. BROWN AND J. TUMLINSON (STSCI))

The picture you should have in your head is like this:

the large dark matter halo that surrounds the galaxy acts like one giant lens,
with the individual galaxies inside each having their own halo, acting like smaller lenses embedded in the large one,
with the dark matter substructure within each galaxy and as part of the cluster itself playing an additional role, creating a large number of small-magnitude lenses as well.

Theoretically, dark matter is most often modeled as completely cold, collisionless, and with no interactions other than gravitational interactions. Most of the simulations that have been coded are based under those assumptions, with the largest uncertainties arising from the structures on the smallest scales. But over recent years, observations have caught up to these predictions, allowing us to compare theory (in the form of numerical simulations) and observations at last.

A Hubble image showcasing many of the galaxies inside a massive galaxy cluster. The presence of not only these galaxies but the dark matter within them as well as within the larger cluster is responsible for the observed lensing effects: rings, arcs, magnified and distorted light, etc. These observations allow us to compare the actual universe with numerical simulations. (NASA, ESA, G. CAMINHA (UNIVERSITY OF GRONINGEN), M. MENEGHETTI (OBSERVATORY OF ASTROPHYSICS AND SPACE SCIENCE OF BOLOGNA), P. NATARAJAN (YALE UNIVERSITY), AND THE CLASH TEAM)

In a new study that was just published earlier this month, observational cosmologists report their results from studying 11 massive galaxy clusters with both ground-based and space-based observatories, where they were able to reconstruct models for the magnitude and number of the various lenses responsible for the signals they saw. On large scales, the simulations and observations lined up very well. But in order to reproduce the details of the observed lensing signatures, the dark matter substructures need to be much richer than simulations predict.

The results are neatly summarized by the study’s authors as follows:

“We report that observed cluster substructures are more efficient lenses than predicted by [cold dark matter] simulations, by more than an order of magnitude.”

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Somehow, for some reason, we see a much greater amount of lensing effects arising on very small scales than simulations predict. Either something that we don’t understand is biasing our simulations on small scales, or — just possibly — dark matter is doing something more interesting than just being cold and collisionless.

A Hubble image of the massive galaxy cluster MACS J1206, with the characteristic arcs, smears, and distorted shapes from gravitational lenses. Overlaid, in blue, are the reconstructed distributions of dark matter halos and substructure within this cluster. (NASA, ESA, G. CAMINHA (UNIVERSITY OF GRONINGEN), M. MENEGHETTI (OBSERVATORY OF ASTROPHYSICS AND SPACE SCIENCE OF BOLOGNA), P. NATARAJAN (YALE UNIVERSITY), THE CLASH TEAM, AND M. KORNMESSER (ESA/HUBBLE))

In many ways, this is the greatest possible type of clue that cosmologists seeking to understand the nature of dark matter could hope for. Simulations have been yielding predictions that don’t quite match up with the details we observe, particularly on very small (sub-galactic) cosmic scales, for approximately 25 years. While adding one simple ingredient — cold, collisionless, invisible dark matter — can simultaneously explain a wide variety of cosmic observations, they’ve often left us wanting more on these small cosmic scales.

Perhaps this is the clue we need. If dark matter has any additional type of interaction in its nature, astrophysical observations like these new cluster measurements could point us in the right direction to uncover exactly what it is. Without the ability to directly detect whatever particles are responsible for dark matter, this interplay of numerical simulations and observed data might be our best path towards solving this mystery. Based on this novel lensing data from rich, massive galaxy clusters, we might at last be one step closer to understanding the true nature and properties of dark matter.

Starts With A Bang is written by Ethan Siegel, Ph.D., author of Beyond The Galaxy, and Treknology: The Science of Star Trek from Tricorders to Warp Drive.