The Elephant in the Universe, page 13
“It just tells me we need to look harder,” Ellis replies. “WIMPs may be more massive than we have assumed.” The problem with that, he adds, is that the WIMP miracle falls by the wayside if the particles are too heavy. “The options are limited. At a mass of around 10 TeV”—ten thousand times the mass of a proton—“you run out of wiggle room. But to probe that mass range, we would need an even bigger detector than the LHC. I don’t know when we will find the answer.”
“When.” Ellis doesn’t say “if.”
Twenty-six years elapsed between the prediction of the neutrino, in 1930, and its discovery, in 1956. For the Higgs boson, the wait lasted forty-eight years. Gravitational waves—minute ripples in the very fabric of spacetime—were predicted by Albert Einstein in 1916 and weren’t discovered until almost a century later, in 2015. Yes, the dark matter hunt at CERN is taking longer than we had expected. But absence of evidence isn’t evidence of absence. Who knows what a next-generation collider will reveal. Who knows what Run 3 will reveal.
Maybe that’s the real problem with dark matter. We don’t know exactly what we’re looking for, so there’s always good reason to keep on searching. Think of a terrestrial treasure hunt. If you knew the exact location of some mythical city, you could just go there and explore the area. If you didn’t find the city, you would conclude that it’s just a myth and call off the search. But if you’re sailing the seven seas in search of a magical island that could be anywhere on the globe, you shouldn’t stop your quest just because you feel it’s taking too long. For all we know, the island could be just beyond the horizon.
The discovery of WIMPs may also be just beyond the horizon. Only time will tell. Time, ingenuity, and perseverance.
11
Simulating the Universe
In the beginning, the universe is without form and void, and darkness is over the face of the deep.
Then I witness how minute density variations in the distribution of dark matter particles begin to evolve into a three-dimensional cobweb-like pattern. Hydrogen and helium atoms—more familiar but much less numerous—follow suit; they can’t help being pulled into the same large-scale structures by the sheer gravity of the weird, invisible stuff.
All around me, I now see gas streaming along serpentine filaments, ending up in the high-density regions where these cosmic tentacles meet. Swept up by gravity and twisted by pervasive magnetic fields, the clouds of gas become much more turbulent than the invisible substrate of dark matter on which they are condensing. As hundreds of millions of years pass by in mere seconds, gas starts to collect in the cores of more-or-less spherical halos of invisible dark matter. Slowly but surely, the universe gives birth to a small cluster of galaxies.
In the distance, in the cluster’s core, I see how puny dwarf galaxies—traces of dark matter clumps—collide and merge into an ever-growing whole. Meanwhile, right before my eyes, a huge gas cloud further collapses under its own weight and starts to spin faster and faster, slowly flattening in the process. Gobbling up smaller satellite systems, it evolves into a beautiful spiral galaxy.
To my right, two spirals crash into each other, slinging away tidal tails of galactic debris. Shocks and density waves produce a baby boom of new, massive stars. Eventually, the resulting merger settles down as a huge elliptical galaxy, surrounded by concentric shells of gas. To my left, the further growth of yet another disk galaxy is inhibited by energetic supernova explosions in its spiral arms and by powerful outflows from its core, where a supermassive black hole is feasting on infalling gas and blowing some of it back into space.
Zooming in on the relatively quiet spiral galaxy in front of me, I can’t wait for the passage of the next nine billion years of accelerated cosmic time. That’s when a yellow, run-of-the-mill star will be born out of a small cloud of gas and dust, somewhere on the inner edge of one of the spiral arms. Orbiting the inconspicuous star will be a tiny, rocky planet—a mote of dust in the cosmic ocean. Before long, hydrocarbons raining down from outer space will turn this barren place into a fertile world, brimming with life. Billion-year-old carbon.
But that’s only happening in my imagination, for I’m not watching the evolution of the real universe. I’ve lost myself in video footage of a highly detailed three-dimensional computer simulation called IllustrisTNG (The Next Generation).1
IllustrisTNG doesn’t simulate the origin of life, but it’s still pretty impressive. Fourteen billion years of cosmic evolution, structure formation in an expanding universe, spiral galaxies with dark matter halos—it’s all there, and it looks uncannily realistic. It’s hard to shake the impression that this is just a sped-up version of the real universe. Like a prosecutor standing before a jury and minutely reconstructing a crime, the simulation so convincing that you can’t help thinking it must have happened this way.
Still image from an IllustrisTNG computer simulation of the growth of the large-scale structure of the universe.
Today computer simulations are an indispensable part of the astrophysicist’s toolkit. Some forty years ago, however, things were different. Physics—and astrophysics—was very much analytical, and progress was usually made by algebraically solving intricate polynomial or differential equations. In fact, Stephen Hawking once remarked that using a computer to solve a problem in general relativity would destroy the beauty of physics.
So when four young, audacious astronomers started to simulate the whole universe on their computers in the early 1980s—an effort that eventually yielded far-reaching conclusions about the possible nature of dark matter—it wasn’t so surprising that they met with skepticism. Indeed, they became known as the Gang of Four, after the group of radical Chinese Communist Party officials who were influential during the last stages of Mao’s Cultural Revolution. But while their peers were suspicious and reluctant at first, Marc Davis, George Efstathiou, Carlos Frenk, and Simon White are now seen as bold pioneers.2 Their numerical simulations of the evolution of large-scale structure in the universe are the basis of present-day projects like IllustrisTNG.
How do you simulate a universe? Or, more precisely, how do you simulate structure formation in the universe? It’s really not that complicated. The Gang of Four focused on nonbaryonic dark matter (the major material constituent of the universe), which doesn’t emit or absorb any light, doesn’t heat up or cool down, and doesn’t respond to magnetic fields. The only game in town is gravity, so you can use the same approach Jim Peebles and Jerry Ostriker did when they ran computer simulations of the evolution and the stability of disk galaxies (see chapter 4). It’s all about an initial distribution of test particles, each one representing a certain amount of dark matter. The computer code calculates the mutual gravitational attraction of the test particles in incremental time steps. Here, too, more test particles and smaller time steps increase the reliability of your results. This sort of system is called an N-body simulation: a model of how a large number of objects (in this case, quantities of dark matter particles) interact under the influence of their mutual gravity.
You can’t do this for the entire universe, of course. Instead, you just consider a large enough cubic chunk of expanding space, assuming that it is representative of the universe as a whole. “Expanding” is a key word here: with every time step, your cubic chunk of space will grow a little bit, the distances between your test particles will increase, and their mutual gravitational attraction will get a bit weaker. Eventually, the formation of large-scale structures is the result of a tug-of-war between gravity and cosmic expansion.
The smoothness of the initial distribution of test particles is critical. If the distribution were perfectly smooth, not much would happen in your expanding chunk of space, so you need to start with tiny density fluctuations. Areas with a slightly higher-than-average dark matter density will spread out and dilute over time thanks to the expansion of the universe, but they will do so more slowly than areas with a lower-than-average density. The end result is that the relative density variations tend to increase—the contrast between over-dense and under-dense areas strengthens as the eons go by.
Finally, simulations need to take into account what type of dark matter we’re talking about. As we saw earlier, there’s a big difference in behavior between hot (fast-moving) particles like neutrinos and cold (relatively slow-moving) particles like WIMPs: hot particles can cluster only on very large scales, while cold particles will aggregate into smaller clumps.
The resulting dark matter distribution will determine where galaxies will form, since the less abundant baryonic matter in the universe (basically atomic nuclei) is expected to flow toward the regions with the highest nonbaryonic matter density. In other words: galaxies are expected to form where dark matter is clumped most strongly.
So in the end, a number of assumptions—or, if you will, initial conditions—go into your simulation of the universe: the overall matter density, the type of dark matter (hot or cold), the spectrum of initial density fluctuations, the cosmic expansion rate, and so on. But once you’ve set all of the dials at the desired values, you just push the start button and wait to see what kind of universe this particular choice of initial conditions will produce after billions of years of evolution.
In the late 1970s, Marc Davis, the oldest member of the Gang of Four, already knew what kind of universe should be produced. In 1977, at Harvard, Davis had started the Center for Astrophysics (CfA) redshift survey, together with John Huchra, David Latham, and John Tonry (see chapter 6). Their first rudimentary 3D map of the distribution of galaxies in the “local” universe wasn’t published until 1983, but initial results had shown that galaxies were grouped in giant walls and filaments, surrounding relatively empty voids. Any credible theory—or computer simulation—of the universe should at least be able to explain or produce this specific kind of large-scale structure.
Most astrophysical N-body simulations at the time were restricted to something like a thousand test particles or so.3 In a 3D simulation, that amounts to a cube of just ten by ten by ten particles—way below the number you need to simulate a universe. But in 1979, Davis learned about novel computer code that could do much better. He was on his way to an international cosmology conference in Tallinn, Estonia, and the easiest way to get there was by ferry across the Baltic Sea from Helsinki, Finland. On board, he met George Efstathiou, who was traveling to the same conference. Efstathiou was a young British grad student, the child of Cypriot immigrants. He had no money; Davis bought him supper, and they became friends for the rest of their lives.
Efstathiou had been in touch with condensed matter physicists who were studying melting processes in atom lattices. Very different from cosmology (for one, gravity doesn’t play any role on the scale of atoms), but those scientists had developed computer code that could handle cubes of 32 × 32 × 32 elements—a whopping 32,768 test particles! Efstathiou was busy converting this code into something that could be used for cosmological purposes. Maybe that would finally enable simulations detailed enough to compare to the CfA redshift surveys—the only available 3D map of the real universe at the time.
Davis had met another member of the gang earlier, during a sabbatical at the University of Cambridge. Simon White had started out as an applied mathematics graduate student, studying in a stuffy, windowless basement in a downtown university building. But after visiting Cambridge’s Institute of Astronomy just west of town, with its sunlit rooms and daffodil-lined lawns, he decided to switch fields. The two met again at the University of California, Berkeley, where White became a senior fellow in 1980 and Davis secured a tenured position in 1981. By then, combining math and astronomy, White was developing computer code to simulate gravitational interactions in galaxy clusters. Would he be interested in an attempt to simulate the whole universe? You bet!
Meanwhile, back in England, Efstathiou had become friends with grad student Carlos Frenk, the son of a German-Mexican medical doctor and a musician. After earning his PhD in 1981 with White in Cambridge, Frenk went to Berkeley to become one of Davis’s first postdocs, working on the analysis of the CfA redshift survey results. And Efstathiou, who had held a postdoc position at Berkeley before but had returned to Cambridge, would regularly fly to California to join his friends and help realize the ambitious goal of simulating the growth of structure in the universe.
Back then, powerful computers were large and slow and scarce. The Berkeley machine—a Digital Equipment VAX-11 / 780—filled the better portion of a room, but it ran on a mere 16 megabytes (MB) of internal memory. One simulation easily took more than a full day. For comparison, a current off-the-shelf MacBook would be able to complete the task in fewer than 30 seconds.
Taking advantage of the Starlink computer network—mutually connected VAX computers at astronomical research centers throughout the United Kingdom—Efstathiou and Frenk used every machine they could lay their hands on. When it turned out that you could only use Starlink for a maximum of two hours at once, after which you had to apply for more computer time, Efstathiou wrote a script that cleverly overruled this limitation. Sure, other researchers complained that they couldn’t get access to the network, but what could be more important than simulating the evolution of the universe?
The first simulations, published in 1983 by White, Frenk, and Davis, showed that hot dark matter (neutrinos, for instance) could not reproduce the real universe.4 Fast-moving particles were shown to slowly cluster together in very large structures, comparable in size to superclusters of galaxies. These structures need to fragment into smaller clumps before galaxies can form. And because of this top-down scenario, the smallest matter concentrations—the seeds of galaxies—are only found within the supercluster-sized structures. The voids in between the superclusters remain completely empty in the simulations.
In contrast, observations reveal that galaxies formed quite early in the history of the universe, before the formation of superclusters. Moreover, voids are not completely empty; they, too, contain isolated galaxies, albeit in small quantities. This is exactly the outcome of simulations with cold dark matter, which soon became the team’s sole focus. Because of the lower particle velocities, cold dark matter first clumps into small dark matter halos, more or less the size of dwarf galaxies. Once the first small galaxies have formed (by accretion of baryonic matter), most of them will start to merge into larger galaxies, which successively gather into groups, clusters and, eventually, superclusters—a process that is still very much ongoing in the universe.
The Gang of Four—the nickname was coined by Berkeley astrophysicist Chris McKee—worked feverishly over the Christmas holidays in late 1983 and during a four-month workshop on the large-scale structure of the cosmos in Santa Barbara in 1984. In May 1985, they published their first results and conclusions in The Astrophysical Journal.5 The title says it all: “The Evolution of Large-Scale Structure in a Universe Dominated by Cold Dark Matter.” “It is remarkable how many aspects of the observed galaxy distribution are reflected quite faithfully by the distribution of CDM,” the authors write. “This seems too good to be true, but perhaps it hints that we are at last approaching a correct resolution of the missing mass problem.”
In a shorter follow-up paper in Nature, published in October, the group presented simulations that showed the formation and occasional merging of individual dark matter subhalos, leading to a pretty realistic population of disk galaxies (with flat rotation curves and all) and ellipticals.6 Was cold dark matter really solving all the riddles astronomers had been struggling with? It sure looked like that. The fact that no cold dark matter particle had ever been observed suddenly seemed to be a minor detail. “These people are magicians,” commented Princeton astrophysicist Richard Gott, who was a referee on the Nature paper.
And the magicians weren’t done yet. In 1987 and 1988, they published three more papers—two in The Astrophysical Journal and one in Nature—in which they expanded on their earlier work.7 Taken together, the Gang’s five landmark publications—collectively known as the DEFW papers, for Davis, Efstathiou, Frenk, and White—firmly put nonbaryonic cold dark matter on the map as the sole candidate for the major constituent of the universe. CDM appeared to be able to explain just about everything.
A major question remained, though: How much dark matter does the universe contain? In the vast majority of their initial simulations, the computer wizards had assumed an overall mass density of the universe equal to the critical density—the amount of gravitating matter that would eventually bring cosmic expansion to a halt without reversing into a collapse. Since the baryonic matter produced by big bang nucleosynthesis accounts for only 5 percent of the critical density, nonbaryonic cold dark matter would have to constitute the remaining 95 percent—a staggering imbalance, much more than one would infer from galaxy dynamics.
The four astronomers came to realize that a critical-density universe was basically just an “aesthetically pleasing idea,” as they called it. (We’ll get back to this in chapter 15.) Nature of course has no compelling reason to meet human aesthetic needs, so what if the total mass density of the universe were much lower than the critical value, and more in line with the earlier mass estimates by Ostriker, Peebles, and Yahil; Gott, Gunn, Schramm, and Tinsley; and Faber and Gallagher?
Indeed, White and Frenk, together with Julio Navarro and August Evrard, concluded in 1993 that either we do not understand big bang nucleosynthesis or the universe cannot have the critical density. The argumentation in their Nature article is quite straightforward.8 Returning to the Coma Cluster of galaxies (the subject of Fritz Zwicky’s much-ignored 1933 paper), they first derived the total dynamical mass of the cluster from the velocities of its member galaxies—the same method that Zwicky had applied. Next, they determined the baryonic mass, taking into account not just the visible galaxies—stars and nebulae—but also the huge amounts of extremely hot gas that X-ray telescopes had revealed between the cluster galaxies. By comparing the two mass estimates, the authors found that the baryonic mass in the Coma Cluster makes up about one-sixth of the total gravitating mass. For other clusters, similar values were found.
