The Elephant in the Universe, page 14
But if baryons account for only 5 percent of the critical density—that’s what big bang nucleosynthesis tells us—and if the universe indeed has the critical density, then the nonbaryonic dark matter in the universe would have to be nineteen times as abundant as the baryonic matter in the form of “normal” atoms, not six times. And given the way in which galaxy clusters are thought to form in an expanding universe (based on the type of computer simulations that the Gang of Four had pioneered), there’s just no way they can end up with a baryon fraction that’s more than three times higher than the average cosmic value. In other words, the high baryon fraction of clusters like Coma must reflect the cosmic average, in which case the universe cannot have the critical density.
With the discovery of the accelerating expansion of the universe in 1998—attributed to yet another mysterious cosmic component called dark energy, described in chapter 15—it became clear that the total mass density of the universe is much lower than the critical density: something on the order of 27 percent of the critical density. Ever since, computer simulations of the growth of cosmic structure have used this value for the amount of gravitating matter in the universe and taken dark energy into account, too. Thanks to an incredible increase in computing power, these simulations are of course much more detailed than those of the Gang of Four, and the close correspondence between contemporary simulations and the real universe out there has contributed considerably to the general acceptance of what is now known as the cosmological concordance model.
To give you an idea of the progress that has been made since the early 1980s, let’s take a look at the groundbreaking Millennium Simulation, run in 2005 by members of the so-called Virgo Consortium.9 Also known as the Millennium Run, the project was led by Volker Springel of the Max Planck Institute for Astrophysics in Garching, Germany; the first Nature paper on the Millennium Simulation results was coauthored by White (Springel’s thesis advisor), Frenk, Navarro, and Evrard, among others.10 While White and Frenk had started out with simulations of just 32,768 particles in a 32 × 32 × 32 cube, the Millennium Simulation followed the mutual gravitational attraction of no fewer than 10 billion dark matter test particles (2160 × 2160 × 2160). And instead of a VAX computer with just 16 MB of internal memory, Springel and his colleagues used an IBM Regatta supercomputer with one terabyte of memory (1 TB, approximately one million MB). Performing 200 billion floating point operations per second, it took this monster machine 28 days—a total of 343,000 processor hours—to complete the simulation, yielding 27 TB of stored data, all of which has been made available to the scientific community.
Like the original Gang of Four simulations, the Millennium Run dealt only with the clumping of dark matter, which is relatively easy because you only need to consider gravity. But what about the baryonic matter? How do familiar atoms aggregate on the invisible skeleton of nonbaryonic dark matter? How do real galaxies form? That’s a much more complicated question, since atomic nuclei (and electrons) are governed not only by gravity but also by radiation, collisional gas drag, and magnetohydrodynamic processes, to name just a few nasty examples. Moreover, since baryonic matter interacts with light, it can heat up and cool down by absorbing or emitting energy.
Astronomers have recently succeeded in developing humongous computer simulations that take all these complications into account. By using a broad range of mathematical tricks, they are now able to model messy problems like cooling flows, galactic winds due to the explosions of massive stars (supernovae), and the energetic effects of supermassive black holes in the cores of galaxies.
In late 2014 and early 2015, two competing groups published results from such enriched simulations, accounting for nonbaryonic and baryonic matter alike. The models, Illustris and EAGLE (Evolution and Assembly of GaLaxies and their Environments), both take you on a mind-boggling tour through space and time, from the very first density perturbations in the early universe all the way to the formation of irregular dwarf galaxies, majestic spirals, and bulky ellipticals.11 As of this writing, the state of the art is a new version of Illustris, the 2017 IllustrisTNG simulation, which can follow the behavior of more than 30 billion test particles (both dark matter and gas) in a cubic chunk of space that expands to a current size of almost one billion light-years across.
Upon publication of the EAGLE simulation in a 2015 paper in Monthly Notices of the Royal Astronomical Society, coauthor Richard Bower of Durham University said, “The universe generated by the computer is just like the real thing. There are galaxies everywhere, with all the shapes, sizes, and colors I’ve seen with the world’s largest telescopes. It is incredible.”12 And the end is not yet in sight, says EAGLE project lead Joop Schaye of Leiden University—in principle, you could go on forever, looking in ever more detail at the birth of stars and the formation of planets.
No one expects that we will be able to simulate the origin of life any time soon. However, flying through eons and gigaparsecs in the IllustrisTNG simulation, witnessing how small variations in the density of dark matter evolve into the large-scale structure of the universe, and zooming in on a budding spiral galaxy in the outskirts of a populous cluster gives you a unique perspective on your own place in time and space. This is how it may have happened. Almost 14 billion years after the big bang, on a grain of sand orbiting a pinprick of light, a curious species started to think about its cosmic roots and its miraculous connection to the great wide open.
Without the prodigious amounts of cold dark matter that fill our universe, we would probably not be here. And even though we have no clue yet as to the real nature of dark matter, we can now be absolutely sure that this mysterious stuff is at the very basis of our existence.
Or can we?
12
The Heretics
I have always felt sympathy for scientific rebels. People who choose to swim against the tide. “Everybody says X? Well I believe it’s Y.” These are creative characters, not easily discouraged by fierce opposition or even ridicule. And no, I don’t mean pseudoscientists who claim that the pyramids were built by aliens or crackpots working on a perpetuum mobile. I’m talking about real scholars, questioning or even attacking prevailing wisdom with original thinking and solid arguments. Iconoclasts.
So when, as a teenager, I read my first astronomy books by the Dutch teacher and science writer Tjomme de Vries, I loved the story about Fred Hoyle and his steady-state model, which took issue with the conventional-wisdom big bang theory of the origin of the universe. And in the mid-1980s, as a beginning science journalist, I got intrigued by the theories of Halton Arp and Margaret Burbidge, who argued that galaxies and quasars might not be as remote as you would infer from their redshifts. What if those dissenters were right?
It must not have been much later that I came across the work of Israeli physicist Mordehai Milgrom—probably in the 1988 book The Dark Matter by Wallace and Karen Tucker.1 Here was someone with a fresh take on a nagging cosmic mystery. While astronomers were becoming convinced that the flat rotation curves of galaxies and the dynamics of galaxy clusters could only be explained by assuming that the universe is dominated by dark matter, “Milgrom took another approach,” the Tuckers wrote. “He tried to change the laws of physics.” Now here was some heretic.
Come to think of it, Milgrom’s idea makes a lot of sense. The velocities of galaxies in clusters are much too high. The outer parts of disk galaxies are rotating much too fast. Galaxies and groups of galaxies are much too heavy. Sure, there’s nothing wrong with the measurements themselves. But what about the qualifications too high, too fast, and too heavy? Those are all based on our assumption that we understand how gravity works. Yet if gravity behaves differently on cosmic scales, then everything might actually be just fine. We wouldn’t need dark matter at all to explain our observations.
If Milgrom were right, it wouldn’t be the first time that an observational riddle was solved by tweaking our theory of gravity. It happened just over a century ago.
In the first half of the nineteenth century, astronomers had noted how Uranus was diverting from its predicted path. Apparently something was tugging on the remote planet. French mathematician Urbain Le Verrier used Isaac Newton’s law of universal gravitation to calculate where the culprit might hide, and, sure enough, Neptune was found in 1846 near the predicted position.2
But the solar system’s innermost planet, Mercury, was slightly misbehaving too. Encouraged by his earlier success, Le Verrier tried to pull off the same mathematical trick again, and in 1859 he proposed the existence of an “intra-Mercurial” planet, which was called Vulcan. But Vulcan was never found, and we now know it doesn’t exist (at least not outside the universe of Star Trek). Instead, Mercury’s “errant” behavior was fully explained by Albert Einstein’s 1915 general theory of relativity—an improved version of Newton’s formulation of gravity.3
What else might be wrong—or at least incomplete—with our understanding of gravity? For instance, we all learned in high school that the pull between two massive bodies decreases with the square of the distance between them. Sensitive laboratory experiments and observations within our solar system confirm this so-called inverse square law. But how can we be so sure that it holds throughout the universe?
In his 1937 paper on the Coma Cluster, Fritz Zwicky was careful enough to note that his conclusions about the mass of the cluster rested “on the assumption that Newton’s inverse square law accurately describes the gravitational interactions among [galaxies].” Likewise, Horace Babcock, in his 1939 thesis on Andromeda, concluded that there must be large amounts of dark mass in the outer parts of the galaxy, “or, perhaps, that new dynamical considerations are required”—in other words, novel ways to treat gravity. Italian astrophysicist Arrigo Finzi went one step further in 1963, by actually proposing how gravity might work differently on very large scales.4
It would take twenty more years before Mordehai Milgrom published his theory of modified Newtonian dynamics, known as MOND. If correct, the theory would undermine the necessity of dark matter. As of this writing, the jury is still out. Some revolutions proceed extremely slowly; many never happen at all.
In September 2019 I met Milgrom at a five-day workshop in Bonn, Germany.5 A tall, slim person, casually dressed in a black T-shirt, black trousers, and sneakers, he was sitting in the front row at every talk, asking questions and initiating lively discussions. In between presentations, he took considerable time to tell me his story.
Trained as a particle physicist, Milgrom, who goes by Moti, has been affiliated with the Weizmann Institute of Science in Rehovot, Israel, since the 1970s. In 1980 and 1981, during a sabbatical at the Institute for Advanced Study in Princeton, he delved into the emerging field of galaxy dynamics and learned about the curious fact that galactic rotation curves always seem to become flat at large distances from the center.
Mordehai Milgrom (left), talking with University of Geneva astrophysicist André Maeder at the Bonn workshop on modified Newtonian dynamics, September 2019.
Dark matter, right? That’s what everybody says. But what if there’s something wrong with Newton’s laws? What happens if you assume that flat rotation curves are produced by some non-Newtonian form of gravity? At first Milgrom was pretty skeptical himself. “If you’d asked me back then whether this would ever lead to something useful, I would’ve given it a slim chance,” he says. Surprisingly, though, he didn’t run into any theoretical inconsistencies as he tried to make sense of the strange observations. Slowly but surely, it became evident that a simple modification of Newtonian gravity could explain flat rotation curves in one fell swoop.
Back home in Israel, Milgrom feverishly worked out all the details—an obsessed thirty-five-year-old scientist, certain that he was onto something big. “I hardly slept. I kept a notebook next to my bed. My wife tells me I was out of touch most of the time.” And he kept everything to himself, lest colleagues call him crazy, or—worse still—steal his ideas. “I was absolutely sure everyone would jump on it; that’s how convinced I was,” he says.
But when Milgrom privately sent his three papers on modified Newtonian dynamics to five eminent theoretical astrophysicists, including Martin Rees and Jerry Ostriker, none of them was overly enthusiastic—although they also didn’t think him completely nuts. And when he submitted the first paper for publication, Astronomy & Astrophysics, The Astrophysical Journal, and Nature all rejected it. Only after a long and frustrating struggle with the editors did The Astrophysical Journal finally accept Milgrom’s second and third papers, on the implications of his new idea for galaxies, galaxy groups, and galaxy clusters. After that, he talked the journal into running the first paper, too.
The three papers were eventually published back to back in the July 15, 1983, issue.6 The very first sentences of the first paper reveal Milgrom’s self-confidence, which has never really left him. “I consider the possibility that there is not, in fact, much hidden mass in galaxies and galaxy systems,” he wrote. “If a certain modified version of the Newtonian dynamics is used to describe the motion of bodies in a gravitational field (of a galaxy, say), the observational results are reproduced with no need to assume hidden mass in appreciable quantities.”
There you have it. Dark matter doesn’t exist.
To explain Milgrom’s hypothesis, I’ll have to bring the concept of a rotation curve back to mind. In our solar system, Neptune has a much lower orbital velocity than Mercury, since it is much farther from the Sun, while gravity falls off with the inverse square of distance—at least, according to Newton. Less gravitational attraction means lower speed. A plot of orbital velocity against distance shows this reduction in speed—a characteristic and continuous curve known as the Keplerian decline, named after Johannes Kepler, who was the first to formulate mathematical laws of planetary motion, in the early seventeenth century.
The rotation curve of a galaxy is expected to look somewhat different from that of a planetary system. To see why, compare our solar system to a galaxy. While almost all of the mass of the solar system is concentrated in the Sun, a galaxy’s mass is distributed over a much larger volume. It turns out that the orbital velocity of a star (or any other object) in the galaxy is determined not only by the mass at the galaxy’s center but also by the total amount of mass at smaller distances from the center. Still, at larger distances, in the galaxy’s dark outskirts, you would expect something close to a Keplerian decline: the more distant a star (or a cloud of hydrogen gas) is from the center of the galaxy, the slower it should orbit.
Instead, as radio observations reveal (see chapter 8), velocities remain constant way beyond the visible disk of a galaxy. In other words, the rotation curve reaches a certain terminal velocity, after which it stays flat, suggesting the existence of large amounts of invisible gravitating matter. This doesn’t mean that galaxies rotate the way solid objects like wagon wheels do: distant orbits have a larger circumference, so despite moving at the same velocity as a star nearer to the center of the galaxy, a more distant star takes longer to complete a revolution.
However, the flat rotation curve raises a critical question, which implicates the dark matter theory: Why would dark matter be precisely distributed in such a way as to produce flat rotation curves, as opposed to some other form of slower-than-Keplerian decline? Milgrom’s answer is simple. If gravity falls off with the inverse of distance—and not with the inverse of the square of the distance—you will automatically end up with a flat rotation curve. No need for dark matter and no need to figure out why it is distributed in a manner that produces flat rotation curves. Problem solved.
But wait, gravity evidently does not behave this way in our solar system. So what sets a galaxy apart from a planetary system? Why would gravity behave differently out there than it does right under our noses? According to MOND, it all has to do with the strength of the gravitational field. If the field strength gets below a certain limit, gravity changes face, and Newton’s inverse square law no longer holds. On the surface of the Earth, we experience a convenient gravitational field of 1 g (which equals a gravitational acceleration of 9.81 m / s2). On the Moon’s surface, the field strength is just 0.16 g. Meanwhile, the Moon is kept in its orbit by the Earth’s gravity, which, at the Moon’s distance, amounts to a mere 1 / 3600 g (that’s because the Moon is 60 times farther away from the Earth’s center than our planet’s surface is). Likewise, it’s easy to show that the Sun’s gravitational field as experienced by the distant dwarf planet Pluto is just 0.00000067 g.
As far as MOND goes, these are all huge numbers. But things get different in the outer regions of galaxies and in intergalactic space, where field strengths are much, much lower. Milgrom’s “tipping point”—where gravity gradually starts to behave differently—lies around one hundred billionth g (corresponding to a gravitational acceleration of 1.2 × 10–10 m / s2, to be precise). If Earth’s gravity were that weak, it would take an apple two days to fall down from a height of one meter.
This may all sound a bit speculative and contrived, and it is. Then again, over the centuries, scientists have always tried to find simple mathematical rules and laws to describe their observations and measurements as best as they could. And modified Newtonian dynamics successfully describes the observed rotational properties of galaxies. “I didn’t know of any physical reason why it would work,” says Milgrom, “but it worked.”
