The Elephant in the Universe, page 5
Zwicky was born on February 14, 1898, in Varna, on the Black Sea coast of Bulgaria.9 His parents, however, were Swiss, and from the age of six on, Fritz lived with his grandparents in Glarus, a village in the eastern Swiss Alps. He studied mathematics and physics at the Swiss Federal Institute of Technology in Zürich, where Albert Einstein had received his teaching diploma in 1900. Zwicky moved to the California Institute of Technology in 1925 to assist Robert Millikan, a giant in the field of solid-state physics, who two years previously had been awarded the Nobel Prize. Before long, however, Zwicky lost interest in solid-state physics and switched to astronomy. Caltech, in Pasadena, was just “down the hill” from Mount Wilson Observatory, with its world-class researchers and telescopes. Soon Zwicky was working with the astronomical hot-shots of the time, including Hale, Hubble, and Walter Baade. Brilliant, colorful, outspoken, and iconoclastic, Zwicky would become a hot-shot himself.
Zwicky’s 1933 paper made use of a key observational technique in astronomy: measuring redshifts. The redshift is a slight wavelength change perceived in the light that we receive from a rapidly receding light source. The faster an object is moving away from us, the redder it appears. This is akin to the Doppler effect we have all experienced when an ambulance is passing by. Although the siren is producing the same sound the whole time, we hear a higher pitch (a shorter wavelength) as the ambulance is approaching and a lower pitch (a longer wavelength) as it is moving away from us. The perceived wavelength change is proportional to the ambulance’s velocity toward or away from us. Light waves behave similarly: if a light source is moving toward us, we perceive a shorter wavelength (a bluer color), while a receding light source appears to be slightly redder.
By the early 1930s, astronomers had measured the redshifts of dozens of galaxies. Surprisingly, these redshifts—and the corresponding recession velocities—had turned out to be larger for more distant galaxies. That remarkable fact had led Lemaître and Hubble to conclude that cosmic distances are not growing because galaxies are racing away from us through intergalactic space but because space itself is expanding, taking the embedded galaxies along for the ride.
Although Zwicky initially hated the idea of an expanding universe, he spent considerable time studying galactic redshifts. In galaxy clusters (huge collections of many hundreds of galaxies grouped together in space), individual cluster members all appear to fly away from us—after all, the distance to the cluster is increasing as a result of cosmic expansion. However, the galaxies in the cluster also move about, like bees in a swarm. The result is that they all have slightly different recession velocities. Some are moving in our direction, to the effect that their recession velocity (and thus their redshift) is a bit lower than the value for the cluster as a whole. Others are moving in the opposite direction, away from us, which slightly increases their recession velocity and corresponding redshift, to values above the cluster average. The observed spread in galaxy redshifts tells you about the motions of the galaxies within the cluster—it is equivalent to a velocity spread. And here, too, these motions are governed by the gravity of the cluster as a whole, just like the motions of stars in our home galaxy are governed by the Milky Way’s mass.
Working with observational data others had obtained with the hundred-inch telescope at Mount Wilson, Zwicky estimated the number of galaxies in the Coma Cluster (named after the location in which it is located on the sky). He then assumed that each galaxy was about a billion times more massive than the Sun and on this basis calculated the total visible mass of the Coma Cluster to be on the order of 1.6 × 1045 grams. In that case, given the spatial extent of the cluster, individual Coma galaxies were expected to show a velocity spread of about 80 kilometers per second.
The Coma Cluster of galaxies, where Fritz Zwicky found evidence for the existence of dark matter.
However, the eight galaxies in the cluster that were bright enough to allow astronomers to measure their redshifts showed a much larger range of velocities, differing from each other by as much as 2,500 kilometers per second. This is far higher than the estimated “escape velocity” of the cluster. In other words, the gravity of 1.6 × 1045 grams of cluster matter is insufficient to keep hold of objects hurtling through space at such tremendous speeds. To prevent the speeding galaxies from flying away into the wider universe, the total mass of the cluster would have to be greater. Much greater.
“In order to obtain [the observed velocity spread], the average density in the Coma system would have to be at least 400 times greater than that derived on the basis of observations of luminous matter,” Zwicky wrote. “If this should be verified, it would lead to the surprising result that dark matter”—“dunkle Materie” in the original German text—“exists in much greater density than luminous matter.” Zwicky published his elegant but quite unnerving analysis in a Swiss physics magazine called Helvetica Physica Acta.10 The title of the paper translates to “The Redshift of Extragalactic Nebulae,” rather underselling the surprising finding within.
Surprising indeed, not to say unbelievable. Jacobus Kapteyn had toyed with the idea that the universe might contain at least some invisible stuff. Fair enough. Jan Oort figured that dark matter in the plane of our Milky way galaxy is about twice as abundant as visible matter. Unexpected maybe, but not completely crazy. But now Fritz Zwicky claimed that the luminous stars and nebulae in the universe constitute no more than 0.25 percent of everything there is. Little wonder, perhaps, that few astronomers paid any attention to the result—it just seemed too bizarre. Also, the whole concept of recession velocities and cosmic expansion was very novel at the time. Surely there was a more satisfying explanation for what Zwicky described as a “noch nicht geklärtes Problem”—a not-yet-solved problem?
Almost ninety years later, the problem of dark matter is still unsolved. In fact, it has become more and more complicated. While Kapteyn, Oort, and Zwicky assumed that dark matter would consist of extremely faint dwarf stars or nonluminous clouds of cold gas, we now realize that it can’t be composed of the elementary particles we’re familiar with—it’s matter, Jim, but not as we know it. And while the initial quantitative results on the invisible stuff were published in small magazines and didn’t raise too many eyebrows, the nagging mystery of dark matter is now all over the place, occupying hundreds of astrophysicists, cosmologists, and particle physicists alike.
Kapteyn of course never knew of this development. He died in 1922, in what we now consider the prehistory of cosmology. His ideas about the layout of the universe were revolutionary, but we now know that, for the most part, they were plain wrong.
Zwicky made errors, too, although it took some time for astronomers to realize this. His initial 1933 conclusions about incredible amounts of dark matter in galaxy clusters appeared to be confirmed by redshift observations of thirty galaxies in the Virgo Cluster, carried out by Mount Wilson astronomer Sinclair Smith in 1936. Zwicky’s own more detailed study of the Coma Cluster in 1937 also lent ballast to his earlier findings.11 He summarized these and other results in his 1957 monograph Morphological Astronomy.12 But we now know that Zwicky had underestimated the number of galaxies in the cluster, as well as the average stellar mass of those galaxies. Moreover, his estimate for the distance of the Coma Cluster was much too high, compromising his results.
Still, even after accounting for Zwicky’s errors, there remained a discrepancy of a factor of about one hundred between the “visible” mass and the “dynamical” mass of galaxy clusters like Coma. Even the discovery, in the early 1970s, that galaxy clusters contain huge amounts of hot, X-ray emitting gas in the space between their individual member galaxies leaves a mismatch of a factor of ten or so. So when Zwicky suddenly died of a heart attack in 1974, astronomers were still facing his forty-two-year-old nicht geklärtes Problem.
And what about the third pioneer? After the Second World War, Oort became director of Leiden Observatory and continued to do research in a diverse range of topics. In the late 1950s, he finally returned to his work on the amount of dark matter in the Milky Way’s central plane. Using better data, he arrived at more-or-less the same conclusions as he had in 1932. He published these new results in 1960, in another paper in the Bulletin of the Astronomical Institutes of the Netherlands.13
However, Oort’s results didn’t stand the test of time. In the late 1980s, Belgian astronomer Koen Kuijken and his thesis advisor Gerry Gilmore of Cambridge University showed that Oort’s work suffered from systematic errors, mainly because he had to rely on observations of a certain type of giant stars: the only ones bright enough for spectroscopic velocity measurements at the time.14 Unfortunately, it is notoriously difficult to estimate the true luminosities, and thus the distances, of these so-called K giants. Moreover, we now know that they’re not really representative of the stellar population of the thin galactic disk. Both of these issues affected Oort’s conclusions.
Using a novel and very efficient multi-object spectrograph at the 3.9-meter Anglo-Australian Telescope in Coonabarabran, New South Wales, Kuijken and Gilmore observed some 800 more “regular” stars and carried out a much more thorough analysis. In three papers in Monthly Notices of the Royal Astronomical Society, they concluded that “available data … provide no robust evidence for the existence of any missing mass associated with the galactic disc.”15
By that time, astronomers realized that our Milky Way galaxy had to be surrounded by an extended, more or less spherical halo of dark matter (we’ll come back to that in the next chapter). But apparently, there is no significant excess of dark matter in the central plane of our home galaxy. Oort had been wrong.
Around 1988, Kuijken gave a colloquium about his and Gilmore’s research in one of the lecture rooms of Leiden Observatory. Jan Oort, brittle and deaf, was in the audience, his hearing aid plugged almost directly into Kuijken’s microphone. He was extremely interested in the new results and later sent a complimentary letter to the young astronomer, who would move to Leiden in 2002 and work as the observatory’s scientific director between 2007 and 2012. Even in the last stage of his life, Oort was looking forward to what Kuijken, his contemporaries, and his successors would learn. When I interviewed Oort in 1987, he speculated that “the huge amounts of dark matter that people are finding at large scales in the universe may have to be explained by … something completely new.… But at the moment, I have no idea where [the solution] might be found.”16
No one did. In November 1992 Oort died, as old as the century on which he had left so many valuable traces. The Hubble Space Telescope had been launched two years before but still suffered from blurry vision due to a slightly misshapen mirror; astronomers had just obtained the very first detailed satellite measurements of the cosmic background radiation; and particle physicists were toying with the concept of xenon detectors. The golden age of dark matter research was about to start.
Yet, despite the huge advances of the past twenty-five years, today’s scientists are still groping in the dark, not so unlike Kapteyn about a century ago, when he first introduced the term “dark matter” in an English-language publication.
When will we finally find the answer to the largest riddle in the universe?
4
The Halo Effect
My husband says dark matter is a reality
not just some theory invented by adolescent computers
he can prove it exists and is everywhere
forming invisible haloes around everything
and somehow because of gravity
holding everything loosely together
The first six lines of “Dark Matter and Dark Energy,” written in 2015 by award-winning poet Alicia Suskin Ostriker, neatly sum up the early work of her spouse, theoretical astrophysicist Jeremiah Ostriker. Both are trying to wrap their head around an enigma—Alicia by meticulously sculpting sentences on white paper, Jerry by feverishly jotting down equations on a blackboard. So far, neither approach has solved the mystery. As the ninth line of the poem reads, “[W]e don’t know what it is but we know it is real.”1
Jerry Ostriker is in a hurry. In less than an hour, he has to dash off to a meeting on the birth of black holes. Talk about enigmas! But that’s more than enough time to discuss his 1970s work on dark matter halos, right? In his small, orderly office on the tenth floor of Columbia University’s Pupin Building, he starts to talk and lecture right away, all the while scribbling down equations on a notepad. Every now and then, he walks over to the blackboard on the wall, chalk in hand, to support or explain his arguments with formulas and crude diagrams.2
A short, balding, friendly but intense man in his early eighties, and in a hurry, yes. Ostriker wants to witness, or maybe even find, the solution to the puzzle. In the past couple of years, he’s been toying with the novel and speculative concept of fuzzy dark matter (more on that in chapter 24). Crazy perhaps, but so far no one has found a way to disprove it. Maybe there’s a 50 percent chance that it’s right, he says. No time to explain the details, though. “Read my paper.”
It’s funny because, back in the 1950s, astronomy wasn’t his first choice. Ostriker pursued chemistry and physics. But upon reading a Fortune magazine story about the great astrophysicist Subrahmanyan Chandrasekhar, he decided to apply for the PhD program at the University of Chicago, where the famous Indian American scientist worked at the university’s Yerkes Observatory, carrying out theoretical research on stellar evolution while editing the prestigious Astrophysical Journal.
Chandrasekhar is best known for his work on white dwarfs—ultra-dense stars that pack the mass of the Sun into a volume comparable to the Earth’s. A few billion years from now, at the end of its life, our own Sun will collapse into such a weird, compact object, with each cubic centimeter weighing as much as a small SUV. During its final collapse, the Sun will spin up dramatically. The focus of Ostriker’s PhD research lay here: the stability of these rapidly rotating white dwarf stars. If spun up fast enough, would they start to lose mass, fly apart, or what? He was still struggling with the stability problem when he moved to the University of Cambridge to work as a postdoc with astrophysicist Donald Lynden-Bell. That was in the mid-1960s; Stephen Hawking was a Cambridge grad student.
Obviously, as is usually the case in astronomy, the stability of a spinning star is not something you can easily test in a laboratory. The nitty-gritty details of the problem also can’t be solved purely analytically, with a neat set of equations. Ostriker had to take a numerical approach instead, relying on computer simulations. That may sound easy enough today, but back then computers filled rooms, there were no standard programming languages, and lines of code had to be entered manually by punching holes in paper tape. It took until 1968 before Ostriker got his code to work properly. By that time, he was back in the United States, at Princeton. Working with fellow astrophysicist Peter Bodenheimer and others, Ostriker produced no fewer than eight papers titled “Rapidly Rotating Stars” between 1968 and 1973.3
So what’s the answer? What happens to a white dwarf—or any other star, for that matter—that spins out of control? We are back in Ostriker’s office, where he starts writing down equations again. Angular momentum. Inertia. Viscosity. Potential energy. Pretty complicated if you have to take everything into account. But the outcome is always the same: first the star starts to flatten at the poles, just like the Earth or any other rotating body. But then something peculiar happens. If the rotation rate goes up, the star changes shape. It becomes elongated—no longer an axisymmetric pumpkin but a tumbling dog bone. Eventually the star may even split in two.
I’m not particularly good at equations. What Ostriker describes as “simple physics” is hard for me to grasp. But when he uses plain language, the message comes across. Rotating objects with a lot of angular momentum are happier when they are elongated like a candy bar and tumbling like a majorette baton. He takes a look at his watch. We haven’t even started to discuss galaxy halos. But we’re almost there. For why would this preference for an elongated shape only work for stars? What about disk-like galaxies like our own Milky Way?
At Princeton, Ostriker had an office in Peyton Hall, just a stone’s throw from Jadwin Hall, where Jim Peebles was coming to grips with the cosmic background radiation and cosmology in general. Jim and Jerry got along very well, discussing such diverse topics as primordial nucleosynthesis, pulsars, the large-scale structure of the universe, cosmic rays, and computer programming. Oh, and the stability of spiral galaxies, of course.
Peebles was dabbling in numerical calculations himself, out of interest in the gravitational effects of dark matter in clusters of galaxies. At the time, Princeton didn’t have powerful enough computers to handle calculations relevant to that problem, so in 1969 he spent a month at the Los Alamos National Laboratory in New Mexico, where he could use the Department of Energy’s number-crunching machines. To make sure he wouldn’t disturb the secret programs at what was, after all, a government weapons lab—Peebles was still a Canadian citizen back then—he had to be supervised at all times, usually by a secretary reading a novel.
Simulating gravity in a computer is rather straightforward. You start out with an initial distribution of “test particles,” each with a certain mass. Using Newton’s laws, you determine the net force that each particle experiences as a result of the gravitational attraction of all the other ones. Next you calculate where each particle ends up after a certain amount of time, as a result of this force. That gives you a new configuration, which serves as the input for the next round of calculations. Larger numbers of test particles and smaller time steps will increase the precision and the credibility of your simulation, but, unfortunately, they will also hugely increase the necessary amount of computer time.
I know all about it. In the early 1980s, I wrote a simple BASIC program for my brand-new eight-bit Commodore 64 home computer. The program would simulate the gravitational chaos resulting from the collision of two rotating disk galaxies—I’m not that bad at equations. Each time step took about fifteen minutes to process. After the program ran for a day, I thought the output looked quite impressive, although there probably was little (if any) connection between the pattern of dots on my monitor and the real world. (We’ll get back to this sort of modeling, known as high-resolution gravitational N-body simulation, in chapter 11.)
