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Mapping the Universe

Author(s): Stephen D. Landy

Source: Scientific American , Vol. 280, No. 6 (JUNE 1999), pp. 38-45

Published by: Scientific American, a division of Nature America, Inc.

Stable URL: https://www.jstor.org/stable/10.2307/26058286

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https://www.jstor.org/stable/10.2307/26058286

Using techniques drawn from the analysis of music, astronomers have been studying how galaxies form into progressively larger groupings

Mapping the Universe

38 Scientific American June 1999

Even for most astronomers, a galaxy is a siz-able thing—a throng of hundreds of billionsof stars, threaded with gargantuan clouds of gas and dust, in a region hundreds of thousands of

light-years across. But for cosmologists, those who

study nature on its very largest scales, a galaxy is

merely the basic unit of matter. Billions of them fill the

observable universe. They congregate into clusters

three million or more light-years across, which in turn

constitute progressively larger assemblages. On all

scales observed thus far by astronomers, galaxies ap-

pear to cluster and form intricate structures—presum-

ably through physical processes that were dominant

during the early expansion of the universe and later

through gravitational interactions.

Yet there is a paradox. The clumpiness of galaxies runs

contrary to one of the essential tenets of modern cosmol-

ogy: the cosmological principle, the concept that the uni-

verse overall is homogeneous and isotropic, that it has

no preferred place or orientation. Whenever cosmolo-

gists discuss the global properties of the universe, such

as its mean density, expansion rate and shape, they do

so under the auspices of this principle. On some large

scale, such as that of the whole observable cosmos with

a radius of 15 billion light-years, the distribution of these

galactic motes should approach uniformity. But how

can the evenness of matter on the ultimate scale be rec-

onciled with the unevenness of matter on smaller scales?

Over the past several years, technological advances

have enabled astronomers and cosmologists to probe

the arrangement of galaxies at great distances. The naive

notion that at some scale the cosmos becomes uniform

has been replaced by an appreciation that the large-scale

structure of the universe must be understood in terms

of random processes. Although the universe is still con-

sidered to be homogeneous and isotropic, this is true

only in a subtle, statistical sense. These insights are help-

ing untangle some of the thorniest issues in cosmology:

by Stephen D. Landy

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What did the universe look like at the dawn of time?

How did it grow and develop into what we live in to-

day? What forms of matter, both mundane and exotic,

does it contain?

The recent work has followed two decades of exciting

discoveries. In the late 1970s and early 1980s, cosmolo-

gists began to map galaxies in a systematic way [see

“Superclusters and Voids in the Distribution of Galax-

ies,” by Stephen A. Gregory and Laird A. Thompson;

Scientific American, March 1982]. In so doing, they

Scientific American June 1999 39

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sought to measure the distribution of all matter, includ-

ing the intergalactic “dark matter” that, unlike galaxies,

does not give off light. (The assumption that luminous

galaxies trace the total mass is no more than an approx-

imation, albeit a constructive one; other research has at-

tempted to quantify the bias that results.)

Cosmo-cartographers discovered that on scales of up

to 100 million light-years, galaxies are distributed as a

fractal with a dimension of between one and two. The

fractal arrangement of matter would be a severe prob-

THREE MILLION GALAXIES, each one containing billions of

stars, appear on the map of 15 percent of the sky centered on

the constellation Sculptor. Although galaxies fill the sky, making

it look roughly the same in every direction, they tend to fall into

clusters, clumps and chains. This map, in which the brightness

of each dot is proportional to the number of galaxies it repre-

sents, was pieced together by the Automated Plate Measuring

Galaxy Survey from black-and-white photographs from the

U.K. Schmidt Telescope. On this color-enhanced version, blue,

green and red dots depict bright, medium and faint galaxies, re-

spectively. The black patches are areas around bright stars that

the survey was unable to probe.

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As the viewer moves out from the Milky Waygalaxy to the entire observable universe, clumpiness finally gives way to smoothness. Each sphere is 10 times wider— and therefore 1,000 times more voluminous— than the previous one. A galaxy is a lump of stars, gas, dust and unclassi- fied “dark matter.” It agglomerates with other galaxies to form galaxy clusters, the largest bodies in the universe held together by gravity. The clus-

40 Scientific American June 1999

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Large-Scale Structures in the Universe

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ters, in turn, are clumped together into superclus- ters and walls, separated by voids of nearly empty intergalactic space. Up to some scale, thought to be around 100 million light-years, these progres- sively larger structures form a fractal pattern— that is, they are equivalently clumpy on every scale. But between this scale and the size of the observable universe, the clumpiness gives way to near uniformity. — S.D.L.

Scientific American June 1999 41

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lem for the cosmological principle if it extended to larger scales, because a fractal distribution is never homogeneous and isotropic. Unlike, say, a crowd of people, a fractal does not approach homogeneity when viewed from a distance; like a coastline, it looks uneven on every scale. In a fractal universe of dimension two, the expected mass within a spher- ical volume centered on a random galaxy would increase as the square of the radius instead of the cube. In such a uni- verse, the mean density would be a function of scale, and other universal parameters such as the cosmic expansion rate would lose their meaning. In short, the fractal findings seemed to pull the rug out from under modern cosmology.

Subsequent surveys, however, indicated that on scales of hundreds of millions of light-years, the fractal nature broke down. The broader distribution of galaxies could be de- scribed in terms of a simple statistical process with a well- defined mean and variance—a noise process. The cosmologi- cal principle was saved. But in the late 1980s new problems rose to threaten it [see “Very Large Structures in the Uni- verse,” by Jack O. Burns; Scientific American, July 1986]. A high-resolution survey detected a “Great Wall” of galaxies 750 million light-years long, more than 250 million light- years wide and 20 million light-years thick. A noise process could not readily explain such a colossal, coherent structure. These discoveries motivated still larger mapping projects, in- cluding the Las Campanas Redshift Survey that my col- leagues and I conducted from 1988 to 1994.

Slicing through the Universe

B ecause the Las Campanas survey sought to measure the distribution of galaxies on a scale several times that of

previous studies, it encountered a number of observational challenges. The most distant galaxies were faint, so pho- tographing them would require a lengthy exposure time. The large survey volume increased the number of objects that had to be observed. In sum, we had to observe more objects with a longer exposure but with only limited telescope time. For these reasons, we decided to construct a survey that would be very deep (out to two billion light-years) and wide (85 degrees across the sky) but thin (1.5 degrees)—effectively sampling the galaxy distribution in only two dimensions. Though thinness compromised the signal, it allowed a first glimpse of the orga- nization of the cosmos on scales of several billion light-years.

The survey made six separate maps and recorded the posi- tions of more than 26,000 galaxies. The data were collected at the Carnegie Observatories on Cerro Las Campanas in the Atacama Desert of Chile. This information was analyzed by Stephen A. Shectman of the Carnegie Observatories, Robert P. Kirshner and Huan Lin of the Harvard-Smithsonian Cen-

ter for Astrophysics, Augustus Oemler and Douglas L. Tuck- er of Yale University, Paul L. Schechter of the Massachusetts Institute of Technology and me.

The survey involved several steps. First, we made photo- metric observations—basically, highly sensitive photographs of the sky—with a charge-coupled device (CCD) camera mounted on the one-meter Swope telescope at Las Cam- panas. For maximum efficiency, we used a specialized tech- nique known as drift-scan photometry, in which we pointed the telescope at the beginning of a survey field and then turned off its automated drive. The telescope stood still as the sky drifted past. Computers read information from the CCD detector at exactly the same rate as the rotation of the earth, producing one long, continuous image at a constant celestial latitude. Completing the photometry took a total of 450 hours.

Second, we analyzed the strips to determine which objects were likely to be galaxies and suitable for inclusion into the survey. Candidates were chosen based on their brightness and galaxylike fuzziness. Finally, we observed these objects with a spectrograph at the 2.5-meter du Pont telescope at Las Campanas. The spectrograph broke the light down into a spectrum of colors, from which we calculated each galaxy’s redshift, a measure of its distance.

Because gathering enough light to measure the spectrum of a galaxy in this survey took about two hours, if we had ob- served only one galaxy at a time, a survey of this size would have been impossible. But Shectman designed a multiple fiber-optic system to measure the spectra of 112 galaxies si- multaneously. This system worked as follows: Once we had chosen the prospective galaxies, we drilled holes in a metal plate to be mounted at the focus of the telescope. These holes corresponded to the positions of the galaxies in the sky. Into these holes we plugged fiber-optic cables that carried the light from each galaxy down to a separate channel on the spectro- graph. Even with this parallel processing, it took us 600 hours of observing time over 100 nights to measure all the spectra.

Sounding Out the Universe

L ooking at the maps produced by the survey, the eye is

struck by the sense that the galaxies are not randomly distributed but instead tend to bunch together [see illustra- tion on page 45]. Yet one must be careful of visual impres- sions. Our brains often seek patterns where none exist. In this case, however, statistical techniques bear out the exis- tence of clustering.

The simplest way to measure clustering is to use correlation functions, which represent the number of pairs of objects as a function of their separation. For example, the distribution of deer in a forest is highly clustered on small scales—say, a few

Mapping the Universe42 Scientific American June 1999

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S TO SPEED UP THE SURVEY of more than 26,000 galaxies, Stephen A. Shect- man designed an instrument capable of measuring 112 galaxies simultaneously. In a metal plate (far left), he drilled holes that corresponded to the positions of the galaxies in the sky. Fiber-optic cables (near left) carried the light from each gal- axy down to a separate channel on a spec- trograph at the 2.5-meter du Pont tele- scope at the Carnegie Observatories on Cerro Las Campanas in Chile.

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tens of yards. In randomly picking out deer in the forest, you would notice that you are much more likely to find another deer a few yards away than a few hundred yards away. The correlation function would show a strong positive signal on the scale of a few tens of yards and a weak or negative signal on the scale of a few hundred yards. It mathematically describes the well-known fact that deer tend to travel in small groups.

A similar analysis can be done on galaxies, and it works well on scales that are much smaller than the size of a survey. But on larger scales it is not very informative. The problem is that the number of galaxies—and therefore the number of galaxy pairs—is set. If there is an excess of pairs at small sep- arations, there must be a deficit of pairs at larger separations, because the total number of pairs is fixed. This zero-sum game contaminates the clustering signal on larger scales.

Fortunately, a complementary technique can reliably mea- sure clustering at large scales: harmonic analysis, also known as power spectrum analysis. Harmonic analysis, as its name suggests, is closely allied to the study of sound. In fact, the mathematical analysis of the distribution of galaxies and of random noise is identical. (The power spectrum is conceptu- ally related to but physically distinct from the kind of spec- trum that astronomers usually study, that of light.)

Many common phenomena, such as the waves on the sur- face of the sea and the air pressure fluctuations in a room, are most naturally described in terms of their power spectra. In fact, the human ear performs a similar analysis on pressure fluctuations—that is, sound. The fluctuations can be thought of as a collection of pure tones, each with a certain strength. The cochleas in our ears decompose the fluctuations into their constituent tones (or frequencies). The signal sent to the brain describes the strength (or amplitude) of each tone.

The power spectrum is a measure of the strength of the pressure fluctuations as a function of frequency. It is what the graphic equalizer of a stereo displays. Large musical instru-

ments, such as a bass or a tuba, put out a large fraction of their power at long wavelengths, which correspond to low frequencies. The sound of breaking glass consists primarily of high frequencies.

Random noise is special because it can be completely de- scribed in terms of its power spectrum [see Mathematical Games, by Martin Gardner; Scientific American, April 1978]. Consider two people who go to visit the same water- fall several minutes apart. Each records several minutes of sound. Although their recordings will not be the same—the sound made by the waterfall is always changing—both will record the characteristic sound of the waterfall. If the ob- servers take their recordings and perform a harmonic analy- sis, they will each find the same power spectrum. The statisti- cal properties of their two recordings are identical.

The Color of Sound

N oise with a flat power spectrum, corresponding to equal power at all frequencies, is called white noise. The term

comes from an analogy with color. Each color has a different frequency; if you add all the colors together equally, you get white. In terms of sound, white noise is the static between ra- dio stations. Its sound is perfectly random; at each instant the sound is unrelated to, or uncorrelated with, the sound that came before. Another special power spectrum is that of pink noise, in which each octave delivers the same power [see il- lustration below]. A waterfall produces pink noise.

Harmonic analysis can reconcile the cosmological principle with the clustering of matter. If the universe is homogeneous and isotropic, observers sitting on planets in separate galaxies should measure the same properties for the universe on its largest scales. Of course, they will see different galaxy distri- butions, just as any two slices in the Las Campanas survey are different. But given enough surveys, or a survey of sufficient size, the two observers should measure the same statistical fluc- tuations. These fluctuations, like those of the sound of a water- fall, can be described in terms of the power spectrum.

As the universe expands and evolves, various physical pro- cesses modify the power spectrum of its large-scale structure. Cosmologists generally believe that quantum-mechanical fluc- tuations imparted the initial power spectrum shortly after the start of the big bang. In the late 1960s English physicist Ed- ward R. Harrison and Russian physicist Yakov B. Zel’dovich derived a shape for this primordial power spectrum—namely, a power law with the functional form of frequency to the neg- ative third power, a pink-noise spectrum in three dimensions.

Harrison and Zel’dovich both reasoned that most natural forces, including gravity, have no intrinsic length scale; they are power laws. Therefore, the initial power spectrum should be some form of power law in frequency, so it does not single out any particular length scale. They also grasped the role of the horizon size in the evolution of the universe. The horizon size is simply the distance a beam of light could have traveled in the universe since the big bang up to any particular mo- ment. Because the influence of gravity also travels at the speed of light, two points in the universe can interact gravita- tionally only if they are separated by a distance less than or equal to the horizon size. As the universe ages, the horizon size grows. Therefore, the horizon size defines a natural length scale over which gravity can operate.

What Harrison and Zel’dovich realized was that if the ini- tial power-law spectrum was not precisely frequency to the

Mapping the Universe Scientific American June 1999 43

WHITE AND PINK NOISE surround us. White noise, the grating sound of static on a badly tuned radio or television, is completely random. The sound fluctuates from instant to instant without any pattern (top). Pink noise, the sound of a waterfall or waves crash- ing on the beach, is fractal (bottom). This distinction is reflected in the power spectra (graphs at right): white noise has equal power at all frequencies, but pink noise has more power in the bass than in the treble, in inverse proportion to the frequency.

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negative third power, then one of two things would occur. If the power law were steeper—say, frequency to the negative fourth power—then fluctuations on very small scales would have been greater. In calculating the density fluctuations in the early history of the universe, when the horizon size was small, they found that many regions would have contained such a high density of matter that they would have quickly collapsed, filling the cosmos with black holes. Fortunately, this did not happen. Our very existence rules out such a pow- er spectrum. On the other hand, if the power law were shal- lower, then at later times the density on large scales would fluctuate hugely. No such fluctuations exist.

Although this argument is quite persuasive to cosmolo- gists, it does not explain how such a spectrum would have arisen. Cosmological inflation provides an explanation, which was an early success for the theory, as well as being one of its few testable consequences [see “The Inflationary Universe,” by Alan H. Guth and Paul J. Steinhardt; Scien- tific American, May 1984].

A Great Number of Great Walls

T he power spectrum of the universe today is very different from the primordial Harrison-Zel’dovich spectrum.

Gravity has amplified the initial fluctuations and led to the growth of such structures as clusters of galaxies. At earlier times, the growth of fluctuations on specific scales was en- hanced or retarded depending on whether the universe was dominated by matter or by radiation and whether elemen- tary particles were light and fast-moving or heavy and slow- moving. One of the great challenges for modern cosmology is to determine how the initial power spectrum evolved into the spectrum observed today. Only in the past several years have observations, such as those of galaxy distribution and of the cosmic microwave background radiation, acquired enough data to put theories to the test.

So-called cold dark matter models are now the most popu- lar explanations for the growth of structure. Their premise is that most of the mass in the universe resides in some unseen (hence, “dark”), relatively massive type of particle. It is “cold” because, being heavy, it travels slowly. The particle, which would interact with ordinary matter only through the force of gravity, could also account for the missing mass in galaxies and galaxy clusters [see “Dark Matter in the Uni- verse,” by Lawrence M. Krauss; Scientific American, De- cember 1986].

One of the surprising results from our survey is its devia- tion from the cold dark matter model on scales of around 600 million light-years. At smaller scales the predictions of the model match our findings, but something strange singles out the large scales [see illustration at right]. Previous surveys had suggested such a discrepancy, and one of the principal re- sults of Las Campanas has been to substantiate it. From the strength of the deviation and the size of the survey, we calcu- lated the probability of seeing such a deviation purely by chance as one in several thousand.

What is very interesting about this deviation is that it can be traced back to the huge structures seen in the galaxy dis- tribution [see illustration on opposite page]. These structures are defined by the sharp boundaries, filaments and voids in the galaxy maps. The largest are almost three billion light- years across, several times the size of the Great Wall. The as- sociation of these walls and voids with the deviation in the

power spectrum is a crucial finding of the Las Campanas sur- vey. It means that on this scale, the galaxy distribution can- not be fully characterized using the mathematics of random noise. Some other physical process must have acted to im- print this characteristic scale on the density fluctuations.

In fact, this inconsistency is what allows these walls and voids to properly be called structures. With a pure-noise pro- cess, walls and voids would occasionally appear by chance. But they would be much rarer, in keeping with the statistics of noise. They would be statistical fluctuations or chance su- perpositions, rather than true structures.

What could be responsible for the mammoth walls and voids? Gravity might be a good explanation except that it causes smaller-scale fluctuations to collapse more quickly, simply because it takes less time for gravity to pull matter to- gether on small scales. If gravity were the culprit, galaxy clus- tering should have begun on small scales and then worked its way up to large scales. For the past two decades, such a bot- tom-up scenario, known as hierarchical clustering, has been the paradigm for explaining structure on scales smaller than about 150 million light-years. Yet the deviations in our sur- vey begin to appear at much larger scales. Hierarchical clus- tering may still apply on the small scales, but it cannot ex- plain the walls and voids on the larger scales.

The New Music of the Spheres

S everal hypotheses have emerged, although none can yet be reconciled with all the data. The first is a hot dark mat-

ter scenario wherein the universe is dominated by light, fast- moving particles such as neutrinos. The result would be a top-down progression in structure formation starting on large scales. Unfortunately, this theory has the side effect of washing out structure on small scales, so it fails to account for the small-scale galaxy clustering.

A second hypothesis posits that the universe is less dense than cosmologists suppose. Most of this decrease in density comes at the expense of exotic dark matter. Ordinary particles such as protons and electrons thus have a proportionately greater influence. They would have constituted a viscous fluid in the

Mapping the Universe44 Scientific American June 1999

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POWER SPECTRUM of the cosmos, as measured by the Las Campanas survey (blue line), generally follows the prediction of the cold dark matter model (pink). But the power increases dra- matically on scales of 600 million to 900 million light-years. This discrepancy means that the universe is much clumpier on those scales than current theories can explain.

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early universe. Before the universe was cool enough for the pro- tons and electrons to combine and form atoms, sound waves reverberated through this fluid. When the protons and electrons recombined, the acoustic waves gave a boost to the gravitation- al collapse on certain scales. Intriguingly, an underdense uni- verse would also resolve other cosmological conundrums [see “Inflation in a Low-Density Universe,” by Martin A. Bucher and David N. Spergel; Scientific American, January].

A third hypothesis points out that 600 million light-years is roughly the horizon distance at the time when the average density of matter in the universe overtook that of radiation. Such a profound change would presumably have affected the power spectrum somehow. Whatever the final explanation, it may be that astronomers are detecting the largest unique length scale associated with any physical process in nature.

Even a survey the size of Las Campanas contains only about 50 independent measurements of the power spectrum at these large scales. Larger surveys are needed, and several are now either in the development stages or under way. An Anglo-Australian consortium called the 2DF Survey is map- ping more than a quarter-million galaxies. Soon the Ameri- can-Japanese Sloan Digital Sky Survey will begin to measure the distances to almost one million galaxies over half of the sky, sampling a volume 20 times greater than that of the Las Campanas survey.

These studies are not the first use of harmonic analysis in the history of astronomy. It was originally Pythagoras in the sixth century B.C. who applied musical analysis to the motion of the sun, moon, stars and planets. He believed that the ce- lestial bodies were holes in a set of crystal spheres through which shone the celestial light. The motions of these spheres, he reasoned, must produce sounds. Their distances and their speeds must be in the same ratios as musical harmonies. This was the first “music of the spheres.”

In the 17th century Johannes Kepler, before formulating his famous laws of celestial motion, believed that the orbits of the planets could be described in terms of heavenly spheres inscribed between the five perfect Pythagorean solids. He rea- soned that the harmonious ratios of music might be derived from these solids, and thus he argued for a fundamental rela- tion between the orbits of the planets and these harmonies. This was the second music of the spheres.

Today our notion of harmonic analysis is quite different. It is based on analyzing the harmonic components of random distributions, and the sound is more like the gush of a water- fall than that of divine instruments. Although this modern endeavor may seem neither as pleasing nor as spiritual as those of the past, the concept of an isotropic universe wed- ded with an understanding of random fields now allows us once again to hear the music of the spheres.

Mapping the Universe Scientific American June 1999 45

TWO SLICES of the universe (right), observed during the Las Campanas survey, graphically reveal the clumpiness of the uni- verse on large scales. The dots, which represent the several thou- sand galaxies each slice contains, are not uniformly spread out; they bunch into walls (dotted lines in inset), which are separat- ed by approximately 600 million light-years.

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The Author

STEPHEN D. LANDY first be- came interested in cosmology when he was lost in the woods one night and had nothing to do but stare up at the stars. After receiving his Ph.D. in physics from Johns Hop- kins University in 1994, he did postdoctoral research work at the Carnegie Observatories in Pasade- na, Calif., and at the University of California, Berkeley. Currently he is a visiting scientist at the College of William and Mary.

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