Chapter 9

Measuring the Cosmic Web—the Sloan Great Wall

After our original papers on the topology of large-scale structure came out, we were anxious to apply the method to larger data sets. In the 1986–87 academic year, I took a sabbatical at the University of Virginia and worked with Trinh Thuan, John Miller, Stephen Schneider, David Weinberg, Charles Gammie, Kevin Polk, Michael Vogeley, Scott Jefferey, Suketu Bhavsar, Adrian Melott, Riccardo Giovanelli, Martha Haynes, Brent Tully, and Andrew Hamilton to analyze a large number of observational data sets. Surprisingly, I had formed a group of 15 people! This is as close to “big science” as I ever got! I am a theorist and usually work alone or with one or two colleagues, but this study analyzing many observational data sets required bringing together a lot of talented people. This is usually how it works: someone has an idea, and people come together to work on it. As science has become more complex, science collaborations have become larger. The WMAP satellite team that measured the cosmic microwave background grew to 21 members. The Sloan Digital Sky Survey, which I also work on (and will describe shortly), involves about 180 people—but I did not form that group. The Planck Satellite Collaboration reported new measurements of the cosmic microwave background in 2013 with a paper having 277 authors. (Of course, the really BIG science is over in physics, where the ATLAS Collaboration looking for the Higgs boson had a paper with an author list beginning Aad, Abbott, Abdallah, Abdel, … , and 3,062 more coauthors!) Today, the challenge for young astronomers is to figure out how to fit into the ever-larger collaborations. How does one get to lead a project? Should one participate in an already-large collaboration and work to advance to a position of leadership, or should one strike out on one’s own and try to have ideas that will draw others in? In a highly competitive environment, it is always helpful to have an army at your back.

In this case, I was able to bring together a remarkable group of people to study topology. Trinh Thuan, from the University of Virginia, was my old friend from graduate school days at Princeton. At Virginia, Thuan and I studied of the distribution of dwarf and low-surface-brightness galaxies. These galaxies were too faint to have their redshifts measured by Geller and Huchra, but their positions in the sky were already listed in other catalogs. With Stephen Schneider, Thuan and I measured the redshifts of these galaxies using a radio telescope by observing the 21-centimeter wavelength line of atomic hydrogen. We discovered that these dwarf and low-surface-brightness galaxies fell on exactly the same structures that de Lapparent, Geller, and Huchra had found. They did not fill in the empty voids.

As for the rest of the topology group, Weinberg, Melott, and Hamilton were already on board. Michael Vogeley was originally an undergraduate at Princeton and is now a professor at Drexel; he and I have continued to work together for many years on topology. Charles Gammie and I worked on a sample of Abell galaxy clusters. Giovanelli and Haynes brought with them their sample of more than 4,000 galaxy redshifts. Tully would bring his catalog of nearby galaxies. He was already a master of cosmic cartography. With Richard Fisher he produced a wonderful atlas of nearby galaxies—it had the flavor of an old-time atlas, with page after page of charts showing their positions. Recently, he has collaborated on a 3D computer movie bringing this atlas into the twenty-first century, as well as mapping the Laniakea Supercluster.

One of the best things about having a collaboration of large but still manageable size is that the collaboration meetings are both fun and personal. We organized a meeting at Melott’s home base, the University of Kansas, in April 1988. As I arrived in the hotel for the meeting, I saw all the happy faces of my friends. I was genuinely touched. Here was something we all were glad to get the chance to work on. I brought with me a bunch of red-blue 3D glasses with white cardboard frames, like those in Figure 6.14. I had red-blue slides of some of our spongelike simulations to show. Afterward, we signed each other’s 3D glasses to take home as souvenirs. At the meeting I shared news I had heard about plans to build a 3.5-meter telescope on Kitt Peak outside Tucson, Arizona, for use as a survey instrument to take the redshifts of 100,000 galaxies. This survey, if completed, would be invaluable to our topology work. The number of topological features we could measure was directly proportional to the number of galaxies in the survey. We were used to seeing surveys containing a few thousand galaxies, so this would be a giant increase. Allotting telescope time always involves competition, but an additional tension exists between devoting a large telescope to individual observers who would apply for time for their own projects and devoting the telescope to a systematic survey that, when finished, would be useful to everyone. Geller and Huchra had shown the benefit of a large survey for understanding the universe. I hoped our meeting would provide some support for the large redshift-survey idea, which would benefit many other projects as well as our own.

Then Richard Kron from the University of Chicago got up to say that he had been thinking about building a special dedicated telescope to do a survey that would measure a million galaxy redshifts. A million! We were amazed and very excited. This would be a dream survey for our topology research. We gave this our hearty endorsement. Ultimately, the people at Kitt Peak never built the survey instrument, but Richard Kron took his idea for a survey telescope to Jim Gunn at Princeton. Gunn decided to expand the idea. The telescope would be both a camera and a redshift-measuring machine. It would produce a digital sky map using a massive CCD digital camera; then, after selecting target galaxies from the sky map, it would use fiber optic cables plugged into the focal plane of the telescope to take hundreds of galaxy spectra at a time. Gunn, a master telescope and camera designer (having been a principal designer of the Wide Field and Planetary camera for the Hubble Space Telescope), devised the whole system—to be placed on a 2.4-meter-diameter telescope at Apache Point, New Mexico. This would become the Sloan Digital Sky Survey, a joint project of the University of Chicago, the Fermi National Accelerator Laboratory, the Institute for Advanced Study, the Japan Participation Group, the Johns Hopkins University, Princeton University, the U.S. Naval Observatory, and the University of Washington. Financial support was provided by the Alfred P. Sloan Foundation, the (U.S.) National Science Foundation, the Japan Ministry of Education, and the participating institutions. It has been amazingly successful.

Our topology group analyzed all the available samples and presented our results in an omnibus paper in 1989. We found that when we smoothed the data and produced density contours, the median density contour always had a spongelike topology. As an example, the Giovanelli and Haynes sample is shown in Figure 9.1.

Figure 9.1. Spongelike topology in the Giovanelli and Haynes sample. The 50%-high-density regions appear at left, the 50%-low-density regions at right. Add the two regions together and you have the whole observational sample. The high- and low-density regions are spongelike and interlocking, with donut holes characteristic of a spongelike topology in agreement with Gaussian random-phase initial conditions. Earth is situated at the back corner of the white square (under each region). The Perseus-Pisces supercluster is contained within the linear structure at the bottom right of the 50%-high-density region. The curved outer edge of the observational sample is at a distance of 574 million light-years from Earth. The data have been smoothed with a smoothing length of 41 million light-years. (Credit: J. Richard Gott et al. Astrophysical Journal, 340: 625, 1989)

This sample of 491 galaxies extends to a distance of 574 million light-years. We applied a smoothing length of 41 million light-years; that is, we blurred each of the galaxies over a scale of 41 million light-years to create a smooth, undulating density field that captures the clustering pattern. We then constructed density contour surfaces. We show here the 50% (median) density contour surface that divides the survey region into a high-density half and a low-density half by volume. On the left we 50% high 50% low show the high-density half. Earth is in the back, at the back corner of the bottom square, behind the survey region. A big high-density filament passes though the survey region. This is the elongated Perseus-Pisces Supercluster. The low-density 50% is shown on the right. If you were to push the two regions together, they would add up to give the entire survey. You can see the curved spherical outer edge of the survey at a distance of 574 million light-years from Earth. The topology is clearly spongelike. The high- and low-density regions are interlocking, with donut holes apparent in both the high- and low-density regions. The genus curve for the Giovanelli and Haynes sample has the expected “W” shape as a function of density, agreeing with the theoretical Gaussian random-phase curve, within the errors.

Overall, we analyzed 12 different data sets of various sizes at various smoothing lengths. We could compare these genus curves with standard biased cold dark matter (CDM) simulations and with simulations in which galaxies were laid down on bubble walls (a Swiss cheese topology). The simulated bubbles had an average diameter of 156 million light-years, typical of the void sizes seen in the Geller and Huchra slice. We could then ask for the odds that the observational genus curves had been drawn at random from the CDM simulations as opposed to the bubble simulations. We found a probability of 98.8% that the observations resembled the CDM simulations as opposed to the bubble simulations. This was an impressive victory for the CDM model and for the spongelike topology expected from inflation.

The IRAS Sample

In 1992, an independent group, headed by Ben Moore from the University of Durham, analyzed the topology of large-scale structure using a sample of galaxies detected in the infrared using the Infrared Astronomical Satellite (IRAS). Other members of the group were Carlos Frenk, David Weinberg, Will Saunders, Andy Lawrence, Richard Ellis, Nick Kaiser, George Efstathiou, and Michael Rowan-Robertson. It was quite a distinguished group, full of leaders in the field. Observing in the infrared penetrates through the dust in our Milky Way, allowing astronomers to survey the entire sky without having to avoid the galactic plane, as one must when observing galaxies in the visible spectrum. Figure 9.2 shows the IRAS sample with the high-density 50% at the top and the low-density 50% at the bottom. The high-density regions form one connected piece, as do the low-density regions. It’s a spongelike topology.

Figure 9.2. The topology of the Moore and colleagues’ IRAS sample is shown: high-density 50% (top) and low-density 50% (bottom). Add the top and bottom halves to get the entire spherical sample centered on Earth with a radius of 487 million light-years. The smoothing length is 52 million light-years. The galactic plane of the Milky Way is horizontal. The upper hemisphere is the North Galactic Hemisphere, and the bottom hemisphere is the South Galactic Hemisphere. (Credit: Ben Moore et al., Monthly Notices of the Royal Astronomical Society, 256: 477, 1992)

If one plots the high-density 10%, the contour breaks up into individual clusters, as expected, as seen in Figure 9.3. This survey went out to a smaller distance.

Figure 9.3. The topology of the high-density 10% of the IRAS sample shows isolated clusters and superclusters as expected for Gaussian random-phase initial conditions. The big clump at the top includes the Coma Cluster and the densest part of the Great Wall of Geller and Huchra. The Perseus-Pisces supercluster, which formed the main part of the high-density region in Figure 9.1, appears here as well but at a smaller scale and from a different angle. (Credit: Ben Moore et al., Monthly Notices of the Royal Astronomical Society, 256: 477, 1992)

Similar plots of low-density regions showed famous voids previously charted by Brent Tully. Given the symmetric, W-shaped, Gaussian random-phase genus curves they were seeing, the IRAS group could rule out a bubble topology having approximately 486-million-light-yeardiameter cells with a probability of 99.9999%. From the number of structures being found as a function of the smoothing length, they could estimate the slope of the power spectrum, which implied more power at large scales than would occur with a random (Poisson) sprinkling of points in the initial conditions. This was the same result Ed Turner and I had obtained by analyzing the frequency distribution of galaxy clusters of different sizes. All this was quite encouraging. It is always important to have independent groups verify your findings. This IRAS sample extended far enough to include some of the Great Wall region, and we were pleased that it showed the spongelike topology we expected from our theory. Another study of the topology of a sample of IRAS galaxies by Canavezes and colleagues in 1998 also found spongelike structure, lending further support to the random-phase nature of the initial conditions.

Vogeley and the Topology of the Great Wall Region

Meanwhile, by 1993 Geller and Huchra at Harvard had completed their 3D volume sample. They allowed us to cooperate with them on its topological analysis. Michael Vogeley, my former Princeton undergraduate student, had by this time moved on to Harvard as a graduate student and was leading the study, with participation by Changbom Park, Geller, Huchra, and me. Figure 9.4 shows the high-density 50% of the survey using a small smoothing length (on the left) and a larger smoothing length (on the right).

The orientation of this figure is the same as in the previous two figures. The plane of the Milky Way galaxy is horizontal. The North Galactic Hemisphere is at the top, and the South Galactic Hemisphere is at the bottom. The expanded CfA survey, shown on the left, included a really thick fan-shaped region in the north, and another substantial cone-shaped region in the south. Earth is at the center of the figure. The bar at the bottom has a length of 243 million light-years. The outer radius of the survey from Earth is 608 million light-years. The smoothing length (in the left-hand picture) is 28 million light-years. The Great Wall snakes from left to right across the upper fan-shaped survey region, with a length of 758 million light-years. The high-density 50% region is in one connected piece and has a spongelike topology. The voids on the near and far sides of the Great Wall are connected by low-density passages. You can swim from the void on the near side to the void on the far side through low-density regions by simply going around the Great Wall. It is a filament. To the right we show the same 50% high-density regions but with a smoothing length of 56 million light-years. This gives a low-resolution look at the same survey. It is smoother and, therefore, shows less detail. The Great Wall clearly appears as a thick filament. A donut hole in the high-density region can be seen above it. The higher resolution picture at the left reveals a finer, more intricate web of minor filaments that the low-resolution picture leaves out, but in both pictures the high- and low-density regions are interlocking and spongelike. A close-up (upside down) high-resolution picture of the Southern extension of the survey is shown in Color Plate 6.

Figure 9.4. The complete 3D Center for Astrophysics (CfA) survey sample’s 50%-highdensity regions are shown at two smoothing lengths: 28 million light-years (left) and 56 million light-years (right). The Great Wall extends across the upper fan-shaped survey region, with a length of 758 million light-years. The 50%-high-density region is in one connected piece with a spongelike topology. The Great Wall is a filament. (Credit: Michael S. Vogeley, Changbom Park, et al. Astrophysical Journal, 420: 525, 1994)

In this color picture of the Southern CfA Survey, we see the 50% highdensity region at the top, where Michael Vogeley has placed a (simulated) red-light source in the middle of the large void in the middle of the survey. You can see the red light shining out into other void regions through tunnels between the voids. At the bottom you can see the 50% low-density regions. If added to the high-density regions, they would produce the entire survey region. The large void in the center can now be seen as a solid blob with extensions (low-density tunnels) connecting it to other void regions. This is again a spongelike topology: the high- and low-density regions are multiply connected and interlocking.

This CfA survey marked an acid test of the spongelike topology, because initially, after the first 2D slice of the region was shown, it looked to Geller and Huchra like a froth of bubbles with a Swiss cheese topology. It appeared that the voids might be surrounded by dense walls on all sides, creating isolated chambers or cells. But when the full 3D structure could be quantitatively measured, it showed a spongelike topology. Voids were connected to other voids by low-density tunnels, and great clusters were connected to each other by dense filaments of galaxies. This was the interlocking spongelike configuration expected from cold dark matter and inflation, a geometry that could be formed from random quantum fluctuations in the early universe. The Great Wall was simply a big filament connecting clusters, part of the overall spongelike structure we now call the cosmic web.

Once a filament formed, gravity would draw it together, making it even narrower. This is a nonlinear effect. Just as a cluster collapses due to gravity, a filament will collapse in the directions perpendicular to its length, with material crashing together to form a very narrow filament. As Zeldovich had imagined, the waves in the original universe would break, like waves in the ocean, and form caustics as the fluctuations became nonlinear fractional density enhancements greater than one. A structure like the Great Wall would form in this way. As the universe expanded, the cosmic web itself would stretch, and the filaments connecting clusters would become longer and narrower as gravity squeezed them and the expansion lengthened them.

Origin of the Name Cosmic Web

Where did the name cosmic web come from? The first paper to use it in either its title or abstract was the 1995 arXiv preprint posted online by Richard Bond, Lev Kofman, and Dmitry Pogosyan. The title of their paper was “How Filaments Are Woven into the Cosmic Web” (1995). Its abstract stated the following:

Observations indicate galaxies are distributed in a filament-dominated weblike structure. Numerical experiments at high and low redshift of viable structure formation theories also show filament-dominance. We present a simple quantitative explanation of why this is so, showing that the final-state web is actually present in embryonic form in the overdensity pattern of the initial fluctuations, with nonlinear dynamics just sharpening the image.

This agrees, of course, with what we had been saying all along, that the sponge was present in the initial conditions and is the same sponge we see today—just enhanced in contrast by gravity. Bond and his colleagues started off their paper with a picture of a computer simulation (showing the present epoch) from Anatoly Klypin using the cold dark matter model. It looked decidedly filamentary (see Figure 9.5).

Figure 9.5. This computer simulation (created by Anatoly Klypin) was featured in a paper by Bond and colleagues (1995), which coined the term cosmic web. This simulation shows the spongelike topology that results from inflationary initial conditions, with narrow filaments connecting clusters in a cosmic web. Voids are connected by tunnels. (Credit: Courtesy of Anatoly Klypin, as appearing in J. R. Bond, L. Kofman, and D. Pogosyan, arXiv:astro-ph/9512141v1, 1995)

Bond and his colleagues were interested in asking why the filaments were so dominant. They analyzed the initial conditions in the computer simulations, looking for patterns in velocity flows. A filament in the initial conditions would produce, via gravitational attraction, peculiar velocity flows drawing particles inward in two dimensions: radially inward toward the linear filament. Imagine the filament as a vertical rod: it would draw particles in toward itself in two horizontal directions by gravitational attraction—like moths being attracted toward a long fluorescent tube. An initial pancake, on the other hand, would produce peculiar velocity flows that were directed inward in one dimension—perpendicular to the pancake. If you imagine a horizontal pancake, it will produce infall velocities just along the single vertical dimension as particles fall toward the pancake from above and below it. The authors found a predominance of initial flows in the computer simulation in two dimensions, as would occur for filaments in the initial conditions. That indicated a predominance of filament-shaped density fluctuations in the initial conditions, as opposed to pancakes; as the universe evolved, nonlinear gravitational effects would simply have made the filaments thinner. Their pictures showed that in the final conditions, the clusters were connected by thin filaments of galaxies. These were, of course, computer simulations based on Gaussian random-phase initial conditions that were meant to explain the structure already seen in the observations by our group and others.

Where did the word web come from? Bond and colleagues started their 1995 paper by showing a computer simulation by Klypin using cold dark matter. In the original 1983 computer-simulation paper. in which Klypin and Shandarin had written about the Zeldovich honey-comb model, they had used the word web. Here is their sentence (which I have quoted before): “The regions of high density seem to form a single three-dimensional web structure.” They then noted, “However it is not clear from our simulation whether honeycomb structure arises or not.” With hindsight it is clear that the initial conditions they were using were Gaussian random phase, so the topology in the initial conditions had to be spongelike. They had initial conditions in which fluctuations on small scales were damped out. Melott, Dickinson, and I had also examined such models in our initial topology paper (see Figure 6.7), along with CDM simulations, and found that they were all spongelike in the initial conditions and that the initial sponges were replicated almost exactly, in enhanced contrast, in the final conditions. Klypin and Shandarin’s computer simulations did not form a honeycomb, as they and Zeldovich would have hoped, but instead formed a sponge.

The term cosmic web captures both the topology of the large-scale structure and the thinness of the filaments, reminiscent of a spider’s web. That name has stuck. The Bond and colleagues’ arXiv paper would eventually be published in 1996 in Nature, with the slightly revised title “How Filaments of Galaxies Are Woven into the Cosmic Web.”

The Sloan Great Wall

If we could see a giant filament in the cosmic web as close to us as the Great Wall, then if we looked deeper in the universe, we might find others. Indeed, our topology group did a computer simulation at the turn of the millennium to show what structures might be found in Jim Gunn’s upcoming Sloan Digital Sky Survey. Wes Colley led the project, with Andreas Berlind joining Changbom Park, David Weinberg, and me. We had 54 million CDM particles in a cubic volume 2.9 billion light-years on a side to simulate the million galaxies that might be included in the Sloan Digital Sky Survey 3D map. (This was one of the first simulations that also included dark energy—a uniform component of the universe discovered in 1997, which we will discuss in Chapter 11. All subsequent simulations include dark energy.) Our simulation produced a spongelike topology, whose median density contour was, of course, spongelike. Nonlinear gravitational effects produced slightly more isolated clusters in the 7% high-density sample than isolated voids in the 7% low-density sample in the final conditions. In other words, the 7% low-density volume is divided into fewer and bigger voids, whereas the 7% high-density volume is divided up into smaller, more numerous clusters. Gravity causes clusters to contract, making them smaller, and being smaller, it takes more of them to make up 7% of the volume. By contrast, voids expand, becoming bigger, so fewer of them are needed to make up the low 7% of the volume. As the fluctuations became of order 1 or more—that is, the density in the highest density regions became denser than 1 + 1, or 2, times the average density in the universe—the fluctuations begin to grow at a faster than linear rate compared to the expansion of the universe. This is called nonlinear evolution. It is what Jim Gunn and I were investigating when we followed the collapse of the Coma cluster. This kind of evolution has to be followed on a computer.

The result that clusters should slightly outnumber voids due to nonlinear effects was discovered in 1994 by Takahiko Matsubara, at the University of Tokyo, who solved the equations for mildly nonlinear gravitational evolution and applied them to topology. The genus curve retained its familiar W shape but was slightly distorted. Isolated clusters slightly outnumbered isolated voids. (This effect can be seen in the final and biased conditions in the computer simulations shown in Figure 6.10, top graph.) The central peak in the genus was also shifted slightly to the left—what we called a meatball shift—because of the prominence of big, high-density features like the Great Wall. Such effects could be accentuated by biased galaxy formation—the fact that galaxies are more likely to form in high-density regions. We had noted such effects already in our omnibus observational paper of 1989; the Sloan Digital Sky Survey would offer a chance to see them in greater detail.

Our computer simulation even found what we called a “great wall complex” extending for a distance of 1.9 billion light-years across the survey. Thus, we predicted that the Sloan Digital Sky Survey would find great walls significantly larger than the Great Wall of Geller and Huchra. This prediction would be vindicated in spades.

In 2003, when the first Sloan data finally came in, Mario Jurić and I set ourselves the task of mapping its structure in a visually compelling way. The first data release was complete for an equatorial slice 4° thick extending in two giant fans out from Earth’s equator. One fan included the Northern Galactic region and the other, the South. The survey avoided the two regions where the Milky Way galactic plane crossed Earth’s equatorial plane. Figure 9.6 shows two fans extending from Earth at the center. Each point represents a galaxy. Earth is at the center. We are looking straight down on the two slices from a viewpoint far above Earth’s North Pole. Distances are plotted as comoving distances, showing the distances the galaxies will have at the present epoch (as defined in note 1 for Chapter 3).

Mario and I saw immediately that the Northern slice had an enormous wall. It had shown up earlier as one connected high-density region in a topology study of a volume-limited sample of this slice (including only intrinsically bright galaxies), which I had done with Fiona Hoyle, Michael Vogeley, and other colleagues in 2002. I thought to name it the Sloan Great Wall, which would honor everyone in the survey. The Great Wall of Geller and Huchra had by now become known as the CfA2 Wall, named after the Center for Astrophysics Survey 2 in which it was discovered. In Figure 9.6 you can also see many small voids, just like the ones found by Geller and Huchra. A particularly nice void is located near us in the southern fan (at bottom); it is punctuated by a couple of rich clusters, which appear as tiny daggers pointing at Earth due to their large internal velocities. The lacework of the cosmic web is apparent. The texture of this picture strongly resembles the texture of our large, rod-shaped, computer simulation using cold dark matter shown in Figure 8.2. In our paper we included a side-by-side comparison of the Sloan Great Wall and the Great Wall of Geller and Huchra (see Figure 9.7).

Figure 9.6. This equatorial slice of the Sloan Digital Sky Survey (SDSS) from Gott, Jurić, and colleagues, shows a 360° panorama looking out from Earth’s equator. Earth is at the center. The points represent galaxies within 2° of the celestial equator (which passes overhead of Earth’s equator). The two fans show the region covered by the SDSS; the two blank regions are close to the Milky Way’s galactic plane and are, therefore, not surveyed. The radius of this picture is 2.80 billion light-years. Many voids and filaments are visible, the most prominent filament being the Sloan Great Wall in the top fan. (Credit: J. Richard Gott, Mario Jurić, et al., Astrophysical Journal, 624: 463, 2005)

Mario and I measured the length of the Sloan Great Wall—it was 1.37 billion light-years long, 1.8 times as long as the Great Wall of Geller and Huchra. It was quite like the original Great Wall, only bigger! Like the Great Wall, the Sloan Great Wall is not gravitationally bound but is a coherent structure that will retain its identity as the universe expands. In the future, it will continue to stretch in length as the universe (and, therefore, the cosmic web) expands, while gravity will keep it as narrow as it is now or make it even narrower, as time goes on. The left hand (Eastern) end of the Sloan Great Wall is particularly spectacular, containing a number of rich clusters. Then it splits into two strands, like a multilane highway becoming a divided highway for a while, before rejoining to make one strand again at the western end. Lorne Hofstetter and I would make a spectacular portrait of the Sloan Great Wall, 60 inches wide, which included tiny pictures of each galaxy from the Sloan data. A small part of this grand view, a close-up of the Eastern end of the Sloan Great Wall, appears in Color Plate 7. To make this picture, we had to enlarge each galaxy by a factor of 50 relative to its true size in order to make each galaxy visible. Put another way, if the distances between the galaxies shown on in the picture were depicted properly, the picture would have to be 50 times larger.

The Sloan Great Wall was reported in Science, the New York Times, New Scientist, and Scientific American, among others. The Sloan Great Wall would eventually end up in the Guinness Book of Records 2006, as the “largest structure in the universe.” This was a record the Great Wall of Geller and Huchra had held previously. There are many “largest” things in the Guinness book, but this is the largest of the largest. Mario and I were both mentioned in the entry. (It held the Guinness record till 2015, when surpassed by a wall from a deeper survey.)

Figure 9.7. The Sloan Great Wall (1.37 billion light-years long) shown to scale with the CfA2 Great Wall of Geller and Huchra (758 million light-years long). Earth is at the bottom point of the fans. (Credit: J. Richard Gott, Mario Jurić, et al., Astrophysical Journal, 624: 463, 2005)

The length of the Sloan Great Wall is ¹⁄₁₀ the radius of the entire visible universe (everything we can see with our telescopes) out to the cosmic microwave background. To put this into perspective, if you made a scale model of the entire visible universe that was as big as Earth, the Sloan Great Wall would be 400 miles long. On this scale, our Milky Way would be about 150 feet across, and the Andromeda Galaxy would be of similar size, about ⁷/₁₀ mile away. The distance between the Sun and Proxima Centauri, the nearest star, would be only ¹⁄₁₃ inch. The solar system would be microscopic on this scale.

To capture the entire universe, including all these scales, on one map, Mario and I presented a logarithmic map in our paper. From left to right, it represented a 360° panorama looking out from Earth’s equator. The vertical coordinate measured distance from the center of Earth, with equally spaced tick marks vertically marking increases by factors of 10 away from Earth: 1 Earth radius, 10 Earth radii, 100 Earth radii, and so forth. The map was conformal, preserving shapes locally, so features like the Sloan Great Wall were neither squashed nor stretched vertically. As one moved up the map, from Earth’s surface (a horizontal line at the bottom of the map), one first encountered artificial satellites orbiting Earth; then the Moon, Sun, and planets; then stars, galaxies, and quasars; and finally, the cosmic microwave background, the most distant thing we can see, at the top (see Color Plate 8, a color version of the top one-sixth of the map).

The Los Angeles Times called it “arguably the most mind-bending map to date.” New Scientist, Astronomy, and the New York Times have reprinted copies of it. The most prominent features in the top section of the map shown in Color Plate 8 are the Whirlpool and Sombrero Galaxies, the Coma Cluster of Galaxies, the CfA Great Wall of Geller and Huchra and the Sloan Great Wall. Objects further up the map, further away from Earth, are shown at smaller scale. The Sloan Great Wall is 3 times further away than the CfA Great Wall and is, therefore, shown at ⅓ the scale; because of this scaling factor, although it is actually about twice as long, the Sloan Great Wall appears ⅔ the size of the CfA Great Wall on this map. The two vertical reddish bands show the regions covered by the SDSS survey. Each red dot is a galaxy or quasar. The blank bands were not covered by the survey. The Cosmic Microwave Background covers the entire sky, stretching 360° across the entire top of the map.

The Millennium-Run Computer Simulation

Perhaps the most beautiful computer simulation of what the cosmic web looks like was produced in 2005 by Volker Springel and his colleagues, who did what was also the largest N-body computer simulation of the time—the Millennium Run—using 10 billion particles to simulate the mass in a cubic volume that has expanded to a size of 2.43 billion light-years on a side at the present epoch. Color Plate 9 presents a slice through the simulation 73 million light-years thick. It shows beautiful filamentary structures connecting the clusters. Some have likened this picture to one of brain neurons interconnected by synapses. A rich cluster in the center, surrounded by strong filaments, can be seen.

In Color Plate 10, several fans are shown. The observations (shown in blue) are the CfA and Sloan Digital Sky surveys (at the top) and the 2dF survey (Colless et al. 2001), using the Anglo-Australian Telescope’s 2°-wide, multiobject spectrograph (at the left). The 2dF Galaxy Redshift Survey (sometimes called 2dFGRS or 2dGRS) is a particularly interesting thick-slice survey. Studies matching the power spectrum of fluctuations in galaxy counts on different scales in the 2dF to the inflationary model allowed Percival and colleagues (2001) to estimate the quantity Ω_matterh = 0.2, where h = H₀/100 kilometers/second/megaparsec. With the current best value of h = 0.67 from the Planck satellite team and the Sloan Digital Sky Survey, this leads to a value of Ω_matter = 0.3. This estimate is based on the 3D locations of the galaxies in space. Separate studies of the magnitude of velocity flows in the 2dF survey led to a completely independent measurement of Ω_matter = 0.3 (Peacock, Cole et al. 2001). One measurement is based on galaxy positions, the other on galaxy peculiar velocities. Both measurements of Ω_matter agree with each other and with the current estimate of Ω_matter = 0.308 from the Planck Collaboration (2014) using the cosmic microwave background radiation. In red (at the bottom and right) are equivalent fans produced from the Millennium Run simulation, which found one great wall complex that was as long as the Sloan Great Wall but not as spectacular. The Millennium Run simulation used Ω_matter = 0.25 and h = 0.73, close to the best estimates (Ω_matter = 0.308 and h = 0.67) available today. The overall agreement between the Millennium Run simulation and the observations is impressive. We don’t expect it to produce structures that are exactly the same, just ones that are similar in their statistical properties. In this it succeeds splendidly. The overall look of the slices compares well.

Juhan Kim and the Horizon Run Simulations

The Sloan Great Wall is so dramatic that one might wonder if it is consistent with the standard CDM inflationary cosmology. To answer this question, Juhan Kim, in collaboration with Changbom Park and other members of our group, did a series of even larger computer simulations called the Horizon Run simulations. The 2011 Horizon Run 3 used a record-breaking 374 billion particles to simulate a cubic volume 53 billion light-years on a side at the present epoch. It is 45,000 times the volume of Park’s original simulation! The particles in the simulation represent cold dark matter. The dynamics of these particles due to the action of gravity are accurately tracked down to a resolution of 730,000 light-years, less than a third the distance from us to the Andromeda Galaxy. Galaxies are identified with cold dark matter halos that are gravitationally bound and dense enough not to be disrupted by tidal gravitational forces from neighboring halos. These are places where we expect normal atoms to congregate, dissipate energy, and form galaxies. From this large sample volume, we can produce 27 independent mock Sloan Digital Sky Survey catalogues. This simulation was performed on the Korean Supercomputer and is large enough to capture the true largescale structure of the universe and give enough samples to provide good statistics for rare features like the Sloan Great Wall.

We used a standard linking algorithm to identify superclusters. Galaxies are considered “friends” if they are separated by less than a certain linking distance. A supercluster is defined as a set of “friends of friends” of a given galaxy. If the linking distance is too small, all galaxies will be singles and there will be no superclusters. Make the linking distance longer, and superclusters will start to form as galaxies link up. But if the linkage becomes too large, eventually the number of superclusters begins to drop as they link up to form the one spongelike high-density region, which is all in one connected piece. We chose our linkage length so that the maximum number of superclusters would be selected. (This picks more, and smaller, superclusters than might be found if a larger linkage length were used. But it is a well-defined procedure.) This algorithm was then applied in identical fashion to the SDSS observations and the mock SDSS surveys from the simulations. Then the richest supercluster was selected (the one with the most members). In the observations, this coincided with the rich eastern end of the Sloan Great Wall. It could then be compared with the median richest supercluster from the simulation’s mock surveys picked the same way. A similar algorithm was used to find the largest volume void complexes—the largest connected regions of especially low density. The largest void complex in the observations was likewise compared with the median largest void complex from the simulations. These comparisons are shown (at the same scale) in Color Plate 11.

The Sloan Great Wall is quite typical of the most dramatic structures we would expect in a volume as large as the Sloan survey. The richest structure we show from the simulations is the median, which means that half the simulated Sloan surveys contained a richest structure richer than this one. And the largest void complex seen in the observations—a large cavernous volume of connected low-density chambers—is also similar to the largest void complexes typically found in the simulations. The simulations show a range for the largest expected supercluster and the largest expected void complex in a Sloan-sized survey. A detailed study showed that sizes of the Sloan Great Wall and the largest observed void complex fit within the 95% confidence limits estimated from the simulations.

Topology of Large-Scale Structure in the Sloan Digital Sky Survey

Once we had surveyed the equatorial slice of the Sloan Digital Sky Survey, the next task was to measure the Sloan 3D topology, a project that Clay Hambrick, Michael Vogeley, and I did, along with our colleagues from the topology group and colleagues in the SDSS.

Figure 9.8 shows the progressively larger samples we have studied, from the tiny 1986 original CfA sample, to the 1994 Geller and Huchra sample, to the 2006 Sloan Digital Sky Survey (SDSS) sample. For the 2006 SDSS sample at right, Earth is in the background, and the two lung-shaped regions are the partially completed regions of the Sloan survey in the foreground. The high-density 50% of the survey is shown as solid. One can easily that see the high-density regions are in a multiply connected spongelike piece. The Sloan Great Wall goes across the bottom lunglike survey region. The low- and high-density regions are completely interpenetrating. At this point in time (2006), the whole survey included about 400,000 galaxies. As we have looked at larger and larger samples, the topology has consistently remained spongelike.

Figure 9.8. The spongelike topology of the 50%-high-density regions (solid areas) is illustrated by three examples (shown at the same scale) of the ever-larger topology surveys that have been done with time. The black line has a length of 100 Mpc/h, or 487 million light-years. At the left is our first small CfA cubical survey from 1986. In the middle is the Vogeley, Park, and colleagues (1994) topology study of the final 3D CfA2 sample, including the Great Wall at the top. At right is the Gott, Hambrick, Vogeley, and colleagues (2008) Sloan Digital Sky Survey sample; the Sloan Great Wall stretches across the top of the lower lunglike survey region. All are spongelike. (Credit: Adapted from: J. Richard Gott, D. Clay Hambrick, et al., Astrophysical Journal, 675: 16, 2008)

The results we were getting from the Sloan Survey using galaxies to trace large-scale structures were supported by an independent survey of cold dark matter made with the Hubble Space Telescope using gravitational lensing (Richard Massey et al. 2007). By measuring the distortion in the shapes of background galaxies, the total matter distribution, which is dominated by cold dark matter, can be mapped, as was done for the Bullet Cluster (see Color Plate 3). By studying the distortion in background galaxies at different redshifts, a 3D map of the matter (dominated by cold dark matter) could be made. Their survey was very narrow (1.3° × 1.3° on the sky) and very deep (out to a redshift of 0.9). Their paper (Massey et al. 2007) was titled “Dark matter maps reveal cosmic scaffolding”; they found the matter arrayed on “a loose network of filaments, growing over time, which intersect in massive structures at the locations of clusters of galaxies.” The ESA/Hubble press release of January 7, 2007 said: “The map is consistent with conventional theories of how structure formed in the evolving Universe under the relentless pull of gravity, making the transition from a smooth distribution of matter into a sponge-like structure of long filaments.”

Meanwhile we were using a new tracer to follow structure formation in the Sloan Survey, LRG galaxies. The LRGs are large, very luminous, elliptical galaxies that are characteristically red in color because of their lack of new star formation. Because the LRG galaxies are so bright, they can be surveyed out to larger distances than regular galaxies, which enables us to cover larger survey volumes. The LRG galaxies, being so large, form in large cold dark matter halos, making it particularly easy to model their formation in an N-body simulation that follows cold dark matter and uses a biased galaxy formation algorithm. Figure 9.9 shows a genus curve of the luminous red galaxies (LRGs) from the Sloan Survey, which we (Yun-Young Choi, Park, Kim, and I) studied in 2009. The wide-angle survey includes galaxies out to a redshift of 0.44; that is, the observed wavelengths (λ_observed) of their spectral lines have been shifted to the red, to wavelengths longer than their wavelengths seen in the lab on Earth by a fractional amount (λ_observed − λ_lab)/λ_lab = 0.44. This shift is due to the Hubble expansion of the universe. The more distant the galaxy, the higher the redshift. We thus include galaxies up to 4.8 billion light-years from us. The topology is studied with a smoothing length of 165 million light-years.

The jagged genus curve shows the observation results for the LRGs: about 80 donut holes are seen in its spongelike median density contour (the peak of the curve at the center). The curve follows the general W shape of the Gaussian random-phase curve but shows more isolated clusters (about 40) than isolated voids (about 30). This excess of clusters over voids is expected due to nonlinear gravitational effects as first explained by Matsubara (described earlier in the discussion of the Sloan Great Wall). Biased galaxy formation (the fact that galaxies are more likely to form in high-density regions of cold dark matter) can enhance this effect. The fainter gray curve gives the average of 12 mock SDSS surveys from the Kim and Park large Horizon Run N-body simulations; it shows what we should expect to find, on average, from our simulations. Comparing the gray curve with the jagged curve, we found that the simulations show the same excess of isolated clusters over voids as found in the observations. No free-fitting parameters are applied to the simulations at all. Even the amplitude of the genus curve is predicted with remarkable accuracy. The agreement between the simulations and the observations—to within the observational errors—is remarkable indeed. Recall that the simulations are started with Gaussian random-phase initial conditions; their success, therefore, supports the proposition that the initial conditions were Gaussian random-phase as predicted by inflation.

Figure 9.9. Genus curve for a sample of Luminous Red Galaxies (LRGs; from the Sloan Digital Sky Survey) out to a redshift of z = 0.44 (jagged line) is compared with the mean of 12 mock surveys from a large Cold Dark Matter computer simulation (faint gray line). Both are smoothed with a smoothing length of 165 million light-years. (Credit: Adapted from: J. Richard Gott, Yun-Young Choi, Changbom Park, and Juhan Kim, Astrophysical Journal, 695: L45, 2009)

In the last several years, the Sloan LRG survey has been extended to larger redshift in a continuation of the survey known as Sloan III. This allows us to study the topology at still-larger scales. The latest genus curve produced by my student Prachi Parihar, Michael Vogeley, Yun-Young Choi, myself, and the members of our topology group is shown in Color Plate 12, along with 12 mock surveys from the Horizon Run 3 simulation by Kim and Park.

Can you tell which one of the 13 jagged curves shows the observations? Give up? It’s the dark blue one. We used a smoothing length of 102 million light-years. It represents the largest volume surveyed to date and contains approximately 500 donut holes in its multiply connected, spongelike, median density contour. The fact that these simulations agree so well with the observations in both amplitude and shape of the genus curve is a great victory for the standard model of inflation. The largest structures in the universe are giant filaments of galaxies stretching between the great clusters—the greatly expanded fossil remnants of initial random quantum fluctuations. Grown by gravity with the help of the mysterious cold dark matter, they form a magnificent, spongelike cosmic web.