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Physics for the 21st Century

Dark Matter Online Textbook

Online Text by Peter Fisher

The videos and online textbook units can be used independently. When using both, it is possible to start with either one. Watching the video first, and then reading the unit from the online textbook is recommended.

Each unit was written by a prominent physicist who describes the cutting edge advances in his or her area of research and the potential impacts of those advances on everyday life. The classical physics related to each new topic is covered briefly to help the reader better understand the research, its effects, and our current understanding of physics.

Click on “Content By Unit” (in the menu to the left) and select a unit title to view the Web version of the online text, which includes links to related material. Or, download PDF versions of the units below.

1. Introduction

Dark Matter Simulation

Figure 1: Distribution of dark matter in the universe.
Source: © Raul Angulo, Max Planck Institute for Astrophysics.
This image shows the distribution of dark matter in the universe according to our best cosmological models. It was generated using the Millennium simulation, a sophisticated numerical computer model that tracks 1010 dark matter particles interacting under the influence of gravity from the beginning of the universe until the present. (Unit: 10)

Dark matter is something beyond the stuff we encounter here on Earth. We all consist of neutrons, protons, and electrons, and our particle physics experiments with cosmic rays and accelerators tell us that a whole set of particles interact with each other to make up the world we see. As we learned in Units 1 and 2, the Standard Model describes these known particles and their interactions. But careful astronomical measurements, computer-based simulations, and nuclear theory calculations have all led us to believe that the particles described by the Standard Model account for only 4 percent of the mass of the universe. What makes up the missing 96 percent? Physicists believe, based on cosmological measurements described in this unit and Unit 11, that 23 percent is dark matter and 73 percent is dark energy. Dark energy and dark matter are very different. We shall learn about dark energy in Unit 11. Here, we focus on dark matter.

The first evidence of dark matter appeared in the 1930s, when astronomer Fritz Zwicky noticed that the motion of galaxies bound together by gravity was not consistent with the laws of gravity we learned about in Unit 3 unless there was a lot more matter in the galaxy cluster than he could see with his telescope. Development of more powerful and more precise theoretical and experimental tools in subsequent decades strengthened the case for dark matter. By the 1990s, dark matter was required to explain not just the motion of galaxies, but also how those galaxies and other large structures in the universe form, and the detailed pattern of temperature fluctuations in the cosmic microwave backgroundradiation left over from the early universe.

Constituents of the Universe

Figure 2: The composition of the universe, with 96 percent invisible and unfamiliar.
Diverse lines of evidence lead us to believe that less than 5 percent of the universe is composed of the familiar particles of the Standard Model. Most of the universe is composed of dark energy, a mysterious phenomenon discussed in Unit 11. The remainder is dark matter, stuff less mysterious only because we have seen evidence of its existence for decades. The dark matter cannot be explained by the Standard Model, but appears to be the dominant form of matter in the universe. This unit will describe experimental evidence for dark matter and various attempts to understand what it could be. (Unit: 10)

 

With these distinct reasons to believe that dark matter is a real part of our universe, scientists struggled to understand what comprises dark matter. Could it consist of familiar objects like brown dwarfs and large planets—made of the stuff of the Standard Model, but not emitting light and therefore invisible to astronomers? Both theory and experiment eventually pointed away from this simple explanation, strongly suggesting that dark matter is something entirely new and different. A generation of experiments was developed to look for new types of particles—beyond the Standard Model—that could account for some or all of dark matter. In parallel, theorists have developed creative visions of what new physics could explain about the motion of galaxies, large scale structure, and variations in the cosmic microwave background in one fell swoop.

The process of discovery has not run smoothly. It has survived successive periods of disinterest, progressing as new technologies developed, scientists made fresh observations in disparate fields, and general scientific interest in the topic increased. In this unit, we describe why we think dark matter exists, its role in determining the structure of galaxies and clusters of galaxies, and how it connects with particle physics. Finally, we discuss the ongoing quest to determine what dark matter is made of in both theory and experiment.

Dark matter and gravity

The connection between dark matter and gravity bears special mention because it is the one thing about dark matter of which physicists are certain. Everything we know about dark matter so far comes from astronomy. The astronomical measurements deal exclusively with the way in which dark matter interacts gravitationally. We have two ways of studying the effects of gravity on astronomical bodies: We can either see how a group of astronomical objects moves under the influence of gravity or measure how gravitation changes the way in which light travels. Experimentally, we have no reason to believe that dark matter interacts with normal matter or with itself in any way other than via gravitation, although there is a great deal of theoretical speculation to the contrary.

Figure 3: Clusters of galaxies contain significantly more dark matter than visible matter.
Source: © ESO.
The bright, extended objects in this image are galaxies in the cluster ACO 3341. This cluster, located almost 500-million light years from the Milky Way, contains numerous galaxies of different sizes, shapes, and luminosities that are bound together by the force of gravity. The cluster is also believed to contain far more dark matter than luminous matter, which accounts for the relative motion of all the galaxies. (Unit: 10)

The effects of dark matter did not become apparent until astronomers began to study the motion of galaxies and clusters of galaxies. Since a galaxy that measures 150,000 light-years across contains 2 to 10 times as much dark matter as normal matter, the gravity from the dark matter plays a large role in its movements. However, the normal matter is clumped in solar systems (stars and planets), while the dark matter is spread out. Typical solar systems are about 10 light-hours across and are separated from each other by about 2 light-years. So, in conventional terms, the galaxy consists of mostly empty space interspersed with very dense clumps of normal matter.

Since a solar system contains far more normal matter than dark matter (2×1030 kilograms vs. 9×109 kilograms), dark matter plays an insignificant role in shaping our solar system. At the next level of size, observations indicate that normal and dark matter play roughly similar roles in determining the dynamics of galaxies. And at the largest-size scales, dark matter dominates the dynamics of galaxy clusters and superclusters—clusters of clusters. To study dark matter, we need to investigate objects the size of a galaxy or larger.

2. Initial Evidence of Dark Matter

Fritz Zwicky, an astronomer at the California Institute of Technology, stumbled across the gravitational effects of dark matter in the early 1930s while studying how galaxies move within the Coma Cluster. The Coma Cluster consists of approximately 1,000 galaxies spread over about two degrees on the sky—roughly the size of your thumb held at arm’s length, and four times the size of the Sun and the Moon seen from Earth. Gravity binds the galaxies together into a cluster, known as a galaxy cluster. Unlike the gravitationally bound planets in our solar system, however, the galaxies do not orbit a central heavy object like the Sun and thus execute more complicated orbits.

To carry out his observations, Zwicky persuaded Caltech to build an 18-inch Schmidt telescope that could capture large numbers of galaxies in a single wide-angle photograph. He used the instrument to make a survey of all the galaxies in the cluster and used measurements of the Doppler shift of their spectra to determine their velocities. He then applied the virial theorem. A straightforward application of classical mechanics, the virial theorem relates the velocity of orbiting objects to the amount of gravitational force acting on them. Isaac Newton’s theory tells us that gravitational force is proportional to the masses of the objects involved, so Zwicky was able to calculate the total mass of the Coma Cluster from his measured galactic velocities.  See The Math below.

Figure 4: The Coma Cluster, which provided the first evidence for dark matter.
Source: © NASA, JPL-Caltech, SDSS, Leigh Jenkins, Ann Hornschemeier (Goddard Space Flight Center) et al.
This image combines data from the Spitzer Space Telescope with the Sloan Digital Sky Survey to show many of the thousands of galaxies in the Coma cluster. By measuring the velocities of these galaxies, Fritz Zwicky realized that there is more to the Coma cluster than meets the eye. Galaxies toward the edge of the cluster were moving far too fast, if their motions were to be explained by the gravitational influence of the other galaxies in the cluster. Zwicky took this as evidence that the cluster must contain a great deal of matter that he couldn’t see with his telescope—the first evidence for dark matter. (Unit: 10)

Zwicky also measured the total light output of all the cluster’s galaxies, which contain about a trillion stars altogether. When he compared the ratio of the total light output to the mass of the Coma Cluster with a similar ratio for the nearby Kapteyn stellar system, he found the light output per unit mass for the cluster fell short of that from a single Kapteyn star by a factor of over 100. He reasoned that the Coma Cluster must contain a large amount of matter not accounted for by the light of the stars. He called it “dark matter.”

Zwicky’s measurements took place just after astronomers had realized that galaxies are very large groups of stars. It took some time for dark matter to become the subject of active research it is today. When Zwicky first observed the Coma Cluster, tests of Einstein’s theory were just starting, the first cosmological measurements were taking place, and nuclear physicists were only beginning to develop the theories that would explain the Big Bang and supernovae. Since galaxies are complex, distant objects, it is not surprising that astronomers did not immediately begin to worry about “the dark matter problem.”

By the early 1970s, technology, astronomy, and particle physics had advanced enough that the dark matter problem seemed more tractable. General relativity and nuclear physics had come together in the Big Bang theory of the early universe, and the detection of microwave photons from the time when the first atoms formed from free electrons and protons had put the theory on a solid footing. Larger telescopes and more precise and more sensitive light detectors made astronomical measurements quicker and better. Just as important, the emergence of affordable mini-computers allowed physics and astronomy departments to purchase their own high-performance computers for dedicated astronomical calculations. Every advance set the scene for a comprehensive study of dark matter, and two very important studies of dark matter soon appeared.

Dark matter appears in galactic simulations

Figure 5: James Peebles (left) and Jeremiah Ostriker (right) found evidence for dark matter in their computer simulations.
Source: © AIP, Physics Today Collection and Tenn Collection
James Peebles (left) and Jeremiah Ostriker (right) of Princeton University performed pioneering numerical computer simulations that showed how the structure of galaxies we observe in the cosmos requires copious amounts of dark matter. Both Ostriker and Peebles have had long, distinguished careers advancing the study of dark matter on the theoretical side and making numerous other contributions to astrophysics and cosmology. (Unit: 10)

In 1973, Princeton University astronomers Jeremiah Ostriker and James Peebles used numerical simulation to study how galaxies evolve. Applying a technique called N-body simulation, they programmed 300 mass points into their computer to represent groups of stars in a galaxy rotating about a central point. Their simulated galaxy had more mass points, or stars, toward the center and fewer toward the edge. The simulation started by computing the gravitational force between each pair of mass points from Newton’s law and working out how the mass points would move in a small interval of time. By repeating this calculation many times, Ostriker and Peebles were able to track the motion of all the mass points in the galaxy over a long period of time.

For a galaxy the size of the Milky Way (4×1020 meters), a mass point about halfway out the edge moves at about 200 kilometers per second and orbits the center in about 50 million years. Ostriker and Peebles found that in a time less than an orbital period, most of the mass points would collapse to a bar-shaped, dense concentration close to the center of the galaxy with only a few mass points at larger radii. This looked nothing like the elegant spiral or elliptical shapes we are used to seeing. However, if they added a static, uniform distribution of mass three to 10 times the size of the total mass of the mass points, they found a more recognizable structure would emerge. Ostriker and Peebles had solid numerical evidence that dark matter was necessary to form the types of galaxies we observe in our universe.

Fresh evidence from the Andromeda galaxy

At about the same time, astronomers Kent Ford and Vera Cooper Rubin at the Carnegie Institution of Washington began a detailed study of the motion of stars in the nearby galaxy of Andromeda. Galaxies are so large that even stars traveling at 200 kilometers per second appear stationary; astronomers must measure their Doppler shifts to obtain their velocities. However, early measurements of stellar velocities in different portions of Andromeda proved very difficult. Since the spectrometers used to measure the shift in frequency took a long time to accumulate enough light, observations of a given portion of Andromeda required several hours or even several nights of observing. Combining images from several observations was difficult and introduced errors into the measurement. However, new and more sensitive photon detectors developed in the early 1970s allowed much shorter measurement times and enabled measurements further out from the center of the galaxy.

FROM CONTROVERSY TO CREDIBILITY

Rubin and Ford measured the velocity of hydrogen gas clouds in and near the Andromeda galaxy using the new detectors. These hydrogen clouds orbit the galaxy much as stars orbit within the galaxy. Rubin and Ford expected to find that the hydrogen gas outside the visible edge of the galaxy would be moving slower than gas at the edge of the galaxy. This is what the virial theorem predicts if the mass in the galaxy is concentrated where the galaxy emits light. Instead, they found the opposite: the orbital velocity of the hydrogen clouds remained constant outside the visible edge of the galaxy. If the virial theorem is to be believed, there must be additional dark matter outside the visible edge of the galaxy. If Andromeda obeyed Newton’s laws, Rubin reasoned, the galaxy must contain dark matter, in quantities that increased with increasing distance from the galactic center.

Galactic Case for Dark Matter

Figure 6: Observed and predicted rotation curves for the galaxy M33, also known as the “Triangulum Galaxy.”
Source: © M33 Image: NOAO, AURA, NSF, T. A. Rector.
The green points on the plot correspond to the observed velocities of objects orbiting the M33 galaxy as a function of their distance from the galactic center. The lower curve on the plot (dashed line) shows what the rotational velocity of objects in the M33 galaxy is expected to be based on the luminous matter in the galaxy. Clearly, the green points do not match the dashed line: the rotational velocity of objects outside the galaxy is far faster than the prediction. If, however, there were a large amount of non-luminous matter in the galaxy, objects far from the galactic center would move much faster. The solid green line is the velocity predicted for the orbiting objects if there is dark matter in M33. These rotation curves provide strong indirect evidence for dark matter. (Unit: 10)

Alternative explanations of the Andromeda observations soon emerged. Theories of Modified Newtonian Dynamics (MOND), for example, aimed to explain the findings by modifying the gravitational interaction over galactic and larger distances. At very low accelerations, which correspond to galactic distances, the theories posit that the gravitational force varies inversely with the distance alone rather than the square of the distance. However, MOND would overturn Einstein’s theory in an incredible way: General relativity is based on the simple idea of the equivalence principle. This states that there is no difference between gravitational mass (the mass that causes the gravitational force) and inertial mass (the mass that resists acceleration). There is no fundamental reason to expect these two masses to be the same, nor is there any reason to expect them to be different. But their equivalence forms the cornerstone of Einstein’s general theory. MOND theories break that equivalence because they modify either gravity or inertia. If MOND were correct, a fundamental assumption underlying all of modern physics would be false.

3. Dark Matter in the Early Universe

By the end of the 1970s, two compelling lines of evidence for dark matter had appeared. The motion of galaxies within clusters and the motion of gas clouds around individual galaxies strongly suggested that either our understanding of gravity is fundamentally wrong, or that there is far more matter in the galaxies and clusters than meets the eye. Further, simulations of galaxy formation showed that the spiral and elliptical galaxies we observe in the night sky cannot form without large amounts of dark matter in addition to the luminous stars. A third line of evidence developed in the 1990s, as radio telescopes above the atmosphere mapped the cosmic microwave background (CMB).

Timeline of the Universe

In our standard model of cosmology, the universe began with a singularity that immediately went through a period of extremely rapid expansion called “inflation.” When inflation was finished, the universe as we know it began. Quarks, photons, and other fundamental particles formed a hot, dense soup that cooled and expanded. As the universe cooled, atomic nuclei formed after about 100 seconds, and then light atoms formed after 390,000 years. At that time, the photons decoupled from the matter, traveling nearly uninterrupted from that time until the present, at which time they were observed with the WMAP satellite. (Unit: 10)

This new evidence for dark matter has its origin in the early universe. About one second after the Big Bang, astrophysicists believe, a very dense mixture of protons, neutrons, photons, electrons, and other subatomic particles filled the universe. The temperature was so high that the electrons could not bind with the protons to form atoms. Instead, all the particles scattered off of each other at high rates, keeping all the different species at the same temperature—that is, in thermal equilibrium—with each other. The photons also scattered off of the electrically charged protons and electrons so much that they could not travel very far.

As the universe expanded, the temperature dropped to about one billion degrees Kelvin (K). At that point, the protons and neutrons began to bind together to form atomic nuclei. At roughly 390,000 years after the Big Bang, continued expansion and cooling had dropped the temperature of the universe to about 3000 K. By that point, all the electrons and protons had bound to form electrically neutral hydrogen atoms, and all the other charged particles had decayed. After the primordial hydrogen formed, the universe became so transparent to photons that they have been traveling throughout it for the entire 13.7 billion years since then. These relic photons from the early universe have a microwave wavelength, and are known as the cosmic microwave background, or CMB.

Density fluctuations and dark matter

Before the neutral hydrogen formed, the matter was distributed almost uniformly in space—although small variations occurred in the density of both normal and dark matter owing to quantum mechanical fluctuations. Gravity pulled the normal and dark matter in toward the center of each fluctuation. While the dark matter continued to move inward, the normal matter fell in only until the pressure of photons pushed it back, causing it to flow outward until the gravitational pressure overcame the photon pressure and the matter began to fall in once more. Each fluctuation “rang” in this way with a frequency that depended on its size. The yo-yoing influenced the temperature of the normal matter. It heated up when it fell in and cooled off when it flowed out. The dark matter, which does not interact with photons, remained unaffected by this ringing effect.

When the neutral hydrogen formed, areas into which the matter had fallen were hotter than the surroundings. Areas from which matter had streamed out, by contrast, were cooler. The temperature of the matter in different regions of the sky—and the photons in thermal equilibrium with it—reflected the distribution of dark matter in the initial density fluctuations and the ringing normal matter. This pattern of temperature variations was frozen into the cosmic microwave background when the electrons and protons formed neutral hydrogen. So a map of the temperature variations in the CMB traces out the location and amount of different types of matter 390,000 years after the Big Bang.

 

Figure 8: Map of the temperature variations in the cosmic microwave background measured by the WMAP satellite.
Source: © NASA, WMAP Science Team.
This map shows the pattern of temperature variations in the cosmic microwave background (CMB) measured with the WMAP satellite. WMAP made a differential measurement of the CMB temperature with two sensitive radio antennae mounted with a fixed displacement between them. As the satellite rotated, the radio antennae traced out temperature variations in the entire sky. The largest temperature differences (between the red and dark blue regions) are about 0.0004 K, and the characteristic angular size of the temperature variations is around 1 degree. By analyzing the detailed pattern in this map, WMAP scientists infer that less than 4 percent of the universe is ordinary matter, and 23 percent is dark matter. (Unit: 10)

 

American physicists Ralph Alpher, Robert Herman, and George Gamow predicted the existence of the CMB in 1948. Seventeen years later, Bell Labs scientists Arno Penzias and Robert Wilson detected them. Initial measurements showed the intensity of the relic photons to be constant across the sky to a fraction of 1 percent. In the early 1990s, however, NASA’s Cosmic Background Explorer (COBE) spacecraft used a pair of radio telescopes to measure differences among relic photons to one part per million between two points in the sky. A subsequent spacecraft, the Wilkinson Microwave Anisotropy Probe (WMAP), made an even more precise map. This revealed hot and cold spots about 1.8 degrees in size across the sky that vary in intensity by a few parts per million.

The angular size and the extent of variation indicate that the universe contained about five times as much dark matter as normal matter when the neutral hydrogen formed. Combined with measurements of supernovae and the clustering of galaxies, this indicates that dark energy comprises 73 percent of the universe, dark matter 23 percent, and normal matter just 4 percent.

4. Dark Matter Bends Light

With three independent reasons to believe that dark matter existed—motion of galaxies, structure simulations, and temperature fluctuations in the cosmic microwave background—increasing numbers of physicists and astronomers turned their attention to trying to understand just what the dark matter is made of, and how it is distributed throughout the universe. Gravitational lensing proved a useful tool with which to probe the dark matter.

Quasars, lensing, and dark matter

Images of quasars gravitationally lensed by galaxies provide insight into the distribution of dark matter inside the lensing galaxies. Quasars are distant objects that emit huge amounts of light and other radiation. Since many quasars are visible behind galaxies, their light must pass through those intervening galaxies on the way to us. We know from general relativity theory that the matter in any galaxy—both normal and dark matter—bends space time. That bending distorts the image of any quasar whose light passes through a galaxy.

Figure 9: Gravitational lensing produces more than one image of distant quasars, as seen in this shot from the Hubble Space Telescope.
Source: © NASA/ESA Hubble Space Telescope, NASA/Goddard Space Flight Center.
As shown above left, the gravitational influence of a massive body can bend the path of light from a distant object as it travels toward telescopes here on Earth. The image of a gravitationally lensed object can be distorted, or even appear as multiple images, as shown above right. This Hubble Space Telescope image of the gravitational lens G2237+0305 is sometimes referred to as the “Einstein Cross.” The four distinct, bright spots are actually all images of the same quasar. The diffuse central spot is a foreground galaxy that has acted as a gravitational lens, bending light from the quasar so that it appears to be in four places at once. Careful measurements of lensed quasars can reveal information about the distribution of dark matter in the galaxy (or galaxy cluster) that acts as a lens. (Unit: 10)

In many cases, this lensing causes several images of the same quasar to appear in our telescopes. Careful measurements of the brightness of the different images of the quasar give hints about the distribution of the matter in the galaxy. Since the matter in each part of the galaxy determines the amount of bending of space time in that part of the galaxy, the brightness of the images tells us how matter, both normal and dark, is distributed. Optical measurements inform astronomers where the normal matter is. They can then use the brightness of the multiple quasar images to trace out the dark matter.

So far, astronomers have identified about 10 such lenses like this. Careful observations have shown that any clumps of dark matter in the galaxies must be smaller than about 3,000 light-years. More sensitive telescopes will find more lenses and will improve our understanding of how dark matter is distributed in galaxies.

Evidence from colliding clusters

Observing colliding galaxy clusters provides another useful way of understanding the nature of dark matter. When two clusters collide, the dark matter in one passes through the other unaffected; dark matter doesn’t interact much with either itself or normal matter. But the normal matter in one cluster does interact with the dark matter and the normal matter in the other cluster, as well as with the dark matter in its own cluster. During the collision, the normal matter is dragged forward by the dark matter in its own cluster and dragged back by both the dark matter and normal matter in the other cluster. The net effect of the collision, therefore, is to cause the normal matter in each cluster to fall behind the dark matter in the same cluster.

Figure 10: X-ray and visible light images of the Bullet Cluster reveal strong evidence for the existence of dark matter.
Source: © X-ray: NASA, CXC, CfA, M. Markevitch et al.; Optical: NASA, STScI; Magellan, U. Arizona, D. Clowe et al.; Lensing Map: NASA, STScI; ESO WFI; Magellan, U. Arizona, D.Clowe et al.
This image of the Bullet Cluster is a composite of an x-ray image from the Chandra X-Ray Observatory and a visible light image from the Hubble Space Telescope. The pink clumps are hot gas in the x-ray image that contain most of the normal baryonic matter in the two colliding clusters. The blue areas, on the other hand, show where the mass in the clusters is concentrated based on measurements of gravitational lensing in the optical image. The blue and pink regions are clearly separated, indicating that most of the mass in the clusters is dark matter. (Unit: 10)

Astronomers gained solid evidence of that scenario when they imaged a pair of colliding galaxy clusters named the Bullet Cluster in two ways: through its emission of visible light and x-rays. The collision between the normal matter in each subcluster heats up the normal matter, causing the colliding subclusters to emit x-rays. In 2004, NASA’s orbiting Chandra x-ray observatory captured an x-ray image of the Bullet Cluster that gives the locations of the normal matter in the two subclusters. At the same time, the entire Bullet Cluster distorts the images of galaxies behind it through the gravitational lensing effect that we reviewed above in the context of quasars. By carefully measuring the shape of the distorted background galaxies, astronomers could determine the average position and mass of each of the subclusters. Since galaxy clusters contain a few times as much dark matter as normal matter, the lensing measurement gives the location of the dark matter, while the x-rays locate the normal matter. The image that combines both measurements shows that the dark matter has run ahead of the normal matter in both subclusters, confirming expectation.

The measurements of the Bullet Cluster were a blow to the MOND theories that we encountered earlier in this unit. Those theories predict no difference between the x-ray and lensing images. Some theorists have tried to modify the MOND approach in such a way that it accommodates the evidence from the Bullet Cluster and other observations, but the clear consensus of astronomers is that dark matter is a reality.

Dark matter in our galaxy

With gravitational lensing successfully being used to “weigh” entire galaxy clusters, the question arose whether it could be brought to bear more locally, to search for dark matter objects in the outer regions of our own Milky Way galaxy. The answer is a resounding yes. A clever gravitational lensing survey to search for clumps of dark matter in the halo of our galaxy began in 1992. The survey was designed to find MACHOs, or massive compact halo objects, which is a fancy term for “chunks of dark matter.” It was initially thought that MACHOs would be failed stars or large, drifting planets—familiar objects that don’t emit light—but the MACHO project was designed to be sensitive to any lump of dark matter with a mass between the Earth’s mass and 10 times the Sun’s mass.

Figure 11: This Australian telescope unsuccessfully sought evidence for the existence of MACHOs based on their putative effect on starlight.
Source: © The Australian National University.
In the MACHO project, the 50-inch telescope at Australia’s Mount Stromlo Observatory monitored millions of objects passing in front of stars in the nearby Large Magellanic Cloud galaxy. The project found no evidence for the existence of MACHOs. (Unit: 10)

The MACHO project used a telescope to monitor the light from stars just outside the Milky Way in a very small satellite galaxy called the “Large Magellanic Cloud.” If a MACHO passes in front of one of these stars, the gravitational lensing effect predicted by Einstein’s general theory of relativity and confirmed in 1979 will increase the measured flux of the starlight by a tiny amount. The Anglo-American-Australian MACHO Project used an automated telescope at Australia’s Mount Stromlo Observatory to observe transits. None showed anywhere near enough change in the starlight to account for dark matter as consisting of faint stars or large planets.

A similar project, named “EROS” and run by the European Organisation for Astronomical Research in the Southern Hemisphere at Chile’s La Silla Observatory, has had the same negative result. For example, a study of 7 million stars revealed only one possible MACHO transit; in theory, MACHOs would have produced 42 events. But physicists refused to give up the hunt. The SuperMACHO survey, a successor to the MACHO Project, used the 4-meter Victor M. Blanco telescope in Chile’s Cerro Tololo Inter-American Observatory to monitor tens of millions of stars in the Large Magellanic Cloud in search of evidence that MACHOS exist. SuperMACHO also found that MACHOs cannot account for the vast amount of dark matter in the galaxy.

The astronomical evidence we have for dark matter ranges from within our galaxy to the farmost regions of space and time that we are able to probe. We now understand that dark matter dominates at the scale of galaxy clusters, normal matter dominates at the subgalactic scale, and they duke it out on the galactic scale. We know that dark matter gravitationally interacts with itself and normal matter, but we still do not know what the dark matter is.

5. From Astronomy to Particle Physics

The abundance of astronomical evidence for dark matter in the early 1970s intrigued physicists working in other fields. Cosmologists and nuclear physicists were developing our current model of cosmology, trying to understand how the universe we live in—dark matter and all—formed. Concurrently, others wondered how the dark matter fit, if at all, into the Standard Model we learned about in Unit 1.

By the late 1970s, the Standard Model of particle interactions had gained a firm experimental footing. At the same time, physicists were refining their standard model of cosmology in which the universe began its existence when a singularity, a point of infinite density and infinite temperature, exploded in the Big Bang and began a process of expansion that continues today. Application of the Standard Model and nuclear theory to the Big Bang model allowed physicists to quantify nucleosynthesis, the process responsible for creating elements out of the protons, neutrons, electrons, and energy that suffused the infant universe.

 

Figure 12: This series of reactions created the lightest elements in the infant universe.
Source: © Wikimedia Commons, Public Domain, Author: Lokal_Profil, 5 August 2008.
The nuclei of the light elements hydrogen, helium, lithium, and their various isotopes were produced when nucleosynthesis took place in the first three minutes after the birth of the universe. Starting with a primordial mixture of protons (p+), neutrons (n0), and photons (), the above reactions successfully predict the abundances of these light elements in the universe. Nucleosynthesis halted as the universe cooled to a temperature too low to support the nuclear reactions required to produce elements heavier than lithium. (Unit: 10)

 

This model of Big Bang nucleosynthesis, supported by careful astronomical observations of the abundance of light elements in the universe, makes a particularly significant prediction about the density of baryons in the first few minutes: The Big Bang could not have created enough normal matter at the start of the universe to account for dark matter. Astrophysicists concluded that dark matter must be some new form of matter not yet observed, possibly even a new type of particle.

New dark matter particles

One of the first attempts to explain dark matter with new particles arose in a surprising place: the Homestake Gold Mine in South Dakota that we first encountered in Unit 1. The Homestake neutrino detector was monitoring neutrinos thought to come from the Sun. In 1976, it became apparent that this experiment only counted about half the predicted number. One explanation was that some new form of heavy particles that did not interact much would collect in the center of the Sun, cooling it off very slightly. This new heavy particle would have the same properties required by dark matter: very weak interaction with other particles, copious in our solar system, and left over from the Big Bang.

We now know that the deficit of neutrinos is due to their oscillation; but at the time, it was an intriguing hint that dark matter could be made up of a new type of particle, possibly not included in the Standard Model. Heavy neutrinos were once considered a candidate for particle dark matter, but large-scale structure simulations of neutrino dark matter have ruled them out. The remainder of this unit will focus on particle dark matter in both theory and experiment. In section 8, we will explore the two leading non-Standard Model candidates for particle dark matter and experimental efforts to detect them. We also will examine how the constant theoretical effort to explain dark matter often generates new possibilities for particle dark matter. The table below summarizes all the possibilities for dark matter that appear in this unit.

6. The Search for Particle Dark Matter

Starting in the late 1980s with the idea that dark matter could be a new kind of particle, nuclear and particle physicists began experiments to detect dark matter in the event that it interacts directly with normal matter. There are two main ideas about what these particles could be. One views the dark matter as a very light particle known as the axion. Hypothesized to explain a confusing property of the strong force that binds quarks together (see Unit 2), an axion would weigh about one-trillionth as much as a proton. The other idea comes from a very broad class of theories that predicts an electrically neutral particle weighing between 100 and 1,000 times as much as a proton. The general name of this kind of particle is a “weakly interacting massive particle” or WIMP. Physicists first introduced this concept to explain the problem of solar neutrinos that we met in Section 5.

Figure 13: If dark matter consists of axions, the Axion Dark Matter Experiment shown here could detect them in the next decade.
Source: © ADMX
The polished metal tubes shown here are the heart of the Axion Dark Matter Experiment, or ADMX. ADMX is a systematic search for dark matter axions left over from the early universe. These relic axions, if they exist, will interact with a magnetic field in the experiment and will be detected by a sensitive radio antenna if it is tuned to exactly the right frequency. If axions are indeed the dark matter, ADMX could find them within the next decade. (Unit: 10)

So far, physicists have found no evidence that axions or WIMPs actually exist; both particles remain in the realm of hypothesis. However, the physics community found the theoretical reasoning that led to the hypotheses were compelling enough to mount experimental searches for them. Some of their experiments have provided fascinating hints of the presence of these peculiar particles.

The types of experiments differ considerably, based on which particle they aim to detect. In each case, they rely on the specific physical properties of the two proposed particles. Because axions are hypothesized to have no electric charge or spin, extremely small masses, and minimal interaction with ordinary matter, experimenters must use indirect methods to detect them. In contrast, theorists see WIMPs as not only possessing large masses but also interacting—although infrequently—with ordinary matter. Thus, it may be possible to detect them directly as well as indirectly.

The quest for axions

The concept of the axion emerged as a solution to the so-called strong-CP problem. We first encountered CP, the product of charge conjugation and parity, in Unit 1. There we discovered that CP violation occurs in weak interactions, but does not appear to occur in strong interactions. In 1977, theorists Roberto Peccei and Helen Quinn suggested that this difference between the strong and the weak force was due to a broken symmetry. In Unit 2, we learned that symmetry breaking is accompanied by a new particle called a “Nambu-Goldstone boson.” The new particle associated with the broken Peccei-Quinn symmetry would interact with ordinary matter so weakly as to be virtually undetectable. MIT theorist Frank Wilczek named it the axion after a laundry detergent because, he said, it cleaned up the strong-CP problem. Later, the weakness of its interactions made it a strong candidate for dark matter.

Figure 14: Axion hunters: two Fermilab physicists with their experiment designed to detect axions.
Source: © Fermilab.
The GammeV experiment at Fermilab, shown here with two project scientists, is designed to detect axions. The experiment is an opportunistic use of a large magnet—the red rectangular object in the photograph—originally designed to be used in the Tevatron. The GammeV team realized that they could use the magnet to create axions, as it is theoretically possible for a photon from a laser beam in a strong magnetic field to turn into an axion. The scientists shine a green laser down the hollow center of the magnet and look for axions appearing at the other end of the experiment. (Unit: 10)

Experimentalists who want to detect the particle can choose either to make their own axions or to search for those that already exist. Many of these experiments attempt to detect axions as they interact with photons. The basic idea is that when an axion collides with a photon, two photons are produced in the collision that have an energy proportional to the axion mass. Dark matter axions do not move very fast and are very light. Therefore, the photons produced would be low energy, with a wavelength roughly corresponding to radio waves. Axions are expected to interact with photons very weakly—much more weakly than electrons or protons—so the trick to detecting axions is to build a very sensitive radio antenna.

Trapping radio waves to identify axions

The process starts with a magnetic field about 200,000 times more powerful than Earth’s field. When an axion interacts with the magnetic field, radio waves are generated. To capture the radio waves, experimentalists use a hollow superconducting cylinder called a “resonant cavity.” The size and shape of the cavity are carefully selected to amplify radio waves of a particular frequency.

Figure 15: SQUID technology boosts the ability of the Axion Dark Matter Experiment to detect the faint signals that would indicate the presence of axions.
Source: © Lawrence Livermore National Laboratory.
The ADMX experiment is a carefully constructed precision experiment that could detect faint traces of axions. The superconducting magnet must be kept cold in a bath of liquid helium, and careful adjustment of the tuning rods ensures that the radio antenna is at exactly the right frequency. Thermal baffles prevent heat transfer with the environment, and the SQUID amplifier boosts the experiment’s sensitivity enough to detect the faint signals that would indicate the presence of axions. (Unit: 10)

For a typical mass of 2µeV, roughly 1030 axions would stream through the detector each second. Over time, the trapped radio waves would build up to a detectable amount. The radio waves built up in the resonant cavity are measured using a tool called a SQUID, for superconducting quantum interference device, which greatly improves the experiment’s ability to detect faint signals. Since physicists do not know the mass of the hypothetical axion, they would have to adjust the radio frequency of the cavity in small steps, like tuning a radio, to scan for a signal from dark matter axions.

The best-known experiment of this type, the Axion Dark Matter Experiment (ADMX), has operated since 1995 without detecting a signal. Physicists at Lawrence Livermore National Laboratory and collaborating institutions improved ADMX in 2008 by adding sensitive amplifiers to the apparatus. Further enhancements include adding a cooling system that will improve the system’s sensitivity. The team will add more improvements and will continue to operate the experiment for many years before exhausting all its potential to hunt for axions.

Other searches for axions have started in recent years. A Japanese project, the Cosmic Axion Research with Rydberg Atoms in a Resonant Cavity (CARRAC) experiment, seeks axions in a range of masses similar to that sought by ADMX. An Italian group’s PVLAS (for Polarizzazione del Vuoto con LASer) experiment looks for minute changes in the polarization of light that might stem from axions. And in contrast to those earthbound methods, the European Nuclear Research Center’s Axion Solar Telescope (CAST) searches for axions produced in the Sun.

Seeking the elusive WIMPs

As theorized, WIMPs interact with normal matter in the simplest way, by colliding with it. They don’t do that very often; they easily penetrate the Earth or Sun without interacting at all. But very occasionally a WIMP will hit an atomic nucleus and cause it to recoil. Theorists believe that 5 million dark matter particles will pass through a 2 kilogram piece of normal matter, containing roughly 1025 atoms, every second. In rough numbers, just one of the WIMPs will hit a nucleus in an entire year. The nucleus will recoil and deposit its energy in the surrounding matter in the form of ionization electrons, which can attach to ions to create neutral atoms, or heat. The amount of energy deposited in this way resembles that of an x-ray photon. Physicists searching for dark matter face the twin challenge of collecting this deposited energy and ensuring that the energy they collect came from a dark matter interaction and not from a conventional physics process.

Distinguishing between dark matter interactions and conventional interactions proves to be very difficult. At sea level, 100 cosmic rays pass through each square meter of the Earth’s surface each second, along with 28 neutrons from cosmic ray interactions in the atmosphere and 10,000 x-rays from low-level contamination in normal materials. In addition, everything contains trace amounts of uranium and thorium, both of which give rise to sequential radioactive decays. All these processes can mimic the scattering of dark matter off a nucleus.

Underground searches for WIMPs

Figure 16: The Large Underground Xenon detector will have 100 times more sensitivity to WIMPs than previous detection methods.
Source: © The LUX Experiment.
The Large Underground Xenon (LUX) detector contains 350 kg of cold liquid xenon that will scintillate when it interacts with a WIMP. The liquid xenon, held in the blue oblong vessel in this cutaway diagram, sits inside an 8-meter-diameter by 6-meter-high tank of water that reduces background signals from gamma radiation by seven orders of magnitude. Isolated from other sources of radiation by almost 1500 meters of rock, LUX will improve sensitivity to WIMPs by a factor of 100 over previous methods. (Unit: 10)

Dark matter recoil experiments address these problems in several ways. Since few cosmic rays penetrate deep underground, experiments placed in tunnels and mines under a kilometer of rock remove that source of interference. The Large Underground Xenon (LUX) detector, which will operate 1,463 meters deep in the familiar Homestake Gold Mine in South Dakota, exemplifies this approach. As its detector, LUX will use a cylinder containing 350 kilograms of liquid and gaseous xenon, which scintillates and becomes ionized when struck by particles, including WIMPs. Several precautions will minimize the number of non-WIMP particles likely to impact the detector. Up to a meter of high-purity lead or copper shielding will absorb x-rays and gamma rays emitted by the walls of the mine. In future experiments, a meter or so of water will absorb neutrons from both cosmic rays and the cavern’s walls. Finally, experimenters will use only tested, low-radioactivity materials to build the detector.

Other groups are also undertaking the underground route to detecting WIMPs. The international Xenon Dark Matter Project uses a xenon detector in a laboratory under Italy’s Gran Sasso Mountain. The second Cryogenic Dark Matter Search (CDMSII) project relies on cryogenic germanium and silicon detectors in Minnesota’s Soudan Mine, another location well used by scientists; the original experiment had taken place in a tunnel under the Stanford University campus. And, the Italian-American WIMP Argon Program (WARP) uses argon in place of the more expensive xenon in its detector.

To clarify their results, the dark matter detectors measure the energy of the recoiling nucleus in two different ways. A neutron or dark matter interaction will divide its energy between heat and ionization electrons, while other radioactive decays will put virtually all their energy into ionization electrons. In the late 1980s, the first dark matter experiments were able to exclude neutrinos as dark matter by measuring the energy only one way. The two energy measurement techniques developed since then have led to an improvement of 10 million in sensitivity to dark matter interactions. Future detectors will have even greater sensitivity.

Monitoring the direction of dark matter

If dark matter WIMPs exist, we could learn more about them by measuring the direction from which they come toward Earth from space. A directional measurement would use gas molecules at about one-twentieth of an atmosphere pressure as targets for the dark matter particles to hit. Each nucleus struck by a WIMP would travel about 1 millimeter. That’s a long enough distance for physicists to measure by collecting the ionization electrons created by the collisions directly or by converting them to scintillation light and using a charge-coupled device (CCD) camera to create an image. Since each struck nucleus will generally travel in the same direction as that in which the dark matter particle traveled before it hit the nucleus, measuring the direction of the recoiling nuclei will give experimenters critical details about dark matter in our galaxy.

 

Detecting the Direction of the WIMP Wind

Figure 17: If they exist, WIMPs could stream toward Earth in a specific direction in a “WIMP wind” that might be experimentally detectable.
If WIMPs exist, theorists suggest that they would form a halo around our Milky Way galaxy. As our solar system rotates around the galactic center, it would continually pass through a “WIMP wind” from the direction of the Cygnus constellation. When bumped by a WIMP, a normal particle would recoil in the direction of that wind. The Anglo-American DRIFT Collaboration uses molecules of carbon disulfide at low pressure in a stainless-steel chamber to capture electrons produced when a WIMP collides with a particle of normal matter and causes it to recoil. (Unit: 10)

In the simplest picture, the normal matter in our Milky Way galaxy rotates through a stationary halo of dark matter. If we could easily detect dark matter on Earth, we would see a “wind” of dark matter coming from the direction in which our solar system is moving through the Milky Way. Since the constellation Cygnus orbits around the galactic center ahead of our solar system, the dark matter would appear to be streaming at us from Cygnus. Thus, a directional experiment would see nuclei recoiling away from Cygnus. Measuring direction in this way not only would yield information about dark matter, but it also would make the experiment more sensitive, since no background source of radiation would follow the trajectory of Cygnus. In addition, a detector able to measure direction would begin to explore the velocity distribution of dark matter in the Milky Way much more directly than ever before. A directional detector would work, in effect, as a dark matter telescope.

Collider and satellite searches for dark matter

If WIMPs comprise dark matter, high-energy collisions may also shed light on their nature. Both the Tevatron and the Large Hadron Collider (LHC) may be able to produce WIMPs by colliding protons and antiprotons or protons and protons at energies high enough to fuse the quarks inside those particles into WIMPs. Teams at both the Tevatron and LHC will continue sifting through vast amounts of data, hoping to find evidence of WIMPs in their detectors.

Fermi Gamma-ray Space Telescope

Figure 18: NASA’s Fermi Gamma-ray Space Telescope has spotted an excess of normal matter particles that may have arisen when WIMPs annihilated each other.
Source: © NASA/Fermi Gamma-ray Space Telescope.
The Fermi Gamma-ray Space Telescope, launched in 2008, looks at the most energetic photons in the universe. These high-energy photons are expected to originate from exotic objects such as supermassive black holes. Gamma rays are also produced when electrons and their antimatter counterpart, positrons, annihilate. In some scenarios, WIMPs will annihilate into electrons and positrons, which in turn annihilate into gamma rays. Excess gamma rays in regions of space expected to contain a high concentration of dark matter would be a strong suggestion that the dark matter is made of WIMPs. (Unit: 10)

Finally, it may be that WIMP dark matter particles annihilate each other in the galaxy to produce extra amounts of normal matter (such as protons, electrons, antiprotons, positrons, neutrinos, or gamma rays), which could be detected from Earth or in space-borne experiments. Separating these extra normal particles from cosmic rays is difficult. But in the last year, two satellite experiments may have observed some hints of dark matter. NASA’s Fermi Gamma-ray Space Telescope, launched in 2008, discovered evidence of more high-energy electrons and their antimatter positrons than anticipated. The excess could stem from WIMP annihilations. About the same time, the European Payload for Antimatter Matter Exploration and Light-nuclei Astrophysics (PAMELA) satellite, launched in 2006, detected more positrons than expected. However, it is much too early to tell whether either satellite has actually seen dark matter.

7. Dark Forces

WIMPs and axions are compelling candidates for dark matter particles, but neither one has been detected experimentally. While ever-more sensitive laboratory experiments are conducted, theorists constantly develop new models, sometimes inventing new possibilities for dark matter. A plausible third candidate for dark matter has recently emerged, called dark forces. The dark forces theory is really an extension of the supersymmetry theory we first reviewed in Unit 2. In addition to the heavy WIMP particles, the latest version of supersymmetry theory posits the existence of light particles called the Greek letter phi. If the exists, it is predicted to be more massive than two electrons, but less massive than 200 electrons. It would interact with other particles just like a photon, but with an interaction strength at least 1,000 times weaker.

The idea for dark forces arose when an Italian cosmic ray experiment called “DAMA/LIBRA” (DArk MAtter/Large sodium Iodide Bulk for RAre processes) observed energetic electrons and positrons unaccompanied by antiprotons. Ordinary WIMPs cannot explain this DAMA/LIBRA result, but in the dark forces version of supersymmetry, heavy WIMP particles would annihilate with one another and produce high-energy φ particles. The φ particles would then decay into energetic electron-positron pairs.

 

Figure 19: A technician works on detectors for the DAMA/LIBRA project, which stimulated the theory of dark forces.
Source: © DAMA/LIBRA.
A technician works on detectors for the DAMA/LIBRA project. DAMA/LIBRA uses 250 kg of sodium iodide inside a high-purity copper shield that sits in the Gran Sasso mine in Italy. In 2008, the DAMA/LIBRA collaboration announced a result that could not be explained by ordinary WIMPs, challenging theorists to come up with alternative explanations. (Unit: 10)

The emergence of the dark forces theory has led to a series of new ideas for current and new experiments. If the theory is correct, WIMPs produced in high-energy collisions at the Tevatron and Large Hadron Collider would decay to several particles. Those particles would then decay to a large number of electrons, positrons, or muons, giving a clear experimental signature. At low-energy colliders, the would manifest itself in rare decays of known particles. In lower-energy electron-proton collisions, extra electrons and positrons in the decay products would indicate that the collision produced φ particles. Physicists would need to gather a huge amount of data to test dark forces. Because the φ interacts with one-thousandth the strength of a photon, only one event in a million might contain a φ.

Although the dark forces theory arose to explain cosmic ray experiments and the DAMA/LIBRA results, it would still be viable even if the experimental basis were shown to be a fluctuation or result of a known process. Like axions and supersymmetry, the dark forces theory as yet has no solid experimental basis. However, it is a perfectly reasonable description of dark matter in every respect and should be experimentally pursued.

Supersymmetry theory has suggested other possible sources of dark matter. They include the gravitino, the supersymmetry partner of the graviton, and the electrically neutral neutralino, a particle with very small mass. Like other dark matter candidates, they have so far defied experimental efforts to detect them.

8. The Search Continues

Dark matter remains an active area of research, with the results of current and planned experiments eagerly anticipated by the entire physics community. In coming years, large-scale studies of galaxies like the continuing Sloan Digital Sky Survey and the Anglo-Australian 2dF Galaxy Redshift Survey, supported by numerical simulations, will continue to develop our picture of the way in which dark matter is distributed over galactic and larger distances. Better cosmological measurements of supernovae and the cosmic microwave background will sharpen our knowledge of cosmological parameters, in particular the total amount of normal and dark matter. Detailed measurements of galaxies using gravitational lensing will tell us more about the distribution of dark matter within a galaxy. New space probes, nuclear recoil, and axion experiments will continue to hunt for evidence that dark matter interacts with normal matter in ways other than gravity. In addition, colliding beam accelerators, particularly the LHC, will try to make dark matter particles in the laboratory.

 

2dF Galaxy Redshift Survey

The Two-degree-Field Galaxy Redshift Survey released this data set in 2003. The survey measured the Doppler shift (redshift) of 100,000 galaxies in thin slices of the sky (indicated in units of hour angle around the edge of the image) out to a distance of 2 billion light-years. The survey results show how galaxies are distributed in huge clusters and long filaments, leaving large empty voids in some regions of space. The size of these structures is telling—if the universe were entirely made of normal matter, even larger structures would be expected to emerge. (Unit: 10)

If some or all of the dark matter consists of WIMPs, the final picture will not emerge from any single endeavor. Rather, physicists will combine evidence produced by many different measurements to understand just what these new particles are. Even though the sensitivity of searches for dark matter on Earth has improved by about a factor of ten every few years over the past two decades, it might still take some time before the first convincing laboratory evidence for dark matter appears. Following first indications, further measurements using different targets will sharpen the picture. But conclusive evidence will require a directional signal as well as consistency with cosmic ray experiments, astronomical observations, and exploration of the Terascale from collider experiments.

What if dark matter consists of axions? In that case, ADMX may make an observation in the next 10 years—if dark matter conforms to theory.

Of course, dark matter may be something completely new and unexpected. It may be a different manifestation of dark energy or it may be that we never find out. Dark matter raises the question of what it means to discover something. We already know what dark matter does: how it regulates the structure of galaxies and clusters of galaxies. This knowledge will certainly improve steadily as we make more astronomical observations. Learning what dark matter actually is, however, will take a big jump—one that we may never make. What does it mean for science if we find that we can’t make this jump? Most likely, we will never have to answer that question. Physicists will continue to probe the universe in expectation of eventually unearthing its deepest secrets.

9. The Math

The Virial Theorem

The virial of a particle is defined as the product of the particle’s momentum, p, and its position, x. The virial theorem states that if the time average of a particle’s virial is zero, then the particle’s kinetic energy, T, is related to the product of the net force, F, acting on the particle and the particle’s position:

 

T= -½F•x

 

For particles—or galaxies—moving under the influence of a gravitational force, ½F•x is equal to the particle’s gravitational potential energy, which depends on the total mass inside the particle’s orbit. Fritz Zwicky used the virial theorem to relate the total average kinetic energy and total average potential energy of the galaxies of the Coma cluster. He argued that the virial for a pair of orbiting masses is zero, and used the principle of superposition to extend the argument to a system of interacting mass points. This allowed him to use the position and velocity measurements he carried out to find the mass of the galaxy cluster.

10. Further Reading

  • W. Goldstein, et al., “Neutrinos, Dark Matter and Nuclear Detection,” NATO Science for Peace and Security Series, Part 2, 2007, p.117.
  • Wayne Hu and Martin White, “The Cosmic Symphony,” Scientific American, Feb. 2004, p. 44.
  • Gordon Kane, “Supersymmetry: Unveiling the Ultimate Laws of Nature,” Basic Books, 2001.
  • Stacy McGaugh, “MOND over Matter,” Astronomy Now, Nov./Jan. 2002, p. 63.
  • Mordehai Milgrom, “Does Dark Matter Really Exist?,” Scientific American, August 2002, p. 43.

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Produced by the Harvard-Smithsonian Center for Astrophysics Science Media Group in association with the Harvard University Department of Physics. 2010.
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  • ISBN: 1-57680-891-2