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.
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.
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.
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.
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
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.
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).
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.
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.
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.
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.
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.
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.
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.
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.
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
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.
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.
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.
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.
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:
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.
10.2 Dark Matter – Video
Since Swiss astrophysicist Fritz Zwicky first inferred its existence in 1933, dark matter has remained one of the greatest unsolved mysteries in cosmology. Invisible to telescopes, dark matter was detected through its effects on visible matter. Astronomical measurements have shown that dark matter is three-fourths of all matter, but at present no one has yet directly observed a dark matter particle. See how astrophysicists are seeking evidence for dark matter at the center of the Milky Way galaxy and how a new detector almost a mile underground will look for dark matter particles in the laboratory.
Supplementary: Unit 10: Dark Matter — Printable Online Text
Supplemental resource for educators and students