Dark matter and dark energy together make up some 96 percent of all the mass and energy in the universe. But their nature remains a mystery. Dark matter was proposed decades ago to explain why galaxies hold together, while dark energy is a more recent prediction which explains why the universe is not just expanding, but is doing so at an ever-increasing pace.
Ever since the dawn of astronomy observers have wanted to know the distance to the stars and the scale of the universe. The methods by which these distances have been measured since the early days of astronomy provide a little history of its own.
The distance to objects in our solar system can be measured by the method of parallax, whereby two images of the same object can be viewed from two places a known distance apart. The Moon, for example, can be seen at the same time against a different star background from two widely spaced points on the surface of the Earth. The difference in its position against the distant stars can be used to calculate its distance from Earth.
Measuring a parallax for the planets is more difficult, but the method still provides a way of finding their distance from the Earth. Measuring a parallax for the stars was a far more difficult problem. It took centuries to solve, but with modern detection techniques the distance of stars about 100 light years away can also be measured by the method of parallax; the baseline used for the stars is a diameter of the Earth’s orbit.
In the 20th century, methods to calculate longer distances became available. The first was developed by Henry Norris Russell (1877–1957), who with Ejnar Hertzsprung (1873–1967) discovered the relationship between the magnitudes and spectra of stars. Confusingly called the “spectroscopic parallax” method, it has little to do with trigonometry, relying instead on the observed properties of stars. The H-R diagram provides the correlation between a star’s spectral type and its absolute magnitude, by which we mean its magnitude if it was located at the “standard” distance of 10 parsecs from the Earth. Using the distance–magnitude relationship, the star’s distance can be inferred from its observed brightness. While less precise than trigonometric parallax, this technique enabled astronomers to estimate distances as far away as 10 kpc.
To measure distances beyond 1 kpc and as far away as 30 Mpc, the best technique is the one developed by Arthur Eddington (1882–1984) and Henrietta Leavitt (1868–1921) using the Cepheid variables. The Cepheids are variable stars glowing brighter and dimmer over a period of several weeks or days. They have a well-known period–luminosity relationship; thus if we know the period of variability of a Cepheid then we know its absolute luminosity. By comparing this with the luminosity observed from Earth we can calculate its distance. Cepheids separate into two types, commonly known as population I and population II, according to their luminosity. Both are useful distance indicators, but the brighter population I Cepheids cover a much wider range of distance and we can observe them in our neighboring galaxies, giving us indicators to estimate the distance to the nearer galaxies.
Other techniques have been developed to measure galactic distances. In the 1970s Brent Tully and Richard Fisher discovered a relationship between the properties of the 21 cm hydrogen line observed in the radio spectrum of a spiral galaxy and its intrinsic luminosity of the galaxy. The hydrogen line is emitted from cold clouds of gas that lie between the stars in the disc of a spiral galaxy and which, like the stars, rotate around the center. This rotational motion is detectable as a broadening of the 21 cm absorption line due to the Doppler effect, and the amount of rotation (and hence the observed width of the line) is driven by the internal gravity of the galaxy. The broader the line, the higher the galactic mass driving the motions, and thus the larger the intrinsic luminosity of the galaxy. It was possible from this broadening effect to calculate the absolute magnitude of a galaxy at the standard 10 kpc, and by comparing the absolute magnitude to the observed magnitude the distance of the galaxy could again be estimated. The Tully–Fisher technique can be used to measure distances up to 150 Mpc.
There is another very useful technique that can be used for measuring distant galaxies. It is based on the observation of the rare event called a supernova Type 1a. The supernovae are so bright that they can be seen in galaxies at distances of well over 1000 Mpc. These supernovae are due to a white dwarf in a binary system accreting matter from its secondary until it is at the Chandrasekhar limit of around 1.4 solar masses for a catastrophic core collapse in a supernova explosion. As the same mass is involved in each explosion, the event follows a similar pattern in terms of the intrinsic luminosity of the outburst and how this is related to the rate at which this brightness subsequently fades away. Thus the observations of the apparent magnitude of a supernova explosion and the rate at which it fades enable a calculation to be made of its distance.
All of these distance-measuring techniques neatly overlap with each other so that a three-dimensional image of the universe is gradually being built up by astronomers. However, there is still one important technique that needs to be discussed; this is the redshift of the distant galaxies, and it is of great significance for it provides the key to the age of the universe.
During the 1920s Edwin Hubble (1889–1953) and Milton Humason (1891–1972) recorded the spectra of many galaxies using the 2.5-meter (100 in) telescope at Mount Wilson. As early as 1917 Vesto Slipher (1875–1969), working at the Lowell Observatory in Arizona, discovered that the spectra from the galaxies were noticeably shifted toward the red end of the spectrum. He rightly concluded that the galaxies were moving away from us. Hubble, however, used the Cepheid variables technique to estimate these distances and derive the distance–redshift relationship known as Hubble’s law. This relationship can also be used to derive an estimated distance of a galaxy from its much more easily observed spectral redshift.
During the 20th century, a great deal of effort and research were devoted to an accurate determination of Hubble’s constant, culminating in a key project using the Hubble Space Telescope. The best estimate for Hubble’s constant is now generally taken as their result of 70 +/- 7 km/s/Mpc, published in 2001. The significance of this result lies in the fact that the inverse of Hubble’s constant gives an estimate for the age of the entire universe.
Consider a distant galaxy rushing away from us. If we know its distance from us and its speed of recession, then the time it has taken to separate from us and the rest of the universe after the Big Bang is given by:
Time = (the distance from us) / (its speed away from us)
As Hubble’s constant is simply the averaged ratio of speed/distance determined from a large number of galaxies, its inverse yields the required time. If 1/(H0) = (1/70) seconds Mpc/km, and using the unit conversion factors 1 Mpc = 3.09 × 1019 km and 1 year = 3.156 × 107 s, we can estimate an age of the universe:
1 / (H0) = (1/70) × (3.09 × 1019) / (3.156 × 107) years
= 1.4 × 1010 years (or 14 billion years).
Hubble’s constant thus provides a good first approximation for the age of the universe. However, as we shall see later in this chapter, the study of the expansion of our universe was going to throw up some surprises for astronomers.
We have seen how the spiral structure of our own galaxy, the Milky Way, has been discovered. The Sun lies well out in one spiral arm of the galaxy. At the center is a great bulge with the spiral arms lying in a disc around it. The bulge is surrounded by a halo of globular clusters consisting of old red stars, but the spiral arms contain younger blue-colored stars. Between the young stars in the disc of the galaxy are clouds of cold, molecular gas and dust which are the reservoir from which stars form. The existence of the dust had long been known from the dark patches apparent within the Milky Way, showing how the dust clouds can be so dense that they completely obscure the light from the stars behind them. The presence of vast quantities of gas was revealed from observations of the luminous nebulae surrounding clusters of newly formed young blue stars. The energetic ultraviolet light from the stars heated and ionized the gas atoms, which produced their own light when they later recombined, causing the nebulae to shine. Analysis of the emission from the gas enabled astronomers to measure the temperatures and densities of the gas nebulae; much of the radiation comes from “forbidden” transitions of ions of common elements that can never be observed in the laboratory since they require an extraordinary low density to occur.
Away from regions of active star formation, the gas clouds remain cold, and thus hidden to optical observations as they are either neutral or even molecular. The discovery of the extent of the neutral hydrogen in our galaxy and others had to await the development of radio astronomy after the Second World War. During the 1940s the theory of the 21 cm hydrogen line was developed. This is a spectral feature in the radio waveband that is generated by what is called a “spin flip” transition of electrons in hydrogen atoms. This is a spontaneous event that occurs very rarely—an individual atom may undergo such a change only once every ten million years—but it is still detectable because of the vast quantity of hydrogen in the galaxy. As radio astronomy developed radio emission lines from more complex molecules were discovered.
Observations of the 21 cm line were used to map out the density and distribution of gas in the plane of the galaxy at much further distances than could be obtained by studying the distribution of the stars. It is much easier to measure the Doppler shifts from the 21 cm line of different clouds of hydrogen than by amassing the shifts from thousands of individual stars, so the radio observations were also of major importance for determining the rate at which our galaxy rotates, and how this changes with distance from the center.
As we saw with the Tully–Fisher distance indicator, the rate at which a spiral galaxy rotates is directly due to its gravitational mass. Any individual object in orbit around the center of a galaxy—such as a neutral gas cloud, nebula or star—is responding to the gravity of all the mass at smaller radii. Thus by plotting the way the rotational velocity of objects in a galaxy changes with radius (known as a “rotation curve”), astronomers knew they could estimate the entire mass of a galaxy, and how it was distributed. Early attempts to determine the rotational velocity of galaxies used the Doppler shift observed from the absorption lines in stellar spectra, or the narrow emission lines of nebulae. By the late 1970s Vera Rubin (b. 1928) and her colleagues established a problem with the observed rotation curves of galaxies, which was later confirmed by more comprehensive observations using the radio 21 cm line as a tracer of the internal galactic dynamics.
All the results showed that the outer parts of the disc of all spiral galaxies (including our own) were rotating much faster than expected. They had sufficient speed to escape completely from the galaxy’s gravity, but they remained attached. The only explanation was that there was far more gravitational mass in the galaxy than was indicated simply by the amount of stars and gas directly observed. A large quantity of invisible matter was required that did not give off radiation at any wavelength; and in all spiral galaxies the amount of such “dark matter” was estimated to be greater than the visible mass by a factor of ten. But what was all this invisible matter?
The idea of “missing matter” was not a new concept, as it had been discovered as early as the 1930s when Fritz Zwicky (1898–1974) was studying clusters of galaxies. The motions of individual galaxies within a cluster are due to the gravitational attraction of the galaxy to the mass of the rest of the cluster. Zwicky was able to show that again, the galaxies were moving too fast to be responding simply to the gravity of the visible galaxies in a cluster. There had to be much more mass present, but this time it outweighed the observable components by a factor of over 100. Zwicky’s original results have long since been confirmed for many clusters of galaxies, from observations of the internal dynamics of a cluster and also from studies of gravitational lensing.
Although it is well established that most of the gravitational mass in the universe is invisible at all wavelengths, the nature of the dark matter remains an open question. Possibilities range from “ordinary” matter which is comparatively well understood, such as brown dwarfs (failed stars), large planets, neutron stars or black holes; to far more exotic (and hitherto undiscovered) subatomic particles such as axions or new types of neutrinos. The latter explanation proposes that a better understanding of particle physics is fundamental to explaining the motions of entire galaxies and clusters of galaxies.
Einstein’s theories reinvented our interpretation of gravity not so much as Newton’s “force at a distance,” but as the way in which space and time warp around the location of a massive object. An important consequence is that light traveling through space will sometimes find itself following a warped path, and indeed the observations of the deflections in the positions of stars whose light passed near the Sun during the 1919 total solar eclipse was the first observational confirmation of Einstein’s theory. Today astronomers observe much more complicated distortions of the light as it passes by a large mass on its journey to Earth. Galaxies that lie behind (and at a far greater distance than) a cluster of galaxies sometimes have their image both magnified and greatly distorted as their light passes through the cluster—this is known as gravitational lensing. Often this distortion takes the form of multiple arcs and arclets. However, the amount of distortion traces the total gravitational rather than the visible mass, so a detailed mapping of the positions of such gravitational mirages can reveal the presence and distribution of dark matter within a cluster.
Since the first studies of galaxies in the early part of the 20th century, it was obvious that the galaxies were not distributed uniformly on the sky—even when located well away from the obscuring effects of our Milky Way. This “clustering” of galaxies was first properly quantified in the 1950s by George Abell (1927–83), who created an extensive catalog of clusters from a detailed visual examination of photographic plates of the sky. His work also demonstrated that there was a range in cluster properties—not just in the number of galaxies, but also the shape and physical size of a cluster.
Abell’s work—and that of other astronomers in the mid-20th century—was limited to the study of a projection of the sky onto two dimensions. Even so, it was clear that the distribution of clusters was also non-uniform in the sky, with regions where clusters themselves seemed to form immense structures known as “superclusters.” A full mapping of the true three-dimensional structure of the universe, however, involves the knowledge of the distance to all the galaxies. This is done most economically by estimating the distance from a measured redshift via Hubble’s law; even so, the determination of the redshift of a sufficient number of galaxies is a huge observational undertaking. For this reason, early surveys were necessarily limited to only small regions of the sky. One of the first attempts at a comprehensive redshift survey was begun by John Huchra (b.1948) and Margaret Geller (b.1947) in the 1980s, and it eventually grew to include over 14,000 galaxies. The resulting map showed some amazing structures, including the discovery of what became known as the Great Wall—a broad filament of clusters and galaxies about 200 million light years distant, which extends over 500 million light years long.
This was just the first (and not the largest) of many such walls and filaments now known to permeate the entire large-scale structure of the universe, and which surround regions of empty space of a similar size, known as “voids.” Today such surveys map out this cellular pattern of structure right across the universe.
The presence of dark matter was discovered by observing the way motions of astronomical objects are dictated by the gravity of an invisible mass. In the same way, the orbital motions of stars and gas at the very core of many galaxies (both spiral and elliptical) have revealed the presence of immense masses at the center. Our own galaxy is thought to have a dark object at its center with a mass of around 2.5 million solar masses but contained in a region less than 20 light days across. Such supermassive black holes are found with masses up to several billion solar masses, and they are thought to lie dormant at the center of nearly all massive galaxies. A galaxy where the central supermassive black hole is still accreting matter is radically changed in appearance, having a very bright core, and is known as an “active” galaxy.
By the latter part of the 20th century, astronomers had thus gained a much better understanding of the mass content (both visible and invisible), the structure and extent, and the rate of expansion of the universe. It was only natural to return to the fundamental question that had been asked many times before. Will the universe last forever or will it stop expanding and collapse into itself? For many years cosmologists debated about whether the universe is “closed,” so that it will eventually fall back on itself and end in a “Big Crunch,” or whether it is “open” and will continue expanding for all time at an ever increasing rate. The outcome depends on the mass content of the universe, and thus whether or not there is enough mutual gravitational attraction eventually to pull everything back together. A further option—favored by most astronomers because of the observed isotropy and homogeneity of the cosmic microwave background—was the “flat” universe; one which lies on the boundary between the open and closed universe.
Consequently, in the 1980s and 1990s, ambitious programs tried to measure the expansion of the universe more precisely than before, with the aim of determining its eventual fate. By attempting to extend Hubble’s law to far further galaxies than had been possible previously, astronomers aimed to see if the relationship between velocity and distance still held, or whether it indicated the first stages of a gradual slowing, or deceleration, that would result from a flat or closed universe. The research was undertaken by two teams of astronomers, one led by Saul Perlmutter (b. 1959) at Berkeley and the other led by Brian Schmidt (b. 1967), then at Harvard Observatory. Both used observations of Type 1a supernovae to establish the distance to very early galaxies, and they independently discovered an astounding result. The expansion of the universe was not found to be continuing at a constant rate, nor was it beginning to slow down. Astronomers were amazed to find that the rate of expansion was increasing with time—it had been accelerating for the last six billion years! This result, announced in 1998, changed the face of modern cosmology, and has since been confirmed by many more and different observations to extend Hubble’s law using different ways of estimating distances.
In order to begin to understand why this unexpected acceleration had occurred, it was necessary to introduce a new concept which went by the (somewhat misleading) name of “dark energy.” Einstein’s famous equation E = mc2 shows how matter and energy are related, and in some sense can be considered as equivalent entities. Astronomers were astounded to discover that to produce the accelerated expansion, dark energy had to account for around three-quarters of the entire mass–energy density of the universe. But a true understanding of dark energy remains elusive, although there are a number of current ideas.
For centuries it has been known that gravity is an attractive force; unlike electricity and magnetism it is not possible under normal conditions for gravity to be repulsive. However, suppose the fundamental nature of gravity changed from an attractive to a repulsive force on the very largest (and truly astronomical) distance scales. Then there might come a point when the galaxies drew a sufficiently immense distance apart that they began to be pushed away faster and further by gravity. Such ideas echo Einstein’s original, but misguided, attempt to include in his equations a cosmological constant representing an anti-gravity that prevented the universe from evolving. It is possible that a modified form of the cosmological constant could be reincorporated in our understanding of gravity to account for the dark energy.
An alternative explanation is suggested by the expectation from particle physics that completely empty regions of space can still produce a “vacuum energy.” It is thought that pairs of particles and their associated anti-particles are continually created out of the vacuum, only to almost immediately annihilate each other and disappear. As they do so, they produce a minute outward pressure. Averaged over the entire voids of the universe, there would be sufficient such “vacuum fluctuations” to produce enough pressure to push the universe further apart. Since this is a property of empty space, as the universe grows larger and the voids grow bigger, the effect of vacuum energy thus becomes increasingly dominant over that of gravity. However, a better understanding of particle physics is required before the vacuum energy theory can be shown to be a reality—current estimates suggest it would be much more powerful than observed even in our accelerating universe. Another rival for dark energy is the suggestion of a new force field which goes by the name of quintessence. Scientists are debating a rigorous mathematical description of quintessence, but it may be a force whose strength and importance changes through the history of the universe. It could be linked to the very early inflationary period of expansion thought to have occurred immediately after the initial Big Bang; if quintessence then lay relatively dormant for a period, we could be in another active phase producing the current accelerated expansion.
Whatever the true nature of the dark energy, if it continues to exert its influence we can speculate on a bleak future for our universe. The galaxies will continue to fly further and further apart ever faster, perhaps leading to an eventual “Big Chill.” Even worse, if the effects of dark energy become increasingly important, it may begin to dominate over gravity on smaller scales, such as within galaxies—leading to a “Big Rip.”