Gravitational Lenses

Type of physical science: Gravitational Lenses, Einstein, Albert, Theory of relativity, general, Gravity, Astronomy and astrophysics

Field of study: Cosmology

Gravity can bend the paths of light rays and focus them into an image. Gravitational lenses are particularly useful in studying galaxies, dark matter, quasars, and cosmology.

Overview

It is convenient to begin the story of gravitational lenses by reviewing some history of the concept of the gravitational force. In the fourth century b.c.e., the great Greek philosopher Aristotle taught that, whether something rises into the air as fire does, or falls to the earth as rain does, it is simply striving to reach its natural level. It seemed obvious to Aristotle that the larger the thing's weight, the greater its capacity would be to strive to reach its natural level. He proposed that the consequence of this was that the speed of a falling object should be proportional to its weight. If an object weighed twice as much as another object, Aristotle reasoned, it should fall twice as fast.

Nearly one thousand years later, in the sixth century c.e.., John Philoponus wrote a commentary on Aristotle's views in which he stated that falling weights all fell with about the same speed, even if one was twice as heavy as another. In spite of this, Aristotle's ideas remained popular. A second thousand years passed, and in 1586 the Dutch scientist Simon Stevinus noted that he had taken two balls of lead, one ten times heavier than the other, and dropped them at the same time from a 10-meter height. He said that he could tell by the sounds of the balls striking a board below that they had struck at the same time. In 1632, Galileo Galilei described a similar result for balls of different weights dropped from the leaning tower of Pisa. It is largely through Galileo's efforts that the Aristotelian rules of motion were overthrown.

Why did it take two thousand years to reach this understanding? One reason is that Aristotle's rule matches our experience with other forces. For example, if one horse can pull a loaded wagon at a certain speed, two horses can pull it faster. For a more sophisticated example, consider two baseballs floating near each other in outer space. Suppose that one million electrons are removed from one ball and placed on the other. Since one ball is now negatively charged and the other ball is positively charged, they will attract each other and begin to draw together. If two million electrons were transferred, the attractive force between them would be larger, and they would draw together faster. The fact that Aristotle was wrong in claiming a similar result for gravity is astounding, and it shows that gravity is especially different from other forces.

In the seventeenth century, Isaac Newton formulated his law of gravitation and his laws of motion. Newton's law of gravitation states that the gravitational force on a body is larger if the body's mass is larger. However, Newton's laws of motion state that a given force acting on a body will produce a smaller acceleration if the body's mass is larger. On August 2, 1971, astronaut David Scott stood on the surface of the Moon and held out a geologist's hammer in one hand and a falcon feather in the other. He released them simultaneously, and since there was no air resistance, they struck the lunar soil simultaneously. Thus, even though the Moon's gravitational pull on the hammer was greater than its pull on the feather, the greater mass of the hammer resisted the effect of that pull more than the mass of the feather did.

What effect might a gravitational field have on a body with no mass? Photons are tiny energy packets of light, and they have no mass. According to Newton's law of gravitation, the gravitational force on a massless particle is zero, so gravity should not affect photons. Yet what if Newton's law of gravitation is incomplete? Since, in the absence of air resistance, bodies of various weights all fall at the same rate, might a massless particle also fall at this rate? Albert Einstein provided motivation for this line of thought with his principle of equivalence. Einstein speculated that conditions inside a rocket ship accelerating at a rate of 1 gravity (g) would be indistinguishable from conditions caused by gravity on Earth. (It is assumed that the ship is far from anything that might otherwise affect it and that g equals the acceleration of gravity at the Earth's surface.) First, suppose that the ship is at rest and that a scientist aims a laser beam parallel to the floor of his cabin and notes the spot where the beam strikes the far wall. If this experiment is repeated while the ship accelerates at 1 g, Einstein reasoned, the light beam would appear to curve downward and would strike the far wall below the first spot. The reason is that although the light beam would appear to travel in a straight line as seen by an observer at rest outside the ship, for a shipboard observer, it must appear to get closer and closer to the floor, since the floor would be accelerating upward toward the light beam. Einstein's equivalence principle predicts that the path of a light beam must also curve in a gravitational field. The capacity of a gravitational field to bend light is the heart of the gravitational lens phenomenon.

Light flows outward from a star in all directions. As an observer moves away from a star, it looks dimmer and dimmer because an ever smaller fraction of the starlight enters the observer's eye. The star would look brighter if it were viewed through a glass lens that gathered light rays over a large area and bent them so that they entered the observer's eye. In a similar fashion, gravity can collect bundles of light rays and focus them into an image. A glass lens, such as the fish-eye lens used in the peep hole in some doors, may produce a distorted image. Gravitational lenses often produce distorted images, and they may also produce multiple images of a single source.

Einstein put this subject on firmer footing with his general theory of relativity. He showed that rather than interpreting gravity as a force, it is better to interpret it as a manifestation of curved space. A simple example will at least suggest that this is possible. Suppose that two brothers decide to do an experiment in the Pacific Ocean. They each take a ship and carefully position them at the equator such that one ship is 100 kilometers east of the other. Then, beginning at the same time, both sail due north. As time passes, they will find themselves drawing closer and closer together. In fact, if they could reach it, they would meet at the North Pole. The brothers might offer two different explanations for this result. On one hand, they might say that since Earth is a sphere, all north-south lines must meet at the pole, so of course their ships would draw closer together and would meet at the pole. On the other hand, they might suppose that Earth were flat, and that since their paths both were perpendicular to the same straight line (the equator), those paths were parallel and should never meet. They might conclude that a sideways force must exist that drew them off their straight-line paths and pulled them together. In an analogous fashion, gravity can be interpreted either as a force or as a manifestation of curved space.

According to Einstein's general theory of relativity, the presence of mass causes space itself to warp and curve. The fact that different weights all fall at the same rate is the consequence of those weights all moving along the same curved space. Even light, which has no mass, follows a path that appears to bend because it is traveling through curved space. Einstein predicted that the path of starlight passing near the Sun would be bent, and this was confirmed by measurements taken during the total solar eclipse of 1919. Seventeen years later, in 1936, Einstein published a one-page paper on gravitational lenses. He showed that if a star passed in front of a more distant star, an observer in exactly the right position should see a ring image of the distant star around the lensing star. Since the ring would be too small to be seen directly, the observer would simply see the lensing star appear to become brighter. Decades passed before technology had advanced enough to show that Einstein had correctly predicted the gravitational microlens.

Applications

The gravitational field of a galaxy or even a cluster of galaxies can produce remarkable lens effects. The first double quasar was discovered by Dennis Walsh, Robert F. Carswell, and Ray J. Weymann in 1979. Since then, several other multiply imaged quasars have been found, including the famous "Einstein cross," discovered with the Hubble Space Telescope in 1985. The Einstein cross consists of four faint blue images of a quasar symmetrically placed around a much brighter red elliptical galaxy. It is likely that a supermassive black hole at the center of the elliptical galaxy is the primary lens. A second crosslike quasar called "the cloverleaf" was found in 1988. If a dozen such crosses can be found, astronomers can probably use measurements of their properties to learn the density of matter in the universe.

In 1986, a new type of lens was discovered. Dozens of blue arcs were found in a compact cluster of galaxies. Gravitational fields of hundreds of galaxies in the cluster combined to form a huge gravitational lens, and the blue arcs are images of galaxies five to ten times farther away than the lensing cluster. The blue color of the arcs shows that these very distant galaxies are dominated by young stars. Except quasars, which are brighter, these arcs are images of the most distant galaxies ever seen. The sources for the blue arcs are probably normal galaxies that would be too dim to be seen if the gravitational lens did not concentrate and focus their light. Since light from an object billions of light-years away has taken billions of years to reach Earth, this kind of gravitational lens gives observers the opportunity to learn what galaxies were like when they were young. Several examples of clusters of galaxies with blue arcs are now known.

Astronomers in recent decades have discovered mounting evidence that more than 90 percent of the matter in the universe is "dark" matter. The dark matter is obviously present, because its gravitational effects are detected--but exactly what dark matter is is currently unknown. It is called "dark" matter because no light from it has been identified. In fact, no kind of radiation emitted or absorbed by dark matter has yet been identified. This is obviously very puzzling, since dark matter must be the dominant form (or forms) of matter in the universe. Gravitational lenses can provide some information on dark matter. The visible matter in the lensing clusters of galaxies described above is not enough to form the blue arcs. Dark matter must also be present. Model calculations of gravitational lenses that can produce these arcs show that the dark matter must be distributed in the cluster in about the same way as the galaxies. That is, dark matter is part of a galaxy, or at least it congregates around galaxies.

It is possible that at least part of the dark matter in our galaxy consists of many faint objects such as small, red stars, white dwarf stars, brown dwarf stars, or rogue planets. (Rogue planets wander through space instead of circling a star.) The orbits of bright stars in the outer parts of our galaxy show that much of the dark matter must form a tenuous halo surrounding the visible galaxy. If a white dwarf in this halo passed directly in front of a more distant star, the dwarf would act as a microlens causing the distant star to grow brighter for a period of days to months. The exact period depends upon such things as the mass of the lens and on how fast the dwarf and the lensed star move with respect to the observer.

Since the alignment of source, lens, and observer must be quite precise, it cannot be expected to occur very often. Any project to observe such microlensing events must monitor millions of stars nightly to have a reasonable hope for success. A few groups do exactly that. Two of these projects are called MACHO (Massive Astrophysical Compact Halo Objects) and OGLE (Optical Gravitational Lensing Experiment). The MACHO project monitors nine million stars in the Large Magellanic Cloud (a satellite galaxy of the Milky Way) and ten million stars in the Galactic Bulge (the nuclear bulge of our own galaxy, the Milky Way). The OGLE project monitors stars of the Galactic Bulge.

Each clear night, these projects make electronic pictures of rich star fields containing millions of stars. Data is fed into computers that make corrections for different viewing conditions and then compare the brightness of each star to its normal brightness. Some stars are variable by nature. These must be identified and removed from candidacy for lens events. Variable stars can be identified because they change brightness by different amounts in visible light and in infrared light, and because they grow bright and dim more than once.

By 1996, the various groups had reported about one hundred microlensing events. Preliminary results showed that none of the events was caused by planet-sized bodies, although a few may have been caused by brown dwarfs. Most of the lensing objects were probably cool white dwarfs. In fact, the MACHO group believes that up to one-half of the dark-matter halo surrounding the Milky Way may be cool white dwarfs. These studies must continue for several more years before any reasonably firm conclusions can be reached. Some events were particularly interesting. In one event, the microlensing body moved across the face of a giant star. This provides an accurate measurement of the speed of the lensing body, and this allows a more accurate determination of its location and mass.

Besides the microlensing events, much other useful data have come from these studies. Since all of the stars in a given field had to be monitored for change, vast numbers of variable stars were identified. For example, the number of known Cepheid variables in the Large Magellanic Cloud has been doubled. This is important because the properties of Cepheid variables allow them to be used as distance indicators. Previously, there was some evidence of a bar extending outward from the nuclear bulge of the galaxy. The microlens studies have confirmed this. That is, the stars at the center of the galaxy are grouped into a gigantic sphere, with a huge cylinder of stars extending outward from this sphere on both sides. The Milky Way is a barred spiral galaxy.

Context

Following World War II, radio astronomers began compiling a list of bright radio sources. Eventually, many were identified with supernova remnants such as the Crab nebula or with galaxies such as Centaurus A. By 1962, two radio sources seemed to be related to faint blue stars--a very curious development, since no other stars were known to be strong radio sources. Astronomers often take starlight and spread it out into a rainbow called a "spectrum." Emission lines are particular colors in the spectrum that are especially bright. (An emission line might be compared with a particular tone in a musical scale.) In 1963, Maarten Schmidt realized that the emission lines in the spectrum of one of these "faint blue stars" had been shifted toward the red end of the spectrum. Such a shift is called a "Doppler shift," and it becomes larger the faster the source recedes from the observer. Using the Hubble law, which relates recessional speed to distance, Schmidt calculated that this faint blue star was 2 billion light-years away. In order for it to appear to be as bright as it did, this "star" would have to be far brighter than a normal galaxy. These faint blue starlike radio sources came to be called "quasars"; from the beginning, the great mystery of quasars was how they could possibly produce so much energy. Some astronomers proposed that the Hubble law might not apply to quasars, that they were closer than they seemed and therefore did not need to generate an exceptional amount of energy.

The discovery of a gravitationally lensed quasar in 1979 provided confirmation that quasars are extremely far away. The quasar in question appeared as a close pair called the "twins." The spectrum of each twin showed exactly the same spectral lines with exactly the same red shift. Astronomers had studied some fifteen hundred quasars by that time but had never seen such a well-matched pair. It turned out that the twins looked so much alike because they were two images of the same quasar. The quasar itself is about 8 billion light-years from Earth, while the lensing galaxy is about 4 billion light-years away. Some quasar light is focused by the lensing galaxy to form image A, while quasar light taking a different path is focused to form image B. Conclusive proof that this is the correct model came when one image brightened and the second image then brightened by the same amount 1.48 years later. (One path is 1.48 light-years longer than the other.)

Since the distance to the lensing galaxy was determined through well-established procedures, and since the quasar must be much farther away than the lensing galaxy, the gravitational lens effect proved that this quasar is far away. Not only does the Hubble law appear to give the correct distance to quasars, but careful measurement of the time lag between the flickering of the various images of a quasar should give information about the Hubble constant itself. The determination of an accurate value for the Hubble constant would allow an accurate calculation of the age and size of the visible universe.

Principal terms

BROWN DWARF: A star that has too little mass to produce energy from nuclear fusion

GRAVITATIONAL LENS: A gravitational field that bends light rays and focuses them into an image

HUBBLE CONSTANT: The constant of proportionality in the Hubble law

HUBBLE LAW: The statement that the speed at which distant galaxies are moving away from Earth is proportional to their distances from Earth--that is, the velocity of recession of a distant galaxy equals the Hubble constant multiplied by the distance to the galaxy

MICROLENS: The term used to emphasize that the gravitational lens is the field from a single object such as a star

QUASAR: A distant galaxy seen as it was very long ago when it had a very bright nucleus; the name is based on the acronym "QSR," for "quasi-stellar radio source"

Bibliography

Begelman, Mitchell C., and Martin Rees. Gravity's Fatal Attraction: Black Holes in the Universe. New York: W. H. Freeman, 1996. A beautifully illustrated, popular-level book on gravity as it relates to stars, black holes, galaxies, quasars, and cosmology. Includes a good description of microlensing.

Chaffee, Frederic H., Jr. "The Discovery of a Gravitational Lens." Scientific American 243 (November, 1980): 70-78. This is an account of the discovery of the first gravitationally lensed quasar, Q0957 + 561AB. Describes the careful work that went into proving that the object was actually two images of the same quasar. Both optical and radio pictures of the lens and quasar images are included.

Thorne, Kip S. Black Holes and Time Warps: Einstein's Outrageous Legacy. New York: W. W. Norton, 1994. Thorne is an important scientist in the field, but he has written this book for the nonscientist. It is a marvelous book in which to explore topics that are normally only encountered in science fiction. Thorne has a fantastic description of the gravitational lens effects to be seen near a black hole. The book includes a chronology of events in the development of gravitational theory, brief biographies of key scientists, an excellent glossary of terms, and an extensive bibliography.

Trimble, Virginia, and George Musser. "Clusters, Lensing, and the Future of the Universe." Mercury 24 (May/June, 1995): 6-9. Trimble is one of the world's leading astrophysicists and a well-known writer of popular-level articles on astronomy. This article places gravitational lenses in the general context of the search for the identity of dark matter.

Tucker, Wallace. "A Brightening Star Reveals Dark Matter." Astronomy, August, 1994, 42-45. A simple discussion of possible forms for dark matter. Describes the microlensing projects and includes a picture sequence of a microlensing event. Also includes helpful drawings showing how microlensing works.

Will, Clifford M. Was Einstein Right? Putting General Relativity to the Test. New York: Basic Books, 1986. This easy-to-read book presents the basic results of general relativity, including curved space and the bending of light rays. As indicated by the title, it explains the various experiments that confirm Einstein's theory. Includes a list of books.