“Space tells matter how to move and
matter tells space how to curve.”
John Wheeler (1911-Present)

On light, fishbowls and gravity
Consider Sid, the fish, in his fish bowl. When you look at Sid through the glass, he looks warped and distorted. The curved glass, of course, causes the illusion: The interface between the water and air refracts the light, and the spherical bowl acts as a lens, producing a magnified, distorted image.

As proposed by Einstein as a consequence of the general theory of relativity, light passing through a gravitational field is affected in a similar way. Though the effect is subtle, it is observed over astronomical distances. Stars or galaxies act like gravitational lenses, magnifying and distorting the images of objects behind them.

Einstein discovered the phenomenon in 1911 using only mathematical logic and physical principles. Immediately, he sought confirmation by experiment, and the best way he realized was to examine the gravitational effects of the Sun. Einstein calculated that a light ray passing very near to the Sun would bend through an angle of 1.74 arc seconds by the gravitational field. (There are 3600 arc seconds in one degree.) (See figure 2.) This would be a very slight change in trajectory, but astronomers could measure it.
Detecting background stars in the glare of the sun is impossible, but such an observation would be possible during a total solar eclipse. In those few minutes of darkness, background stars appearing very near the sun could be photographed. Stars If Einstein was correct, the positions of the stars during the eclipse would be different from their positions when measured at night—by precisely 1.74 arc seconds.

Einstein presented his general theory of relativity to the Prussian Academy of Sciences in 1915. World War I prevented direct communication of the discovery to British scientists, but news leaked quickly. Arthur Stanley Eddington, the director of Cambridge Observatories, received copies of the paper and recognized the importance of Einstein’s work. He immediately promoted the theory and sought means to confirm it.

The astronomer, Sir Frank Watson Dyson realized that the May 29th, 1919 total solar eclipse would provide the ideal opportunity. A cluster of stars, known as the Hyades, would pass near to the sun during this eclipse providing many bright stars to measure. The path of totality would pass across the Atlantic Ocean from Brazil to West Africa. Dyson planned two expeditions to observe the eclipse: one to the island of Principe, off the coast of Spanish Guinea in West Africa and one to Sobral in northern Brazil.

The details of the expeditions are too involved to be recounted here.1 Both teams faced unexpected hardships from the weather and problems with their equipment. The best observations came from photographs taken through a modest telescope with a 4inch diameter objective lens. After careful analysis of the images, Eddington confirmed the gravitational effect. The experiment immediately turned the 40-year-old Einstein into an international celebrity. Einstein himself, in a postcard to his mother, expressed his excitement: “…joyous news today. H.A. Lorentz telegraphed that the English expeditions have actually measured the deflection of starlight from the Sun.” (Coles, 2001)

Since 1919, the Sun’s effect on light has been measured to high precision, and astronomers have discovered examples of gravitational lenses elsewhere. Galaxies and galaxy clusters have been discovered that bend the light of distant objects behind them. Today, the gravitational lensing phenomenon is applied at the forefront of astronomical research to study the universe. Astronomers study lenses to find missing dark matter; they investigate lenses to probe the Big Bang, to measure the expansion of the universe, and to answer such questions as the age of the universe. Gravitational lenses are powerful tools for understanding the universe.

Relatively speaking…
The physics behind gravitational lensing is general relativity, a field invented and developed by Einstein at the beginning of the 20th century. Relativity described the dynamics of space, time, and matter in a completely new way that demolished the foundations set by Isaac Newton in the 17th century.

Newton viewed the universe as a giant machine ticking at a constant rate and functioning in a regular way. Through the application of the laws of physics, Newton believed that all future states of the machine could be predicted. Newton was very successful; with a few simple laws he could describe the motion of billiard balls on a table, or calculate the positions of the planets orbiting the sun.

Einstein changed this concept of the universe completely. Instead of a static, clockwork machine, steadily ticking, Einstein proposed a universe that is dynamic. Space itself, Einstein claimed, responded to the matter it contained. Matter warps space, just as a bowling ball would warp the surface of a trampoline. Not only can the geometry of space not be relied upon, but time itself, Einstein postulated, does not always flow at the same rate. In Einstein’s universe, everything depends on the observer: what you see in the universe relative to yourself is different from what I see relative to myself.

How does this cause light to bend? Under relativity, gravity is not considered to be a force but is a consequence of the matter warping space. A massive object warps space causing other objects to “fall” into the indentation. Gravitational attraction is thus caused by the geometry of space. Light, bound by space, must also follow the curvature. As light travels, the rays follow the contours of space, and thus are bent in the same way that the sun bends a planet’s path. (See figure 4.) Although the concept is abstract (even specialists don’t try to imagine space warping), astronomers have beautifully observed the bending of light by gravity. The powerful optics of the Hubble Space Telescope and the Keck telescopes in Hawaii have caught stunning examples of gravitational lenses in space.

Cosmic gravitational lenses
The shifts in star position measured by Eddington were only a few thousandths of a degree; more dramatic are the deflections of light by galaxies with masses a trillion times the Sun’s mass. Galaxies act as extreme lenses, focusing the light of distant sources. The distortions produced depend upon the alignment of us, the lensing galaxy, and the background source being lensed. In a perfect alignment, the background source appears as a ring around the lensing galaxy. This ring is named the Einstein ring, and an example is shown in figure 5. If the alignment is not perfect, we see multiple images of the background source. To understand why this happens, consider the diagram in figure 3. The images produced typically are extremely distorted into arcs. (Figure 7) As if from a magnifying glass, the images produced also can show different degrees of magnification.

Hundreds of objects in the sky have been discovered that seem to be false images, produced by cosmic gravitational lenses. But how can astronomers be sure, and then how can the false images be differentiated from the real? The first quality that an astronomer notices in a gravitational lens is symmetry. Generally, when there are multiple images, the images are arranged symmetrically; when there are four images, they are positioned at the corners of a diamond with the real object in the center. The next important characteristic is that, although the images may be distorted or magnified, no light is lost through the lensing effect. Thus, the total brightness of each image is the same as the brightness of the actual object. In addition, when the spectra of the images are examined to determine chemical composition, their features are identical. Astronomers can only make guesses at the identities of astronomical objects, but they have many clues to work from.

The first gravitational lens (besides our sun) was not discovered until 1979, and is shown in figure 6. It is a distant quasar imaged twice by an intervening galaxy. (Quasars are galaxies powered by super massive black holes. They are extraordinarily luminous and thus are seen at great distances.) The lens was discovered serendipitously at Kitt Peak Observatory in Arizona by Dennis Walsh, Bob Carswell, and Ray Weymann. The pair of quasars were immediately considered peculiar because of the similarities of the two objects. In the original paper, the discoverers stated, “The two sources show great similarity in their spectral characteristics. A conventional interpretation could regard as coincidence the similarity of emission spectra. … A less conventional view would find the quasars to be two images of the same object produced by a gravitational lens.” (Walsh, 1979) It turned out that their suspicions were correct. New observations have revealed the lensing object, confirming that the two images actually represented one quasar split by a gravitational lens.

Since that initial discovery, many other gravitational lenses have been identified. Today, one of the leading tools in discovery is the Hubble Space Telescope orbiting Earth. Above Earth’s atmosphere, the Hubble Space Telescope is able to obtain much higher resolution observations than can ground-based telescopes, which are affected by atmospheric blurring. In one survey completed by Hubble, astronomers discovered ten new gravitational lenses over an area the size of the full moon. (Ratnatunga, 2001)

Microlensing: Searching for the invisible
Gravitational lenses come in two sizes: micro and macro. Macrolenses are high-mass galaxies or clusters of galaxies, composed of billions of stars; microlenses are compact, low-mass objects, such as a single star. Both types of lenses produce the same imaging effects, but to different degrees. Astronomers detect microlenses within our own galaxy. Stars in are in constant motion and as they cross paths along our line of sight, they cause microlensing events to appear and disappear. If a star is in front of another star, from our perspective we will see a lensing effect and the background star will appear to be distorted. However, because the microlensing star is relatively low mass, multiple images will form, but they will overlap. Generally these effects cannot be resolved and astronomers only observe that the background star brightens.

The events occur randomly and cannot be predicted, making microlensing difficult to study; however, despite the difficulties, there is great motivation for searching for them. With microlensing astronomers can detect objects that may not be possible to detect in any more direct way. For instance, free-floating, Jupiter-sized planets in our galaxy cannot are difficult to observe because they do not emit their own light. Generally they can only be detected via their gravitational effects. If a planet moves in front of a star, the star is lensed. The star may appear to brighten from our perspective on Earth for a short period while the planet and the star are aligned. As the planet moves away, the star dims to its normal brightness. The change in brightness of the star happens in a predictable way distinguishing the microlensing event from other sources of variability (such as variable stars). (See figure 8 for a plot of the characteristic brightness curve.)

Cosmic scales for weighing galaxies
Not merely curiosities, gravitational lenses are useful for attacking many problems. Mass is often difficult to determine for astronomers just from observational data. The gravitational lens, however, gives a direct measurement of mass: the gravitational field dictates the strength of the effect. Astronomers use gravitational lenses to “weigh” the lensing body, and to infer the existence and measure the mass of a body, like a planet or a black hole, from its gravitational effect even if it cannot be seen. Gravitational lensing is the prime way of detecting such “dark” matter.

The methodology for deriving mass from observations of a gravitational lens was first developed by the astronomer Fritz Zwicky in the 1940s, long before the first galaxy acting as a gravitational lens had been discovered. He determined that the angular distance separating the false images is proportional to the mass of the lens. Astronomers use this principle to infer the mass of lenses.

Astronomers have long known that the matter that we see in the universe in the form of stars only makes up a fraction of the mass of the universe. There is missing mass of some sort, aptly named “dark matter,” that astronomers cannot detect. Zwicky was a prominent proponent for the existence of dark matter and set the foundations for future research. In 1933, he measured the velocities of galaxies in a galaxy cluster and found that the mass he calculated from the visible matter could not account for the high orbital velocities. He concluded the existence of dark matter that neither emits nor absorbs light. The idea has since stuck and the idea of dark matter has become commonplace. Yet, astronomers have discovered few clues to its true identity.

Dark matter can only be inferred from its gravitational effects. Thus gravitational lenses provide a good tool for studying it. Macrolensing is used to study the total mass of other galaxies, and microlensing is used to detect dark matter within our own Milky Way Galaxy.

If there is dark matter in other galaxies, there should be dark matter in our own galaxy as well. Microlensing provides a good tool for finding it. One source of dark matter is normal compact objects such as free-floating planets, faint brown dwarf stars or even black holes in our galaxy. It is difficult to constrain the total number of these objects and their importance in the total mass of the galaxy. Microlensing may be successful in finding such objects and quantifying their significance. Consider figure 9, a microlensing event identified by the brightening of a background star. The lens is not visible, but it has been inferred to be six times the mass of the Sun. The best explanation for this object is a free-floating black hole, suggesting that these types of objects may be common. (Bennet, 2002)

A number of ongoing research programs monitor the sky for microlensing events. Since microlensing events are extremely rare, millions of stars must be monitored over a period of years to get useful results. The MACHO (Massive Compact Halo Objects) group, using the 50-in telescope on Mount Stromlo in Australia, has monitored 18 million stars since 1992 and has identified 55 microlensing events. The results of this group and others’ research, suggest that hard-to-detect objects, like free-floating planets and brown dwarfs, may contribute significantly to the mass of the galaxy.

Cosmic measuring sticks
When a gravitational lens system is not symmetric, the different paths that the light follows have different lengths. This produces time delays between the images. In this case, the images produced by a gravitational lens represent different moments in time for the source. The time delays become especially interesting when the source object shows regular variability. Just like a surveyor can use lasers to precisely measure distance on Earth, astronomers can use the time delay of light from a gravitational lens to measure cosmic distance.

Figure 10 shows an example. This gravitational lens system (B0218+357) is one of the few that have been measured accurately enough to obtain a time delay. The system consists of a distant quasar lensed by a foreground galaxy. Two images are produced and the distance the light travels for the two images is different. Consequently, variations in the brightness of the quasar are seen in one image before the other. The time delay has been estimated at 10.5 days. Using the speed of light, this time can be translated into a distance. If the distance to the close lensing galaxy is known, the distance to the quasar can be derived geometrically. (Biggs, 1999)

Doing cosmology with gravitational lenses
Cosmology is concerned with answering the grandest questions in nature, such as, “How old is the universe?” “Where did it come from?” “Where is it going?” and “What is its shape and size?” It is a testament to modern physics that these questions are actually approachable. Extraordinary progress has been made over the past few decades to the point where astronomers can make consistent estimates of the size, shape, mass and age of the universe.

A number of ongoing and planned experiments should end debate on such vital issues as the geometry and rate of expansion of the universe. Gravitational lenses promise to be an important tool in solving these problems. It is well established that the universe is expanding as a result of the Big Bang birth of the universe. Edwin Hubble first quantified the expansion in the 1920s, yet today the rate of expansion is not well known. Different methods of measurement arrive at answers that disagree by 30%.

As a consequence of the Big Bang, all galaxies (ignoring local gravitational attractions) are moving away from every other galaxy; for instance, from Earth, we observe all galaxies receding. Furthermore, the velocity of the recession is proportional to distance and the rate of expansion; that is, we see distant galaxies moving away from us faster than nearer galaxies. Velocities of galaxies are measured using a Doppler effect: the redshift. Similar to the Doppler shift of sound from a receding siren, light emitted from a source moving away from Earth is shifted to lower energies, or towards the red in the optical portion of the electromagnetic spectrum. By measuring the recessional velocity of a galaxy, astronomers determine its relative distance from Earth. The fundamental problem is the conversion of redshift, determined from velocity, into true physical distances; to make the conversion, the expansion rate must be known.

Not only is the expansion rate necessary to find distance, it is needed to find the age of the universe. To find the age of the universe from the rate of expansion, the universe is merely “run backwards” and deflated to find the time when the universe was of zero size.

Gravitational lenses provide an excellent tool for measuring the expansion rate because they give a direct measurement of distance. The relative distances between Earth, the lens, and the source can be determined by observation of redshift. If the time delay between two images produced by the lens can be measured, the true distance, and, thus, the expansion rate of the universe, can be calculated.

Two measurements must be made from a gravitational lens to get all the information. First, the time delay has to be measured. This is not an easy task. Most multiply imaged subjects are frustratingly static, and so no estimate can be made. In addition, some lensing systems, even if they are regularly variable, are nearly perfectly symmetric so that the time delay between the images is not appreciable. Finally, even when a good lensing candidate is discovered, it is difficult to make the hundreds of observations necessary to determine the time delay precisely.

Second, even if the time delay can be found, a good distance approximation requires that the gravitational field of the lens must be understood. When the lens is fairly simple, such as a single galaxy, the gravitational field can be well estimated. However, in most cases, the lens is made up of contributions from many galaxies, as in a galaxy cluster, and the mass in the lens cannot be well traced. Modeling the lens is a challenging problem that requires both theory and good observations.

However, in a few cases, gravitational lenses have been used to estimate the expansion rate, and thus the age of the universe. Table 1 lists the results obtained from three gravitational lenses.
Although the current predictions are not consistent and do not surpass the accuracy of other techniques, the ideal gravitational lens potentially could beat the competition. The race is on to find that perfect lens.

Gravitational lenses as astronomical tools
Gravitational lensing has finally come of age as a practical tool for studying the universe. Gravitational lenses hint that dark matter exists in our galaxy and others; they suggest new estimates of the age and size of the universe; and over the next decade they will provide powerful tools for contributing to astronomical research.

After formulating his theory of general relativity, Einstein realized the scientific potential of gravitational lenses, but, noting the technology of the day, he remarked, “there is no great chance of observing this phenomenon.” It is a shame that Einstein could never gaze at Hubble Space Telescope images and see the great beauty he had predicted.

Acknowledgements
I appreciate Dian De Shaw for her helpful insights on the clarity and style of the paper. I thank Professor Roger Blandford for sharing his expertise.

References
Bennet, D. and others. 2002, Gravitational Microlensing Events Due to Stellar Mass Black Holes. The Astrophysical Journal, 579,2:639.

Biggs, A.D., Browne, I.W.A., Helbig, P., Koopmans, L.V.E., Wilkinson, P.N., Perley, R.A., Time delay for the gravitational lens system B0218+357, 1999, Monthly Notices of the Royal Astronomical Society, 304, 349.

Blandford, R.D. and R. Narayan. 1992. Cosmological Applications of Gravitational Lensing. Annual Review of Astronomy and Astrophysics. 30:311-58.

Coles, P. 2001. Einstein, Eddington and the 1919 Eclipse, Historical Development of Modern Cosmology, ASP Conference Proceedings Vol. 252. Edited by V.J. Martinez, V. Trimble and M.J. Pons-Borderia. San Francisco: Astronomical Society of the Pacific, p. 21.

Fischer, P., Bernstein, G., Rhee, G., and Tyson, J.A., 1997, The Mass Distribution of the Cluster 0957+561 From Gravitational Lensing, The Astronomical Journal, v113, p.521.

Ratnatunga, K., Griffiths, R., Knudson, A. 2001, Detection of Gravitational Lens Candidates in HST WFPC2 Data, Gravitational Lensing: Recent Progress and Future Go, ASP Conference Proceedings, Vol. 237. Edited by T.G. Brainerd and C.S. Kochanek. San Francisco: Astronomical Society of the Pacific, 2001, p33.

Walsh, D., Carswell, R.F., Weymann, R.J., 1979, 0957+561 A, B – Twin quasi-stellar objects or gravitational lens, Nature, v279, pp381.

Williams, L.L.R and P.L. Scheter. 1997. The quest for the golden lens. Astronomy and Geophysics. 38(5): 10-14.