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The Rainbows of Gravity

by John G. Cramer

Alternate View Column AV-29
Keywords: gravitation, lensing, Einstein ring, cosmic arc
Published in the November-1988 issue of Analog Science Fiction & Fact Magazine;
This column was written and submitted 4/1/88 and is copyrighted © 1988, John G. Cramer. All rights reserved.
No part may be reproduced in any form without the explicit permission of the author.


    I recall many years ago reading an SF story in which explorers travelling to a distant part of the universe thousands of light years from home come upon a planet that seemed identical to the Earth in all respects, right down to the shapes of the continents, etc. But on landing they found that the replication was an illusion. The planet was a bare and lifeless ball of rock upon which ghostlike images of white clouds and grassy plains and blue oceans were somehow being projected, to give the illusion of the Earth as it was many thousands of years ago. How could such an illusion exist? The resolution of the mystery came when it was realized that there was a large warp is space exactly half way between Earth and this ghost planet. The light rays and even gravitational pull were radiating out from the real Earth, to be refocused by the space warp to a 1:1 image at this distant point, thereby making a visual replica of the Earth as it was when the light started on its journey many thousands of years ago. That, of course, was only science fiction. Nothing like that could actually happen ... right? Or could it? This AV column is about real space warps (made by gravity) and about the astrophysical illusions which they may have produced.

    Astrophysics is a spectator science. The practitioner cannot go to his laboratory and do astrophysics experiments. He can only sit as a groundling in a vast audience, watching the show that Nature has staged in the heavens. Fortunately that show is sufficiently rich and varied that the scientific cycle of making hypotheses and testing them moves as rapidly in astrophysics as in sciences where laboratory experiments are possible. The universe is a large and wondrous laboratory bench on which billion year-old "experiments" are there for the observation, and new lessons are being learned every day. The most recent example of this is the recent discovery of "cosmic arcs".

    In mid-1987 two groups of astronomers almost simultaneously announced separate observations in rather different parts of the sky of a single narrow elongated arc of light about 20 arc-seconds in length contouring around the central region of a rich cluster of galaxies. This discovery caused great excitement in the astrophysics community. In the science press the arcs were heralded as the largest and most mysterious objects in the universe, millions of light years in length and of no known origin, a new phenomenon begging for explanation.

    What could these arcs be? Were they an illusion? Could anything so large be a real physical object? A giant linear galaxy, perhaps? An extended star cluster stretching along a cosmic string? Tongue in cheek, Arthur C. Clarke speculated that they might be the scaffolding left behind by some derelict contractor who went bankrupt during the construction of the universe.

    More detailed observations always help in understanding new phenomena. The first order of business for the astronomers was to get more detailed data on the light from the arcs. It was soon learned that the color and wavelength spectrum of the light was consistent with light from a fairly ordinary Sb-type galaxy like Andromeda. There were also indications that at least one the arcs showed a considerably larger red shift than that of the "nearby" galactic cluster at its center, an indication that the arc might actually be considerably more distant. Many astrophysicists began to suspect that the arcs were not real objects but optical illusions, artifacts of a phenomenon called a gravitational lens, a sort of rainbow produced by the bending of light by gravity.

    The deflection of light by gravity is of special significance in the history of physics. Seven decades ago in 1919 a pivotal confirmation of Albert Einstein's general theory of relativity came with the observation of the bending of star light by the gravitational pull of the sun during a total solar eclipse. The execution of this test had been delayed for several years by the more pressing matters of World War I. Finally in April of 1919 a group of British astrophysicists led by Sir Arthur Eddington voyaged to the remote equatorial island of Príncipe in the Gulf of Guinea off the coast of west central Africa to await a total eclipse of the sun that was scheduled to occur there on May 29, 1919.

    It was raining on the morning of the 29th, and the party did not glimpse the sun until the eclipse was already in progress. But during the maximum of the eclipse they were able to photograph the pattern of stars near the edge of the sun, to be compared with the same pattern photographed in the the same region of the sky in the previous January. The images of stars nearest the sun were seen to be displaced in the eclipse photographs because of the deflection of their light as it passed through the sun's gravity well. The amount of the displacement was just that predicted by Einstein. One of the crucial predictions of general relativity had been confirmed. To celebrate his accomplishment Eddington wrote a parody of the Rubaiyat which concluded with the lines:

                Oh leave the Wise our measures to collate.
                    One thing at least is certain, LIGHT has WEIGHT.
                One thing is certain, and the rest debate -
                    Light-rays, when near the Sun, DO NOT GO STRAIGHT.

    The deflection of light by gravity is well established, but focusing is not the same as bending, and the idea that gravity could act as a lens did not come until 1936, when Einstein demonstrated mathematically that in the proper circumstances a massive object could collect the diverging light from a distant object and bring it to a focus. He showed that a distant bright light source, for example a bright galaxy, that happened to be on the same line-of-sight with a closer massive object, perhaps a cluster of galaxies or a black hole, would be imaged as a ring. This ring-image is now known as an "Einstein ring". If the light source is slightly displaced from the line through the focusing mass, the ring image becomes distorted into a pair of circular arcs.

    This interesting prediction of general relativity remains unconfirmed. Double quasar images attributed to gravitational lensing have been found by astronomers, but no example of a true Einstein ring has ever been seen, perhaps because the precise alignment requirements are not very likely. The Einstein ring is not, strictly speaking, an image of the sort made by a lens. Instead it is a "caustic", a limiting condition on the bending of many rays causing many rays coming from slightly different directions pile up in the same place and appear as a bright line.

    Another example of a caustic is the familiar rainbow. The sun's rays, passing through falling raindrops, are bent and reflected to form a caustic, the very bright edge of the circle of allowed scattering. Because the angle at which this caustic occurs is slightly different for different wavelengths of visible light the familiar multicolored arch of the rainbow results. The sky is bright within the arch were much of the sunlight is scattered and dark outside the arch because scattering cannot occur outside the caustic limit. The Einstein ring can therefore be regarded as "Gravity's Rainbow", recalling the title of Thomas Pynchon's novel.

    Could the cosmic arcs be Einstein rings? Some observational evidence has been taken to indicate that they are not. Einstein rings should have two equal arcs on opposite sides of the focusing mass. Astronomers have examined each of the observed arcs for any sign of a matching arc on the other side of the galactic cluster that is assumed to be the focusing mass, but none has been found. The absence of the second arc has been used to argue against the Einstein ring explanation of the phenomenon. A recent paper, however, may have provide an explanation of why the arcs do not have matching twins. The calculations of Einstein assumed that the focusing mass producing the ring was perfectly symmetric. That assumption is reasonable for a black hole, but not for the irregular cluster of galaxies that are assumed to be the focusing masses.

    Scott A. Grossman and Ramesh Narayan of the University of Arizona have taken the calculations of Einstein a step further by including the possibility that the gravity field of the focusing mass is irregular, and pulls harder in one direction than in another. This would be expected if the distribution of galaxies was slightly oblong. Under this more realistic assumption the double arc of the Einstein calculation becomes a single arc.

    Grossman and Narayan did computer simulations of the focusing effects of randomly generated galactic clusters and found that even quite rough and irregular mass clusters produced smooth single arcs of about the same angular size as those observed. The conclusion of this work is that the cosmic arcs are not giant and mysterious structures. They are caustics, rainbows produced by gravity bending and concentrating the light from a very distant but fairly normal galaxy.

    The new calculations indicate that if one looks carefully enough, such arcs may be fairly common. Further, where one arc occurs, there should be other fainter arcs present also. A detailed study of such a group of arcs would provide a new way of examining mass distributions of galactic clusters. Nature has given us a glimpse of an object that is so far away as to be invisible under ordinary circumstances.

    We will not find distant gravitational and optical images of the Earth or our sun somewhere out in the universe. The space warps made by gravity are too imperfect as lenses to do the kind of imaging that the writer imagined. But true Einstein rings may be out there waiting to be found, produced by massive black holes that would signal their presence with a matching pair of gravity's rainbows.


Cosmic Arcs:

G. Soucail, B. Fort, Y. Mellier, and J. P. Picat, Astr. Ap. 172, L14 (1987).

R. Lynds and V. Petrosian, Bull. AAS, 18, 1014 (1987).

S. A. Grossman and R. Narayan, Astrophysical Journal 324, L37 (1988).

Einstein Rings:

A. Einstein, Science 84, 506 (1936).

SF Novels by John Cramer:  my two hard SF novels, Twistor and Einstein's Bridge, are newly released as eBooks by Book View Cafe and are available at : .

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