Black Hole

by Marcia Bartusiak

  Schwarzschild’s accomplishment was even more astounding when you consider the circumstances in which he carried out his calculations. It was at the height of World War I, and Schwarzschild, serving as a lieutenant in the German army, was then posted on the Russian front. His job was to calculate trajectories for long-range projectiles. Relativity was on his mind because, while on leave, he had been in the audience at the Prussian Academy on 18 November 1915 when Einstein presented his successful calculation of Mercury’s perihelion advance. Previously cautious that Einstein’s ideas could be astronomically verified, he was now convinced. On returning to the battlefront, he received copies of Einstein’s finalized theory and swiftly completed two papers on the subject. As he wrote in his letter to Einstein, “As you see, the war is kindly disposed toward me, allowing me, despite fierce gunfire at a decidedly terrestrial distance, to take this walk into this your land of ideas.” Known for his warmth and outgoing personality (always ready for a good beer to quench his thirst), Schwarzschild seems to have retained this demeanor even in the midst of war.

  Schwarzschild’s first battlefront solution was communicated to the Berlin Academy on 13 January 1916 by Einstein himself, who described the result as splendid. “I would not have expected that the exact solution to the problem could be formulated so simply,” replied Einstein to Schwarzschild. “The mathematical treatment of the subject appeals to me exceedingly.”

  Sadly, Schwarzschild didn’t have long to bask in Einstein’s praise. While in the trenches, he contracted pemphigus, a rare and then fatal autoimmune disease that attacks the skin. Critically ill, the noted astronomer returned to Potsdam in March 1916 and succumbed to his illness on 11 May, just four months after his academy triumph. He was forty-two years old.

  Though Schwarzschild may not have thought that his solution applied to the real universe, others considered the possibility. Writing in the Philosophical Magazine in 1920, the Irish physicist Alexander Anderson of University College, Galway, pondered what would happen if the Sun’s girth were to contract to below its magical sphere width. This was a time when many still thought that the Sun generated its energy through slow gravitational contraction. So, should the Sun keep on shrinking, wrote Anderson, “there will come a time when it will be shrouded in darkness, not because it has no light to emit, but because its gravitational field will become impermeable to light.”

  Contemplating such a gravitational collapse was a prescient thought, yet few followed up on it. One notable exception was the British physicist Sir Oliver Lodge, who in 1921 also noted that the gravity of a sufficiently dense star would prevent its light from escaping. This would happen, he noted, if the mass of the Sun were squeezed into a globe some three kilometers (just under two miles) in radius. “But,” he concluded, “concentration to that extent is beyond the range of rational attention.”

  However, although Lodge doubted that a single stellar nugget would form on its own, he boldly imagined that the light-swallowing effect might occur with larger collections of celestial matter. “A stellar system—say a super spiral nebula—of aggregate mass equal to 1016 suns … might have a group radius of 300 parsecs [around 1,000 light-years] … without much light being able to escape from it. This really does not seem an utterly impossible concentration of matter.” He was right. Lodge was crudely anticipating the existence of supermassive black holes, the kind found in the centers of most galaxies.

  But all these speculations went nowhere and wouldn’t be reconsidered for another two decades. The concept of the black hole—or, more correctly, its early equivalent—was still in its infancy. What pushed it along was the discovery of strange, new stars in the celestial sky—of a type that no astronomer had ever anticipated beforehand.

  4

  There Should Be a Law of Nature to Prevent a Star from Behaving in This Absurd Way!

  When Schwarzschild singularities were first introduced, they were essentially theoretical oddities. No one really expected them to jump off the page of a scientific journal into the real world. But new and startling astronomical findings in the early twentieth century made it difficult for theorists to maintain that attitude for long. If any single observation could be blamed, it would be the one concerning the faint companion that slowly circles Sirius, the brightest star in the nighttime sky and long known as the “Dog Star” because it’s situated in the northern constellation Canis Major.

  The story of Sirius and its tagalong commences in the nineteenth century at the Königsberg Observatory in Prussia, where Friedrich Wilhelm Bessel was setting new standards in positional astronomy. The observatory director had already gained fame in 1838 for being the first person to directly measure the distance to a star, astronomy’s biggest challenge at the time. Afterward, he turned his attention to stellar movements.

  For a number of years Bessel went through old stellar catalogs, as well as making his own measurements, to track how the stars Sirius and Procyon were moving over time across the celestial sky. By 1844 he had enough data to announce that Sirius and Procyon weren’t traveling smoothly, as expected; instead, each star displayed a slight but distinct wobble—up and down, up and down. With great cleverness, Bessel deduced that each star’s quivering must result from the pull of a dark, invisible object circling it, like a little boy tugging on his mother’s skirt. Sirius’s companion, he estimated, completed one orbit around Sirius every fifty years.

  Bessel was clearly excited by his find; in his communication to Great Britain’s Royal Astronomical Society he wrote, “The subject … seems to me so important for the whole of practical astronomy, that I think it worthy of having your attention directed to it.”

  Astronomers did take notice, and some tried to discern Sirius’s companion through their telescopes. Unfortunately, at the time Bessel reported his discovery, Sirius B (as the tiny companion came to be known) was at its closest to gleaming Sirius (from the point of view of an observer on Earth) and thus lost in the glare. But even years later, no one was successful in spotting the bright star’s partner.

  That all changed on 31 January 1862. That night in Cambridgeport, Massachusetts, Alvan Clark, the best telescope manufacturer in the United States, and his younger son, Alvan Graham Clark, were testing the optics for a new refractor they had been building for the University of Mississippi. It was going to be the biggest refracting telescope in the world. Looking at notable stars to carry out a color test of their 18.5-inch lens, the son observed a faint star very close to Sirius.

  This momentous sighting might have gone unrecorded. But fortunately the father was an avid double-star observer and possibly encouraged his son to report the discovery to the nearby Harvard College Observatory. In fact, according to historian Barbara Welther, rather than its being an accidental discovery, as long asserted in astronomy books, “there might have been a [prearranged] connection between the elder Clark and someone at Harvard” to look for Sirius’s companion.

  Whatever the case, George Bond, the observatory’s director, confirmed the find a week later, and he soon wrote up two papers: first a brief notice to a German journal of astronomy, then a more candid report to the American Journal of Science. This second paper revealed that one question was uppermost on Bond’s mind: “It remains to be seen,” he wrote, “whether this will prove to be the hitherto invisible body disturbing the motions of Sirius.” The newfound star seemed to be in the right place to explain the direction of Sirius’s wavelike motions, but its luminosity was extremely feeble—so dim, in fact, that it suggested at the time a star too small to have enough mass to account for the wobble. Here was the first clue to Sirius B’s uniqueness.

  For revealing Sirius’s dark companion, Alvan Graham Clark in 1862 garnered the prestigious Lalande Prize, given by the French Academy of Sciences for the year’s most outstanding achievement. Astronomers around the globe continued over the years to observe the orbital dance of Sirius and its partner and eventually determined that the companion was hefty enough (an entire solar mass) to pull
on Sirius, though with a light output less than a hundredth of our Sun’s. But no one worried about this disparity right away. They just shrugged their shoulders and figured that Sirius B was a sunlike star cooling off at the end of its life.

  At this point, no one had yet secured a spectrum of the light emanating from Sirius B—in other words, a breakdown of the distinct wavelengths emanating from the tiny orb. This was a difficult task owing to the overwhelming brightness of the binary’s primary star. Until they could obtain the star’s spectrum, astronomers just assumed that Sirius B was either yellow or red, like other dim and cooler stars. That’s because astronomy had a general rule at the time: the hotter the star, the brighter. The brightest stars’ colors were white, blue-white, or blue.

  But in 1910, Princeton astronomer Henry Norris Russell noticed something that cast doubt on that rule. On a Harvard Observatory photographic plate, a faint companion of the star 40 Eridani—a companion known since 1783—was labeled as blue-white. Russell doubted that such a classification could be correct, but in 1914, Walter Adams at the Mount Wilson Observatory in California confirmed the spectrum. How could a star be white-hot, yet dim? “I was flabbergasted,” recalled Russell. “I was really baffled trying to make out what it meant.” Then, in 1915, Adams determined that Sirius’s faint companion, too, displayed the spectral features of a blazing blue-white star—at 25,000 Kelvin, far hotter than our Sun. So why wasn’t it as fiercely bright to our eyes as Sirius itself? How could a fiery, white star emit such paltry radiation? If such a star replaced the Sun, it would appear only one four-hundredth as bright to us.

  Arthur Eddington (American Institute of Physics Emilio Segrè Visual Archives, gift of Subrahmanyan Chandrasekhar)

  Soon theorists, such as the Estonian Ernst Öpik and the British astrophysicist Arthur Eddington, figured out what was going on. If a star is both white and hotter than our Sun, it must be emitting more light over each square centimeter of its surface. But since Sirius B is so faint, that could only mean it had less surface area than our Sun—in other words, it is far denser and smaller. It fact, it had to be just a little larger than the size of the Earth. (So astounding was the density he calculated, around twenty-five thousand times more than the Sun, that Öpik at first declared it “an impossible result.”) Such stars came to be called “white dwarfs.”

  With a Sun’s worth of mass being squeezed into such a tiny volume, astronomers and physicists alike were powerless to explain how a star could remain stable in this incredibly compressed state. Physics at that stage couldn’t explain how such densities could be continually sustained. As Eddington later remarked mischievously, “The message of the Companion of Sirius when it was decoded ran: ‘I am composed of material 3,000 times denser than anything you have ever come across; a ton of my material would be a little nugget that you could put in a matchbox.’ What reply can one make to such a message? The reply which most of us made … was—’Shut up. Don’t talk nonsense.’”

  It took quantum mechanics, under development in the 1920s, finally to solve the puzzle. With the mass of the entire Sun crushed into an Earth-sized space—creating the densest matter then known in the universe—British theorist Ralph Fowler in 1926 figured out that pressures inside the compact dwarf star become so extreme that all its atomic nuclei, like droves of little marbles, are packed into the smallest volume possible. Atoms are largely empty space. (If an atom were blown up to the size of a football stadium, the nucleus would look like a pea perched on the fifty-yard line, with the tiny electrons buzzing around the farthest seats.) But all that extra space is drastically reduced within a white dwarf star. At the same time, its free electrons generate an internal energy and pressure that keep the atom from collapsing further. With the electrons elbowing one another with a vengeance (a quantum mechanical rule formulated by Wolfgang Pauli forbids them to merge), they resist additional compression. And that is the key to a white dwarf’s stability: the incredible pressure exerted by the highly confined and fast-moving electrons—known as a “degeneracy pressure”—prevents the star from further compaction. This pressure exceeds the crushing forces found at the center of our Sun a million times over. Such a pressure was inconceivable until the arrival of quantum mechanics.

  A white dwarf’s ultradense material is impossible to assemble here on Earth; only the star’s extreme environment makes it feasible. Astronomers later learned that such densities are always the end stage for a star like our Sun. The white dwarf is the luminous stellar core left behind after the star runs out of fuel and releases its gaseous outer envelope into space. Such will be our Sun’s fate some five billion years from now. Radiating the energy left over from its fiery past, the white dwarf, like a dying ember, eventually cools down and fades away.

  The discovery of the extremely dense white dwarf star turned out to be only the first volley in a startling stellar revolution. By the 1930s, working with the new laws of both quantum mechanics and relativity, theorists were astonished (and disturbed) to find that dying stars, if they had enough mass, might face even stranger fates than turning into a white dwarf. The discovery of the white dwarf—and the understanding of its physics—opened up a whole can of cosmic worms.

  The first steps in opening up that can were taken in the summer of 1930, just as the global economy was sinking into its Great Depression. The advance commenced during an eighteen-day sea voyage from India. The traveler was nineteen-year-old Subrahmanyan Chandrasekhar, a dignified youth known by one and all as simply Chandra. While journeying to England, first by ship and then by train, to begin his graduate studies with Ralph Fowler at Cambridge University on scholarship, he explored the physics of white dwarf stars, a subject he had become enchanted with during his earlier studies at the University of Madras. Before his departure he had already prepared a paper on the density of white dwarfs, which combined Fowler’s idea with Arthur Eddington’s model of a star.

  Fowler had just shown how the pressure from electrons, tightly packed in the compact star at a density of a metric ton per cubic centimeter, keeps a white dwarf intact. But can this go on forever? Chandra further mused on the ship. What happens, asked the young student, if a white dwarf is more massive? With plenty of time to think on the long voyage, which took him through the Suez Canal into the Mediterranean, Chandra had an epiphany. He came to realize that as the white dwarf got heavier and heavier, many of the electrons moving within the dense stellar nugget would approach the speed of light. And that meant it was necessary to apply the rules of relativity to the star’s behavior, something Fowler did not do.

  Having acquainted himself with quantum mechanics and relativity as an undergraduate, Chandra carried out a calculation right there on the steamer and, to his surprise, concluded that there is a maximum limit to the mass of a white dwarf (now known to be 1.4 solar masses). An avid reader of the scientific literature, he happened to have read the key books that allowed him to work this out and had three with him onboard to consult. “It is something which is so simple and elementary that anyone could do it,” Chandra modestly recalled in 1971. Past his calculated limit, the white dwarf star could not support itself against gravity. What exactly occurred at that boundary was completely unknown territory. Chandra had no idea what the white dwarf would turn into if it were heavier. “I didn’t know how it would end,” he said further, thinking back on that moment of discovery. Yet he quickly wrote a paper on the finding upon his arrival.

  Subrahmanyan Chandrasekhar at Cambridge University in 1934. (American Institute of Physics Emilio Segrè Visual Archives, gift of Subrahmanyan Chandrasekhar)

  Fowler communicated Chandra’s pre-voyage paper on the density of white dwarfs to the Philosophical Magazine but sent his relativistic solution to another expert to assess. After waiting months with no feedback, the young researcher, by then disappointed that publication in Great Britain was unlikely, went ahead on his own and mailed that second article off to America. The result was a brief 1931 paper published in the Astrophysical Journal and
titled “The Maximum Mass of Ideal White Dwarfs,” which almost got rejected. A referee had initially doubted one of Chandra’s equations, until provided a detailed proof. “I am sorry that I was in error in criticizing his equation,” the referee told the editor, “but it seems to me a rather remarkable thing that this equation is true. I should not have expected it at the first glance.”

  When Chandra first started on his calculations, he didn’t know that others—Edmund Stoner in England and Wilhelm Anderson in Estonia—had already published earlier estimates of an upper bound to a white dwarf’s density. They thought of it as the tightest space that atoms could feasibly jam together. But Chandra used a more sophisticated model of a star, which in the end arrived at a stronger (and stranger) conclusion. His equations were telling him that past his threshold, the star appeared headed toward total collapse, with its density going to infinity (a result he deemed “inconceivable”).

  It’s not surprising that Chandra was not alone in his pursuit. The problem of stellar mass was in the air. It was a time when astrophysicists were starting to analyze the internal structure of a star—how it was powered, how it was built. For centuries, astronomers had solely tracked the positions and movements of the stars; now, they wanted to crack open the star (in theory) and find out how it worked. Just as Chandra was musing on white dwarfs in England, the brilliant theorist Lev Landau was doing the same in the Soviet Union. By pondering the question of a star’s inner structure, Landau thought he might make some startling new discoveries in nuclear physics, his specialty. After setting up a simplified model of a star as a lump of cold matter, he also concluded in 1931 that “there exists in the whole quantum theory no cause preventing the system from collapsing to a point,” if the star were heavier than 1.5 solar masses. But this was obviously a “ridiculous” result, he decided. He knew there were stars more massive. What could possibly explain this obvious contradiction? To answer that, Landau reasoned that the laws of physics must be breaking down within the heart of a star, following up on a thought that the Danish atomic physicist Niels Bohr had earlier expressed. The stellar core was a “pathological” region, as Landau put it, where matter becomes so dense it forms “one gigantic nucleus.” While seemingly prescient, it was more a harbinger of revelations to come.