How a Star Dies

An excerpt from astronomer Chris Impey’s new book, Einstein’s Monsters: The Life and Times of Black Holes

click to enlarge “Einstein’s Monsters” is now available via W.W. Norton & Company Inc. - COURTESY PHOTO
Courtesy Photo
“Einstein’s Monsters” is now available via W.W. Norton & Company Inc.

Black Holes from Star Death

Science hinges on the interplay between theory and observation. Over the millennia, humans have had many imaginative ideas about how the universe works. But without data drawn from observations, even the cleverest idea remains in the realm of speculation. Is there actually any evidence that mass can disappear from view in the universe?

Despite the challenge of imagining them, black holes are real. That's the firm conclusion from nearly fifty years of research on the end states of stars. An isolated black hole is completely invisible. The rupture it creates in spacetime is so small that it's undetectable with any telescope. But most stars are in binary or multiple systems, so the visible star can be a pointer to the dark companion.

The Forces of Light and Darkness

When you look at the Sun, it's hard to believe you're watching a titanic battle between the forces of light and darkness. Although the Sun seems barely to change from day to day or year to year, particles are careering around at near the speed of light and planet-size parcels of plasma are constantly churning; it's a thermostatically controlled nuclear furnace. At every point within it there is a balance between the inward force of gravity and the outward force from radiation released in the fusion of hydrogen into helium. As long as the fuel for fusion remains, neither force gains the upper hand.

If you're placing a bet on the long-term outcome of this battle, gravity would be the smart choice. Nuclear fuel is finite but gravity is eternal. After hydrogen is exhausted in stars like the Sun, the interior pressure is lost and the core of the star collapses to a hotter and denser configuration where helium can be fused into carbon. This reaction goes quickly, and when the helium is exhausted the temperature can't rise high enough to ignite new nuclear reactions. The pressure support is lost and the core of the star is once again faced with gravitational collapse. The Sun will have a brief pyrotechnic phase as the last fuel is used up, ejecting about a third of its mass in a shell of gas moving at supersonic speed. The fast-moving gas heats up and glows, producing the gorgeous hues of a planetary nebula. Anyone watching the Sun from another star system in 5 billion years will see a spectacular light show. Anyone watching from the Earth will be in a lot of trouble, since the ejected gas will vaporize the biosphere and obliterate all life.

A star's life and death is governed by its mass. The diverse fates of stars are all preordained at birth. Depending on their masses, all stars will become either white dwarfs, neutron stars, or black holes. There isn't a "typical" mass or size for a star, although the process by which stars form from chaotic clouds of gas produces more small stars than large stars by a substantial factor. The Sun is toward the lower end of the mass range, and below it are dim stars called red dwarfs. There are several hundred times as many red dwarfs as there are stars like the Sun. Lifetime is also dictated by mass, since gravity determines the temperature of the core, which in turn indicates how quickly nuclear reactions will run and therefore how long the nuclear fuel will last. A star like the Sun will fuse hydrogen into helium for 10 billion years; we're halfway through that span. A star half the mass of the Sun has a lifetime of 55 billion years, so no star of that mass has ever died in the history of the universe, which has only spanned 14 billion years. A red dwarf a tenth the mass of the Sun, which is as puny as a star can be and still have fusion reactions, will spend its fuel like a miser. Such a star would theoretically live more than a trillion years— an unimaginably long time. Even so, the dwarf star is just delaying the inevitable because one day the fuel must be exhausted, the dim light must flicker out, and gravity will be rewarded for its patience.

Stars more massive than the Sun have shorter and more spectacular lives. They all do what the Sun is doing now—fuse hydrogen into helium—but they have more gravity so have hotter cores and use up their fuel at a ferocious rate. The more massive the star, the hotter its core temperature and the shorter its lifetime. Massive stars can fuse all the elements in the periodic table up to iron, the most stable element. When nuclear reactions stop at iron, the core is in a bizarre physical state: it's an iron plasma 100 times denser than water at a temperature of a billion degrees. Without pressure from the core, it collapses, and the compression wave inward bounces into a multi-billion-degree blast wave outward, wherein heavy elements up to uranium are fused in split seconds. This is a supernova, one of the most dramatic events in the universe. Precious metals are flung into space to become part of a next generation of stars and planets. Much of the original mass of the star is ejected, but what remains is squeezed tightly by gravity's unrelenting grip.

Artist’s impression of a black hole. - COURTESY NASA, ESA, D. COE, G. BACON
Courtesy NASA, ESA, D. Coe, G. Bacon
Artist’s impression of a black hole.

Gravity and Darkness Are the Final Victors

The remnants of stars are truly bizarre states of matter. We have no way to create them in the lab. All we can do is use the laws of physics and hope that our theories are sturdy enough for the task. Some of the best minds in twentieth-century astrophysics were consumed with understanding stellar remnants.

A star's aftermath depends on the mass a star has when it starts its life. Stars are born in the fragmentation and collapse of large gas clouds that produce many more low-mass stars than high-mass stars. All stars lose some fraction of their mass as they age. The processes by which this happens are complex, so boundaries between the different outcomes are not precise. Stars that start their lives below 8 times the mass of the Sun collapse to an unusually dense state of matter called a white dwarf. The vast majority of stars are less massive than the Sun, so over 95% of all stars will end up this way. For example, the Sun will shed about half its mass during its pyrotechnic late stage of life before dying as a white dwarf.

The English astronomer William Herschel accidentally discovered a star called 40 Eridani B in 1783, but he had no way to measure its size so he didn't realize that the star was unusual.

In 1910, astronomers refocused their attention on this dim star, which is in a binary system. The orbit revealed its mass to be about the same as that of the Sun. They knew its distance, and deduced that it was 10,000 times fainter than the Sun would be at the same distance. Yet it was white, therefore much hotter than the Sun. To see why this is puzzling, think about electric hot plates on a stove, viewed in a darkened room. One hot plate is turned on low and glows orange, like the Sun. A second hot plate is turned on high and is much hotter, so it glows white. The white hot plate is much brighter than the orange hot plate. For the white hot plate to appear much fainter than the orange hot plate, it would have to be much smaller. By the same logic, the faint star in the 40 Eridani system had to be much smaller than the Sun. With the same mass as the Sun, it had to be much denser as well.

Ernst Öpik calculated that 40 Eridani B should have a density 25,000 times higher than that of the Sun, which he called "impossible." Arthur Eddington, who popularized the term "white dwarf," described the incredulous reaction a white dwarf produces: "We learn about the stars by receiving and interpreting the messages which their light brings to us. The message... 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 most of us made in 1914 was— 'Shut up. Don't talk nonsense.' "

Eddington was not a humble man. When a colleague said to him, "Professor Eddington, you must be one of only three people in the world who understand relativity," he paused, so the colleague said, "Don't be so modest." Eddington replied, "On the contrary, I'm trying to think who the third person is." Even though Eddington was a master of the astrophysics that predicted white dwarfs, he called them "impossible stars."

A typical white dwarf is the size of the Earth but has the mass of the Sun. Its density is a million times higher than water. With no energy release from fusion, and so no outward pressure, gravity shrinks the gas, crushing the atomic structure and forming a plasma of unbound nuclei and electrons. Only at this point is gravity finally thwarted. In 1925, Wolfgang Pauli came up with the exclusion principle, which says that no two electrons can have exactly the same set of quantum properties. Its effect is to provide pressure that stops the stellar corpse from collapsing any further. A white dwarf will form with a temperature as hot as 100,000 Kelvin, and then steadily radiate its heat into space. Fade to black.

Subrahmanyan Chandrasekhar, at the time a nineteen-year-old Cambridge student on an Indian government scholarship, calculated that regardless of the starting mass of a star, its white dwarf remnant can never be larger than about 1.4 times the mass of the Sun. Above this mass, gravity trumps quantum mechanics and the star collapses to a singularity. The maximum mass of a white dwarf is called the Chandrasekhar limit. It was a brilliant calculation—so Chandrasekhar was understandably disappointed when Arthur Eddington, his idol, publicly ridiculed the idea of collapse to a singularity. Chandrasekhar felt betrayed, believing that the slight was in part racially motivated. We'd like to think science is a meritocracy, but scientists can be jealous and short-sighted. (Quantum pioneer Paul Dirac, who experienced similar resistance, pithily observed that science advances one funeral at a time.) Chandrasekhar was eventually vindicated, and won the Nobel Prize in Physics for his insights into the structure and evolution of stars.

Chandrasekhar opened the door for physicists to imagine what happens if a star collapses beyond a white dwarf. A few years later, California astronomers Walter Baade and Fritz Zwicky suggested, almost casually, that above the Chandrasekhar limit, pure neutron material might result from star collapse, but they didn't do any calculations to support the conjecture. In 1939, chain-smoking, hard-driving Robert Oppenheimer did the math. With a graduate student, he established the mass range of neutron stars. The same year... he showed that with a stellar remnant above this mass range—more than 3 times the mass of the Sun—a black hole must form.

All stars lose mass before they die. As mentioned above, the Sun will lose half of its mass before it dies as a white dwarf. All stars beginning their lives with up to 8 times the mass of the Sun will leave behind white dwarfs with masses up to 1.4 times the mass of the Sun. If the initial mass of a star is roughly between 8 and 25 times the mass of the Sun, the core collapse continues until all the protons and electrons merge into pure neutron material. Since there's no electrical force, the neutrons jam together like eggs in an egg carton. The material is supported against further collapse by the strong nuclear force and a stronger version of the quantum force that prevents white dwarfs shrinking further. This is a neutron star, the smallest and densest type of star in the universe. Above 25 solar masses, we're faced with the prospect of Einstein's monster [a black hole].

Neutron stars challenge the imagination. A neutron star is like a city-sized atomic nucleus with an atomic number of 1057. Its material is 1,000 trillion times denser than water. A sugar cube amount of white dwarf material brought to the Earth would weigh a ton, but a sugar cube amount of neutron star material brought to the Earth would weigh as much as Mount Everest. When a star shrinks this much, the magnetic field is squeezed and concentrated too. Some neutron stars have magnetic fields a quadrillion times stronger than the Earth's. The gravity near the surface is so strong that an object falling from a height of a meter would accelerate to 3 million miles per hour at the moment of impact. Conservation of angular momentum means the normally sedate rotation of a star like the Sun is amplified when a star collapses. The fastest spinning neutron star spins 716 times per second, or 42,000 rpm. Such a rapidly spinning solid object isn't completely stable, so the solid crust can violently shift in an event called a starquake.

How can a neutron star be detected? These city-sized stars should emit no light because they are not fusing elements the way normal stars do. For a couple of decades astronomers consigned them to the category of astrophysical curiosities: something to be imagined but never witnessed. Then in 1967, young graduate student Jocelyn Bell and her thesis advisor, Tony Hewish, detected radio pulses with a period of 1.3373 seconds from an unknown object in the constellation of Vulpecula. The pulses were so powerful and regular that Bell and Hewish thought the object might be a beacon, so they jokingly named it LGM- 1 (for "Little Green Men"). Other "pulsars" were soon discovered, and Bell and Hewish made the connection with the earlier prediction of neutron stars. The intense magnetic field drives radio emission from hot spots on the neutron star's surface, and when the spinning neutron star sweeps that emission across a radio telescope, like a lighthouse beam, pulses are seen.

Controversy erupted seven years later when a Nobel Prize for the discovery of pulsars was awarded to Hewish and Martin Ryle, the head of the radio observatory, but not to Jocelyn Bell, who made the actual discovery. It is clear to many in the scientific community that she was excluded from the honor because she was a young woman. Just over 200 scientists have won the Nobel Prize in Physics, and only two have been women: Marie Curie in 1903 and Maria Goeppert-Mayer in 1963.

Surveys with radio telescopes have steadily increased the number of pulsars to over 3,000. However, the conditions that lead to a hot spot are rare, so very few neutron stars are radio pulsars. The vast majority of the millions of neutron stars in the galaxy are spinning quietly in deep space, dark and undetectable.

Excerpted with permission from "Einstein's Monsters: The Life and Times of Black Holes," published by W.W. Norton & Company. Copyright © 2018 by Chris Impey. All rights reserved.

Note: Certain references to graphs and endnotes found in the full copy of Einstein's Monsters have been omitted from this excerpt.

Read an interview with the author here.