Star Collapse and Black Holes: Exploring the Connection

From the lecture series: What Einstein Got Wrong

By Dan Hooper, Ph.D., University of Chicago

Astronomer Karl Schwarzschild’s discovery about curved spacetime supported the possibility of black holes. But his abrupt death left physicists with many intriguing and unanswered questions. Could black holes exist, even hypothetically?

If so, do they exist in our universe? And if they do, how do they form?

The answers to these questions would gradually be revealed over the decades that followed. As it turns out, to understand the formation of black holes, scientists first needed to understand the inner working and evolution of stars.

A computer animation of a gamma-ray burst destroying a star.
When a star runs out of fuel, the core of the star collapses without disturbing the star’s outer part. A black hole forms inside the star and within a few seconds, it launches a jet of matter away from the black hole. (Image: NASA/SkyWorks Digital/www.nasa.gov)

This is a transcript from the video series What Einstein Got Wrong. Watch it now, on The Great Courses Plus.

What Powers the Sun?

During the period when Einstein’s Theory of General Relativity was being developed, scientists knew very little about how stars evolved or even how they were powered.

Sun
Where does the Sun gets the energy needed to produce its sunlight? (Image: NASA/SDO/www.nasa.gov)

The question of where the Sun gets the energy needed to produce its sunlight had been a stubbornly unanswered question for a long time.

Ordinary ways of storing and releasing energy didn’t come close to accounting for the huge quantity of energy that had been released by the Sun over its lifetime. For example, imagine that the Sun generated energy through chemical processes—like the way that a car extracts energy from fossil fuels, or that our bodies exact energy from food.

Even if the entire mass of the Sun—all two million trillion-trillion kilograms of it—was made up of gasoline, at the current output of sunlight, the Sun would run out of fuel in about 7,000 years.

To account for the quantity of energy that has been released by the Sun over the past 4.6 billion years, there had to be a fuel that was at least hundreds of thousands of times more efficient.

Throughout the 1800s, many physicists thought that the Sun was powered by its gradual gravitational collapse. As gravity compressed the Sun, they argued, the gravitational potential energy could be transformed into heat and sunlight.

The most optimistic estimates, however, suggested that this might be able to generate enough energy to power the Sun for a few tens of millions of years. In 1800, this seemed plausible—geologists didn’t know yet about how old the Earth and Sun were.

But by 1900 or so, it was clear that the Earth was billions—not millions—of years old. Gravity could not be the primary energy source of the Sun.

Learn more about how Karl Schwarzschild gained a detailed understanding of the theoretical properties of black holes

Converting Mass into Energy

With the introduction of the theory of relativity, however, there appeared another possibility for the source of the Sun’s energy. According to Einstein’s most famous equation, E=mc2, mass could—at least in principle—be transformed into energy, and at a very generous exchange rate.

A single gram of matter contains 90 trillion joules of energy—the equivalent of more than 20,000 tons of TNT. If there was some process going on in the Sun that was able to convert even a tiny amount of the Sun’s mass into energy, that process could plausibly provide enough energy to power the Sun for tens of billions of years.

By around 1920 or so, physicists had begun to recognize that the most likely way that stars could convert their mass into energy was through the process known as nuclear fusion.

Arthur Stanley Eddington
Astronomer Arthur Stanley Eddington (1882-1944) proposed that stars might generate their energy through the gradual transformation of hydrogen into helium nuclei. (Image: Smithsonian Institution/Public domain)

In particular, the English astronomer and physicist Arthur Eddington proposed that stars like the Sun might generate their energy through the gradual transformation of hydrogen into helium nuclei. This process destroys a small fraction of the star’s mass and steadily releases a great deal of energy in its place.

A few years after making this proposal, Eddington wrote a book entitled The Internal Constitution of Stars. In this book, he described stars as being in a constant balance between the contracting force of gravity and the outward pressure of nuclear fusion.

Today, this is how we understand how stars work. In his book, Eddington recognized one particularly interesting consequence of his theory.

Whereas gravity will continue to compress a star forever, a star’s ability to undergo nuclear fusion will eventually run out once it has exhausted all or at least most of the hydrogen in its core.

Once the process of fusion ends in a star, it seems logical that gravity should be expected to compress the star into a much smaller volume. Eddington remained essentially neutral regarding what takes place when a star runs out of its nuclear fuel, remarking only that one could, “make many fanciful suggestions as to what actually will happen.”

Learn more about the discovery that the expansion of the universe is accelerating

The Curious Case of Sirius B

Although no one had realized it yet, astronomers had already found a clue to the mystery of what happens to stars when they run out of nuclear fuel. For years, astronomers had been studying a strange star that they called Sirius B.

By studying the orbits of this star and its binary companion star, astronomers had learned that the mass of Sirius B is similar to that of the Sun. But the light emitted by this star told astronomers that Sirius B was very different—both much hotter and more luminous than ordinary stars are.

Strangest of all, the density of Sirius B is about a billion times the density of water—wildly more dense than ordinary stars. Sirius B is a tiny star, which contains a Sun’s worth of mass within a volume that is about the size of the Earth.

It was unlike any star that had ever been seen before. No one understood what it was made of or how it came to be that way.

Ralph H. Fowler
British astrophysicist Ralph Fowler (1889-1944) offered answers to the questions of the nature of Sirius B and what happens to stars when they run out of fuel. (Image: Unknown/ https://academictree.org )

It was the British astrophysicist Ralph Fowler who first offered an answer to the question of the nature of Sirius B. In so doing, he also provided an answer to Eddington’s question of what happens to stars when they run out of nuclear fuel.

Fowler argued than when a star could no longer support itself with nuclear fusion, gravity would suddenly compress it into a much smaller volume. The novel element that Fowler introduced came from the new theory of quantum mechanics.

According to quantum theory, there seemed to be a minimum size to which matter can be compressed. This leads to a phenomenon called quantum degeneracy pressure, which forces electrons to keep their distance from one another, and thus prevents the matter that makes up a star from becoming compressed into too small of a volume.

As it turns out, the minimum size that Fowler calculated for a typical star was similar to the observed size of Sirius B. Sirius B and other stars like it are supported against the force of gravity, not by nuclear fusion like ordinary stars, but by the strange effects of quantum mechanics. Stars like this are called white dwarfs.

Learn more about Einstein’s proof that light is made up of discrete quanta

New Findings on White Dwarfs

Although Fowler’s insights into the nature of white dwarf stars were certainly important, it turns out that his arguments only apply to stars with a relatively modest mass. The scientist who first reached this conclusion was the young Indian physics student, Subrahmanyan Chandrasekhar.

Chandrasekhar grew up in India as part of a wealthy and privileged family. But even given those advantages, his talents were staggering and evident from a young age.

Upon finishing college at the age of 19, Chandrasekhar was invited to pursue graduate studies at Cambridge and study under Ralph Fowler, who had recently proposed the existence of white dwarf stars.

Subrahmanyan Chandrasekhar
Subrahmanyan Chandrasekhar (1910-1995) discovered that only stars retaining mass more than 1.4 times the mass of the Sun end up being white dwarfs. (Image: Startchild Project NASA/Public domain)

Chandrasekhar was not one to waste time and he spent the long sea voyage to England reading physics papers, including the paper on white dwarfs by his soon-to-be advisor, Ralph Fowler. Not only did the 19-year-old Chandrasekhar understand Fowler’s paper, but he was the first to really recognize its limitations.

Fowler’s arguments—Chandrasekhar deduced—were valid for medium-sized stars, but break down for stars that are too massive. For any star with more mass than about 1.4 times the mass of the Sun, the force of gravity will be strong enough to overcome the quantum degeneracy pressure that supports a white dwarf.

Any star that is more massive than this will continue to collapse when it runs out of nuclear fuel, shrinking to a size even smaller than a white dwarf.

Learn more about the futile search for a unified field theory that would unite general relativity with Maxwell’s theory of electromagnetism

The Behavior of Neutron Stars

Over the next decade or so, Chandrasekhar, Fowler, Eddington, and others debated back and forth about what happens to massive stars when their nuclear fuel becomes exhausted. By the end of the 1930s, it had become clear that massive stars collapse well beyond the white dwarf stage, forming something denser, called a neutron star.

A neutron star is an object that consists almost entirely of neutrons—without the protons or electrons that are found in all forms of ordinary matter. Because it contains no electrically charged particles, this all-neutron matter can be compressed into ridiculously small volumes of space, and reach unimaginably high densities.

A typical neutron star contains a couple of Sun’s worth of mass, confined within a volume the size of a small city—about seven miles in radius. To put it another way, the density of a neutron star is roughly equivalent to that of the entire Earth if you were to squeeze it into a sphere the width of a football field.

But even this was the end of the story for the very most massive of stars. For those stars that are more massive than a few times the mass of the Sun, even this all-neutron state isn’t stable.

Learn more about the detection of gravity waves from distant colliding black holes in 2015

The calculations of several physicists, including Robert Oppenheimer—who would later become the head of the Manhattan Project—had shown that even a neutron star will collapse if it’s heavier than a few times the mass of the Sun. Once this threshold is passed, there is nothing that can prevent a star from collapsing indefinitely.

A very massive star, once out of nuclear fuel, will inevitably collapse beyond the size of a white dwarf or even a neutron star. Such a star will become a black hole.

Common Questions About Star Collapse

Q: What makes a star collapse?

While stars are growing, they fuse atomic matter and emit energy. As they begin to stop fusing matter, they cool off inside, and this creates a pressure imbalance that results in collapse.

Q: How long will it take a star to collapse?

There are many types of stars and all act differently when dying, depending on their mass. A core-collapse star, or supernova, takes millions of years to die and around 15 seconds for core-collapse. After this, it takes a few hours as a shockwave reaches the surface and blows precious materials outward; this process continues for about a few months and then after a few years, they fade away in brightness.

Q: Do white dwarf stars still shine?

While not emitting energy, neutron stars do glow for some time before eventually becoming a black dwarf, which is essentially a ball of iron ash.

Q: What type of star is the Sun?

The Sun is a very common star, the type of which comprises around 99 percent of known stars in the universe. The Sun is called G-type and is considered a main-sequence star in the category of sequences.

This article was updated on November 29, 2019

Keep Reading
The Manhattan Project: Einstein’s Devastating Legacy
Wave or Particle—What Is Light?
Searching for Diamond Dust in the Milky Way