Gravity / Quantum Physics / Quantum Physics


The Chandrasekhar Limit: The Threshold That Makes Life Possible

There is a thin line between a bang and a whimper.

For stars, this line is called the Chandrasekhar Limit, and it is the difference between dying in a blaze of glory and going out in a slow fade to black. For our universe, this line means much more: Only by exceeding it can stars sow the seeds of life throughout the cosmos.

The Chandrasekhar Limit is named for Subrahmanyan Chandrasekhar, one of the great child prodigies. Chandrasekhar graduated with a degree in physics before reaching his twentieth birthday. He was awarded a Government of India scholarship to study at Cambridge, and in the fall of 1930 boarded a ship to travel to England. While aboard the ship—still before reaching his twentieth birthday—he did the bulk of the work for which he would later be awarded a Nobel Prize.

By the 1920s—a decade before Chandrasekhar began his journey to England—astronomers had realized that Sirius B, the white dwarf companion to the bright star Sirius, had an astoundingly high density—more than a million times the density of the sun. An object of this density could only exist if the atoms comprising the star were so tightly compressed that they were no longer individual atoms. Gravitational pressure would compress atoms so much that the star would consist of positively-charged ions surrounded by a sea of electrons.

Prior to the discovery of quantum mechanics, physicists knew of no force capable of supporting any star against such gravitational pressure. Quantum mechanics, though, suggested a new way for a star to hold itself up against the force of gravity. According to the rules of quantum mechanics, no two electrons can be in the exact same state. Inside an extremely dense star like Sirius B, this means that some electrons are forced out of low energy states into higher ones, generating a pressure called electron degeneracy pressure that resists the gravitational force. This makes it possible for a star like Sirius B to achieve such extreme density without collapsing in on itself.

This discovery was made by Ralph Fowler, who would later become Chandrasekhar’s graduate supervisor. But Chandrasekhar realized what Fowler had missed: The high-energy electrons inside the white dwarf would have to be traveling at velocities near the speed of light, invoking a set of bizarre relativistic effects. When Chandrasekhar took these relativistic effects into account, something spectacular happened. He found a firm upper limit for the mass of any body which could be supported by electron degeneracy pressure. Once this limit—the Chandraskehar limit—was exceeded, the object could no longer resist the force of gravity, and it would begin to collapse.

When Chandrasekhar published these results in 1931, he set off a battle with one of the greatest astrophysicists of the era, Sir Arthur Eddington, who believed that the white dwarf state was the eventual fate of every star. At a conference in 1935, Eddington told his audience that Chandrasehkar’s work “was almost a reduction ad absurdum of the relativistic degeneracy formula. Various accidents may intervene to save a star, but I want more protection than that. I think there should be a law of Nature to prevent a star from behaving in this absurd way!”

Chandrasekhar was deeply hurt by Eddington’s reaction, but colleagues can disagree profoundly and still remain friends. Chandrasekhar and Eddington remained friends, went to the Wimbledon tennis tournament together and went for bicycle rides in the English countryside. When Eddington passed away in 1944, Chandrasekhar spoke at his funeral, saying “I believe that anyone who has known Eddington will agree that he was a man of the highest integrity and character. I do not believe, for example, that he ever thought harshly of anyone. That was why it was so easy to disagree with him on scientific matters. You can always be certain he would never misjudge you or think ill of you on that account.”

Vindication would eventually come to Chandrasekhar when he was awarded the Nobel Prize in 1983 for his work. The Chandrasekhar Limit is now accepted to be approximately 1.4 times the mass of the sun; any white dwarf with less than this mass will stay a white dwarf forever, while a star that exceeds this mass is destined to end its life in that most violent of explosions: a supernova. In so doing, the star itself dies but furthers the growth process of the universe—it both generates and distributes the elements on which life depends.

The life of a star is characterized by thermonuclear fusion; hydrogen fuses to helium, helium to carbon, and so on, creating heavier and heavier elements. However, thermonuclear fusion cannot create elements heavier than iron. Only a supernova explosion can create copper, silver, gold, and the “trace elements” that are important for the processes of life.

Lighter elements like carbon, oxygen, and nitrogen are also essential to life, but without supernova explosions, they would remain forever locked up in stars. Being heavier than the hydrogen and helium that comprise most of the initial mass of the stars, they sink to form the central core of the star—just as most of the iron on Earth is locked up in its core. If stars are, as Eddington believed, destined to become white dwarfs, those elements would remain confined to the stellar interior, or at best be delivered in relatively minute quantities to the universe as a whole via stellar winds. Life as we know it requires rocky planets to form, and there simply is no way to get enough rocky material out into the universe unless stars can deliver that material in wholesale quantities. And supernovae do just that.

The Chandrasekhar Limit is therefore not just as upper limit to the maximum mass of an ideal white dwarf, but also a threshold. A star surpassing this threshold no longer hoards its precious cargo of heavy elements. Instead, it delivers them to the universe at large in a supernova that marks its own death but makes it possible for living beings to exist.

Go Deeper
Editor’s picks for further reading

BBC: Test Tubes and Tantrums: Arthur Stanley Eddington and Subrahmanyan Chandrasekhar
In this radio program, discover the history of one of the nastiest disagreements in astrophysics.

FQXi: Exploding the Supernova Paradigm
In this blog post, Zeeya Merali investigates gaps in our understanding of supernova explosions. Subramanyan Chandrasekhar – Autobiobraphy

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James Stein

    James D. Stein is a past member of the Institute of Advanced Studies and is currently a professor of Mathematics at California State University (Long Beach). His list of publications includes: How to Shoot from the Hip Without Getting Shot in the Foot (with Herbert L. Stone and Charles V. Harlow); How Math Explains the World (a Scientific American Book Club selection); The Right Decision (also a Scientific American Book Club selection); and How Math Can Save Your Life. He has been a guest blogger for Psychology Today and his work has been featured in the Los Angeles Times. His latest book is Cosmic Numbers: The Numbers That Define Our Universe. He lives in Redondo Beach, California.