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This was the challenge of Chandrasekhar, the genius without whom what we know today about stars and black holes might not yet be within our grasp.

The story of Subrahmanyan Chandrasekhar (1910-1995) is almost as exciting as his achievements in the field of astrophysics. His childhood in India at the beginning of the 20th century was marked by the way in which his parents knew how to encourage his curiosity and stimulate his passion for study. His innate skill with numbers led him to stand out very early in the field of physics and mathematics, and with only 19 years old he graduated in physics from the University of Madras.

His outstanding academic record was awarded by the Government of his country with the possibility of traveling to England to continue his studies at the University of Cambridge, an opportunity that Chandrasekhar did not miss. He was admitted to the prestigious Trinity College under the tutelage of the British physicist and astronomer Ralph Howard Fowler, who, precisely, was the author of some of the scientific articles that had helped him immerse yourself in quantum physics which in the 1930s was still taking its first steps.

During the main sequence stage, stars continually readjust to equilibrate from gravitational contraction and pressure from gases and radiation.

Chandrasekhar was fascinated by the branch of astrophysics that sought to understand the stages through which stellar evolution went through. At that time, astrophysicists already knew that stars consume most of their fuel in a phase known as the main sequence, and also that during this stage they manage to stay in balance continually readjusting thanks to the tension of two opposing forces: gravitational contraction, which pulls the matter of the star inwards, and the pressure of gases and radiation, which pulls the matter out.

Astronomers knew quite precisely the state of hydrostatic equilibrium that stars are in for most of their lives, but they also knew that there was a peculiar type of stars, white dwarfs, that were much denser than any object that they could have studied on Earth. In fact, its density and its equilibrium state escaped his understanding Because they could not be explained by the laws of classical physics, they decided to turn to the still incipient quantum mechanics in the hope that it would help them understand what was going on inside.

The secret of the white dwarfs

Chandrasekhar was passionate about quantum physics. The scientific articles of the astrophysicists Fowler and Eddington helped him to immerse himself in it, and it was precisely his tutor at Trinity College who in 1926, when the young Indian was still studying in his native country, managed to describe the mechanism that allows the white dwarfs keep their balance. Equipped with the tools of quantum mechanics, Fowler published an article in which he managed to explain how a phenomenon known as electronic degeneration he was responsible for keeping the white dwarfs in balance.


Until that moment, astrophysicists had observed that these stars had left behind the stage in which they consumed their fuel reserves, but, surprisingly, despite not having the pressure of radiation and gases resulting from the ignition of the matter they agglutinate , they managed to stay in balance. There must necessarily be a force that was capable of counteracting gravitational contraction to allow the equilibrium of the white dwarfs to be possible.

Fortunately, the electronic degeneracy described by Fowler managed to explain this phenomenon. Broadly speaking, and leaving aside the more complicated details, this mechanism predicts that gravitational contraction manages to compress the matter of the star so much that the electrons bound to the atomic nuclei hardly have room to move. Each one of them gets locked up in 10,000 times smaller space than the one it originally had, causing it to start shaking uncontrollably, hitting adjacent electrons, which are in exactly the same situation.

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Nothing can stop this degenerate movement of electrons. Not even the gradual cooling of the white dwarfs that have already used up their fuel. In fact, electronic degeneration is maintained even though the matter is at absolute zero temperature (-273.15 ºC). The origin of this phenomenon is closely linked to wave / particle duality as quantum physics explains it to us, which, again broadly speaking, tells us that, in reality, waves and particles are the same. All particles sometimes behave like a wave, and at the same time all waves sometimes behave like a particle.

In his article, Fowler proposed that electronic degeneration is the mechanism responsible for the force that counteracts the gravitational contraction of white dwarfs. And, therefore, it is also responsible for keep in balance. This idea haunted Chandrasekhar during his years of study in India, and when he had the opportunity to delve into it during his time in England working closely with Fowler, he did not hesitate to take advantage of it.

And came the war unleashed by the “limit of Chandrasekhar”

The long trips he made between England and India gave Chandrasekhar the opportunity to immerse himself in his thoughts away from the exams and commitments that his studies at Trinity College entailed. Fowler had managed to explain why white dwarfs they kept in balance, but his research had failed to provide a satisfactory description of the internal structure of these stars. And Chandrasekhar was determined to pick up this challenge.

What the numbers told Chandrasekhar was that gravitational contraction could only be counteracted if the star’s mass was less than 1.4 solar masses.

During one of his travels, and while he was deep in thought, it occurred to him that it might be a good idea to introduce the laws of Special Relativity that Albert Einstein had conceived not many years before in the calculations that Fowler had made. And he did. His background in astrophysics was still very limited, and, moreover, the great physicists and mathematicians who at that time were struggling to reconcile Relativity and quantum physics had not obtained any promising results, but this did not discourage Chandrasekhar.

After spending several days doing calculations and reviewing the latest articles Eddington and Fowler had published, he got a result. But it was not just any result; it was a strange result, and, at the same time, extraordinarily promising. What the numbers told Chandrasekhar was that gravitational contraction could only be counteracted if the mass of the star was less than 1.4 solar masses. If the mass of the white dwarf exceeded this figure, not even electron degeneration could prevent the star’s gravitational collapse, which opened the doors wide to the existence of black holes.


A cubic centimeter fragment of a neutron star weighs approximately 1 billion tons. The degenerate matter that constitutes it is no longer made up of protons, neutrons and electrons, like ordinary matter.

Currently, astrophysicists defend that a star can adopt two more states before ending its days by acquiring the entity of a black hole: neutron stars and the still hypothetical quark stars (we talk about both in depth in the article that I link right here). But in the 1930s what Chandrasekhar proposed it was hard to assume. In fact, the first astrophysicists to whom he submitted his scientific paper, among whom was Fowler, did not understand his proof.

Finally Chandrasekhar got his text published in the American Astrophysical Journal after having been previously approved by the physicist Carl Eckart. This endorsement gave his research a lot of visibility, and more and more astrophysicists were accepting his conclusion, although all of them were opposed to the existence of black holes. They could not admit that nature accepted that those aberrations really existed. There must be some law preventing its existence beyond the correctness of the demonstration that the young Indian astrophysicist had made.

Eddington, Dirac, and the possibility that fundamental constants are not actually set in stone

The rejection of the scientific community it was a hard blow for Chandrasekhar, but what hurt the most was that his demonstration was strongly dismissed by Arthur Eddington, who until then had served as one of his most enthusiastic tutors. In fact, Eddington even ridiculed the possibility that a white dwarf could not have a mass greater than 1.4 solar masses during one of his lectures at the Royal Astronomical Society in London, in which, of course, Chandrasekhar was present. .

In 1983 Subrahmanyan Chandrasekhar and William Fowler received the Nobel Prize in Physics

Eddington maintained his fierce opposition to the “Limit of Chandrasekhar” throughout his life, and disappointed by the rejection he was being subjected to, Chandrasekhar abandoned the study of white dwarfs in the late 1930s and did not return to it until two decades later. For almost six decades this Indian genius taught astrophysics at the University of Chicago, and finally his essential contribution to the knowledge of stellar evolution and the process of formation of black holes was recognized.

In 1983 Subrahmanyan Chandrasekhar and William Fowler received the Nobel Prize in Physics. It is impossible to know how astrophysics would have evolved without the contributions of Chandrasekhar, but there is no doubt that without his work, perhaps what we know today about stars and black holes would not yet be within our grasp.

Bibliography | ‘Black holes and curved time’, by Kip S. Thorne | ‘Statistical Physics: Volume 1 of Modern Classical Physics’, by Roger D. Blandford and Kip S. Thorne | ‘History of time: from the Big Bang to black holes’, by Stephen W. Hawking

Imágenes | NASA | NASA Goddard Space Flight Center | NASA/JPL-Caltech | M. Helfenbein, Yale University / OPAC