# Prof. Dr. Subrahmanyan Chandrasekhar > Research Profile

*by Luisa Bonolis*

**Subrahmanyan Chandrasekhar**

**One of the Nobel Prizes in Physics 1983 "for his theoretical studies of the physical processes of importance to the structure and evolution of the stars".**

**The destiny of a star**

In his Nobel lecture, Subrahmanyan Chandrasekhar wrote «There have been seven periods in my life. They are briefly: 1) stellar structure, including the theory of white dwarfs(1929-1939); 2) stellar dynamics, including the theory of Brownian motion (1938-1943); 3) the theory of radiative transfer, the theory of the illumination and the polarisation of sunlit sky (1943-1950); 4) hydrodynamic and hydromagnetic stability (1952-1961); 5) the equilibrium and stability of ellipsoidal figures of equilibrium (1961-1968); 6) the general theory of relativity and relativistic astrophysics (1962-71) and 7) the mathematical theory of black holes (1974-1983).» Chandrasekhar would devote 5-10 years to different topics he wished to study in depth. He would take a year to master the subject, a few more years to publish a series of journal articles demolishing the problems that he could solve, and then a few more years writing a definitive book that surveyed the subject as he left it for his successors. Once the book was finished, he left that field alone and looked for the next topic to study. As he himself explained in his related autobiography: «After the early preparatory years, my scientific work has followed a certain pattern motivated, principally, by a quest after perspectives. In practice, this quest has consisted in my choosing (after some trials and tribulations) a certain area which appears amenable to cultivation and compatible with my taste, abilities, and temperament. And when after some years of study, I feel that I have accumulated a sufficient body of knowledge and achieved a view of my own, I have the urge to present my point of view, *ab initio*, in a coherent account with order, form, and structure.»

The Universe, as the grandest conceivable scale on which the human mind can strive to understand nature, was the stage in which he lived his intellectual adventure as a scientist.

Subrahmanyan Chandrasekhar was known throughout his life as Chandra. He was born in 1910 in Lahore, Pakistan (then a part of colonial British India), from a highly educated South Indian family. He was educated at home until he was 11. When he entered high school, he was such a brilliant student that he was placed immediately in the third form and already at 15 he entered the prestigious Presidency College in Madras. After two years in college, Chandra wished to specialise in mathematics, also because he was fascinated with the legendary work of the mathematician Srinivasa Ramanujan. His father wished him to study physics and to follow him into Indian Civil Service, but his mother encouraged Chandra to follow his desire to become a scientist. He had a role model in his paternal uncle Chandrasekhara Venkata Raman, who had resigned a high level government post to pursue an academic and research career in physics. In 1928, Raman discovered the change in the wavelength occurring when a beam of light is scattered by molecules, later to become known as the Raman effect, for which he was awarded the 1930 Nobel Prize for Physics. Chandra spent the summer months in Calcutta, staying with his uncle Raman and working in the laboratory where the discovery was made. In that year, 1928, Arnold Sommerfeld visited Presidency College on a lecture tour. Chandra, who read far beyond the curriculum, knew his *Atomic Structure* *and Spectral Lines*, and managed to meet Sommerfeld. The latter shocked Chandra informing him that the quantum theory in the book was out-dated and told him about recent discoveries - Erwin Schrödinger's wave mechanics and the new quantum mechanics of Werner Heisenberg, Paul Dirac, Wolfgang Pauli, and others. Sommerfeld gave him a copy of the galley proofs of his as yet unpublished a paper on the electron theory of metals, which was an early application of Fermi-Dirac quantum statistics. The new statistics had also been used by the theoretical astrophysicist Ralph H. Fowler in his pioneering work on the constitution of white dwarf stars, dense collapsed configurations of stars in their terminal stages, with planetary dimensions but as massive as the Sun.

All this inspired Chandra to write his first scientific paper, which was communicated by Fowler to the *Proceedings of the Royal Society*, while he was still an 18-year old undergraduate student. Ralph Fowler accepted him as a research student at the University of Cambridge, where the great astrophysicist Arthur Eddington, was also teaching. Eddington had recently published *On the internal constitution of stars* which exerted a great influence on a whole generation of students.

Chandra's first article was so appreciated that he was awarded a special three-year scholarship from the Indian government to finance his graduate studies in England, and at the end of July 1930, when he was 19 years old, he left India to study at Trinity College.

After reading Eddington’s book on the stars and Fowler’s book on quantum-statistical mechanics, Chandrasekhar had become fascinated by white dwarf stars --- stars that have exhausted their supply of nuclear energy by burning hydrogen to make helium or carbon and oxygen. White dwarfs collapse gravitationally to a density many thousands of time greater than normal matter, and then slowly cool down by radiating away their residual heat. Fowler's calculations of the relation between the density and mass of a white dwarf, agreed well with the scanty observations available at that time. A white dwarf as a whole is electrically neutral, so all the electrons must have a corresponding proton, which is some 2,000 times more massive. Consequently, protons must supply the bulk of the gravitational compression. However, electrons in the central regions of white dwarf stars might be moving fast enough to make relativistic effects important. So Chandra repeated Fowler's calculation of the behaviour of a white dwarf star, but with the electrons obeying the laws of Einstein's special relativity. Fowler had calculated that for a given chemical composition the density of a white dwarf would be proportional to the square of its mass. The more massive the star, the stronger the force of gravity and the more tightly the star would be squeezed together. The more massive stars would be smaller and fainter. This explained the fact that no white dwarfs much more massive than the Sun had been seen. Chandrasekhar asked himself: Is there any upper limit to how massive a white dwarf can be before it collapses under the force of its own gravitation? Modifications due to special relativity led to a startling conclusion on the behaviour of white dwarf stars: Special relativity makes the matter in the stars more compressible, so that the density becomes greater for a star of given mass. The density does not merely increase faster than the mass, it tends to infinity as the mass reaches a finite value. This maximum became known as the Chandrasekhar limit and equals about 1.5 times the mass of the sun for stars that have burned up all their hydrogen. Any dwarf more massive than this cannot be stable.

Fowler was perplexed by this second paper. He sent it to Edward Arthur Milne, a leading astronomer in Great Britain, who Fowler thought was more familiar with the subject. As no response had arrived after many months, and seeing no possibility of its publication in the *Monthly Notices of the Royal Astronomical Society*, Chandra sent his paper “The Maximum Mass of Ideal White Dwarfs” to the *Astrophysical Journal* in November 1930. He continued his research and published new papers, but he did not receive any encouragement in Cambridge and began to have doubts about the value of the work he was doing in astrophysics.

As suggested by Paul Dirac, his mentor, he spent his third graduate year at Niels Bohr's Institute for Theoretical Physics in Copenhagen, where he found a friendly climate and met many interesting young people and visitors from all Europe. For his thesis he prepared a series of papers on distorted polytropes (used as crude approximations to realistic stellar models) and self-gravitating gaseous spheres in which the pressure and density have a power-law relationship.

In the summer of 1933, after having completed his Ph.D. degree, he was determined to extend his stay in Europe, even if his father was pressing him to return to India. With little hope, he applied for a fellowship at Trinity College, a dream that came true, even if the competition was really formidable. Chandra was very proud, as the only other Indian who had been elected a Trinity fellow was Ramanujan, some 16 years before. He would now have four more years in Cambridge. During a visit to Russia in 1934, Chandra met the astrophysicist Viktor Ambartsumian, head of the Astrophysical Department at the University of Leningrad, and founder of the school of theoretical astrophysics in the Soviet Union. Ambartsumian, who became well known for his theories concerning the origin and evolution of stars and stellar systems, was quite enthusiastic about his discovery and suggested Chandra should work out the exact, complete theory rid of some simplifying assumptions he had made.

Chandra worked hard and made detailed, tedious numerical calculations in order to obtain as exact a theory of the white dwarf as one could construct within the framework of relativistic quantum statistics and the known features of stellar interiors. He pointed out: «Finally, it is necessary to emphasize one major result of the whole investigation, namely, that the life-history of a star of small mass must be essentially different from the life-history of a star of large mass. For a star of small mass, the natural white-dwarf stage is an initial step towards complete extinction. A star of large mass (> Mc) cannot pass into the white-dwarf stage, and one is left speculating on other possibilities.»

He submitted two papers to the Royal Astronomical Society by the end of 1934 and was invited to present an account of his results at the January 1935 meeting of the academy. Chandra's presentation of extensive numerical analysis indicating that the fate of massive stars must be something other than gradually cooling white dwarfs raised challenging and fundamental questions: What happens to the more massive stars as they continue to collapse? Are there other terminal stages different from white dwarfs?

Chandrasekhar’s result deeply disturbed Eddington. He was not pleased with Chandra's answer and announced that there is no such thing as relativistic degeneracy. Unless some mechanism could be found for limiting the mass of any star that was eventually going to compress itself into a dwarf, or unless Chandra’s result was wrong, massive stars were fated to collapse gravitationally into oblivion. Eddington found this intolerable and proceeded to attack Chandrasekhar’s use of quantum statistics - both publicly and privately. He characterized the theory of the limiting mass for the white dwarfs as “a stellar buffoonery”. The criticism by such an authority in astrophysical questions devastated Chandrasekhar. He stopped further work on the theory of white dwarfs and researched in other areas: «If I was right, then it would be known as right. For myself, I was positive that a fact of such clear significance for evolution of the stars would in time be established or disproved. I didn't see a need to stay there, so I just left it.» Astronomers had good reason in 1930 to react with scepticism to Chandra’s statements. Chandra’s calculation says that when those stars burn up their nuclear fuel, there will exist no equilibrium states into which they can cool down. What then, can a massive star do when it runs out of fuel? Chandra had no answer to that question, and neither did anyone else when he raised it in 1930. The answer was discovered in 1939 by J. Robert Oppenheimer and his student Hartland Snyder. They published their solution in a paper, “On Continued Gravitational Contraction”, in which they accepted Chandra’s conclusion that there exists no static equilibrium state for a cold star with mass larger than the Chandrasekhar limit. Therefore, the fate of a massive star at the end of its life must be dynamic. They worked out the solution to the equations of general relativity for a massive star collapsing under its own weight and discovered that the star is in a state of permanent free fall - that is, the star continues forever to fall inward toward its centre. General relativity allows that paradoxical behaviour because the time measured by an observer outside the star runs faster than the time measured by an observer inside the star. The gravitational collapse becomes a state of permanent free fall and it is, so far as we know, the actual state of every massive object that has run out of fuel. We know that such objects are abundant in the universe. We call them black holes, a term used coined by John Wheeler in the 1960s.

With hindsight, we can see that Chandra’s discovery of a limiting mass and the Oppenheimer-Snyder discovery of permanent free fall were major turning points in the history of science. Those discoveries marked the end of the Aristotelian vision that had dominated astronomy for 2000 years: the heavens as the realm of peace and perfection, contrasted with Earth as the realm of strife and change. Since the 1930s, observational evidence demonstrated the existence of violent events in the heavens, like supernova explosions, during which heavy atoms are ejected into space after having been cooked in the core of massive stars. Radio and X-ray telescopes revealed a universe full of shock waves and high-temperature plasmas, with outbursts of extreme violence associated in one way or another with black holes.

The New World

During the fall of the difficult year 1935, which marked the white dwarf controversy with Eddington, Chandra received an offer of a lectureship at Harvard University. During the three months of his visit, he established excellent relationships and was offered a position from Harvard and another from Yerkes. He chose Yerkes Observatory, at the University of Chicago, where a group of young theorists and observational astronomers was in the making. But by that time he had been away from home for nearly six years, and he felt it was time to go back to see his family. During his stay in Madras, he married Lalitha Doraiswamy, whom he knew since they were undergraduate students at Presidency College, and who had been waiting for him during all those years. In 1937, they arrived in the US and Chandra immediately took on the task of developing a graduate program in astronomy and astrophysics at Yerkes. Very soon his reputation as a fascinating teacher and his enthusiasm for research began to attract students from all parts of the world. At Yerkes, his first research priority was the completion of his book *An Introduction to the Study of Stellar Structure*, which appeared in 1939. Many of his research papers in 1936-39 included proofs of theorems to be included in the book. It was the second classic text on stellar structure after Eddington's *The Internal Construction of the Stars*. It contained almost everything that could be learnt on the internal structure of white dwarfs and other types of stars without the aid of a powerful computer.

After he had completed the book, Chandra carried out very few further researches on stellar structure and as a natural progression of his interests in the structure and evolution of stars he moved to the field of stellar dynamics. The realisation in the 1920s and 1930s that the Universe was composed of galaxies of a variety of shapes and the discovery of the rotation of our galaxy stimulated interest in trying to understand the equilibrium distribution of the motions of stars inside galaxies and the processes by which equilibrium was approached or departures from equilibrium could arise. In 1942, Chandra published his monograph *Principles of Stellar Dynamics*, describing his highly original work on the statistical theory of stellar motions in clusters and in galaxies. That same year he became an associate professor, and in 1944 he became full professor and member of the Royal Society. The old controversy with Eddington was a thing of the past and the latter was very definite that Chandra ought to be elected.

At that time a new change in direction of his researches occurred, which now turned to radiative transfer and stellar atmospheres. In his work on radiative transfer he gave the first accurate theory of radiation transport in stellar atmospheres introducing new techniques or considerably developing the existing ones for solving the equation of transfer. In his book *Radiative transfer*, published in 1950, he stressed that his techniques had much wider use than in astronomy alone. He emphasised how that had been his justification for writing the book. And indeed the development of nuclear power led to a major work on neutron diffusion, which is a closely similar mathematical problem. The physics of the Cosmic Microwave Background is actually based on straightforward application of the theory of radiative transfer to the relic radiation from the big bang through the cosmic eons. Chandra's classical text has in fact been cited in the seminal papers and in subsequent reviews on Cosmic Microwave Background anisotropy and polarisation, testifying the long-term impact of his fundamental work in each of the fields he tackled during his life.

In 1953, he and his wife Lalitha took the U.S. citizenship. Chandra's father, who had continued to hope that his son would return to India and take a position there, considered it a betrayal of their mother country.

In 1952, Chandra became Managing Editor of the* Astrophysical Journal*, a local University of Chicago publication, founded in 1895. He retained this post until 1971. During his tenure the journal grew in stature to become the national publication of the American Astronomical Society and then a leading international journal. By the time he retired, it had become the premier journal in astronomy and astrophysics.

Despite the fact that he was still sole editor of *The Astrophysical Journal*, Chandra spent as much time on research as did his most dedicated students. Beginning his work at 5 am, he finished each 13-hour workday late in the evening. John Friedman, in the volume dedicated to Chandra on the centenary of his birthday, recalled: «As part of his moral instruction to us, Chandra did not hesitate to point out that by the time his colleagues arrived in the morning, he had already put in half as many hours as they would work in a day.»

Around 1952, Enrico Fermi invited him to become a member of the Research Institute (now the Enrico Fermi Institute) and the physics department of the University of Chicago. Physics began to dominate Chandra's research. After completing his book on radiative transfer, he dedicated the next ten years to what has become the field of magnetohydrodynamics, the study of the dynamics of electrically conducting fluids. Examples of such fluids include plasmas, or liquid metals. The field was initiated in the early 1940s by Hannes Alfvén, who was awarded the Nobel Prize in Physics in 1970. Over the course of roughly a decade, from the late 1950s through the early 1960s, Chandrasekhar made fundamental contributions to basic plasma physics, and studied the effect of magnetic fields on the dynamics of astrophysical plasmas. He followed four general themes: the statistical properties of turbulence, problems in astrophysical magnetohydrodynamics, basic plasma physics, and hydrodynamic and magnetohydrodynamic instabilities. His *Hydrodynamic and Hydromagnetic Stability*, published in 1961, provides a foundation for the theory of all kinds of astronomical objects - including stars, accretion disks, and galaxies - that may become unstable as a result of differential rotation. Chandra solved an old problem by finding all the possible equilibrium configurations of an incompressible liquid mass rotating in its own gravitational field. The problem had been studied by the great mathematicians of the 19th century -- Carl Jacobi, Richard Dedekind, Peter Lejeune Dirichlet, and Bernhard Riemann -- who were unable to determine which of the various configurations were stable. Chandra made a special study of their little known papers on rotating ellipsoids, summarized in the volume *Ellipsoidal Figures of Equilibrium*, published in 1969.

**General relativity and black holes**

Since the early 1950s Chandra began to teach regular physics courses instead of only the astronomy and astrophysics courses and became the first one to teach general relativity at the University of Chicago, a circumstance that also led him to research in relativity. From the late 1960’s on, he was working seriously on the mathematical study of black holes and of colliding waves. By then it was clear that stars more massive than the Chandrasekhar limit that had exhausted their nuclear fuel could contract to much denser neutron stars, which have a similar but larger mass limit, and that still more massive stars could contract to black holes, if they did not explode completely as supernovae. With his postdoctoral research fellows and Ph.D. students, Chandra worked out many of the properties of black holes of all masses

After the ellipsoidal figures opus came a gap of 15 years before the appearance of *The Mathematical Theory of Black Holes* in 1983, which Roger Penrose, well known for his outstanding contributions to general relativity and cosmology, called "a masterpiece". During these years, Chandra explored in depth the foundations of the equations of general relativity working hardest and most intensively on the subject closest to his heart: the precise mathematical description of black holes and their interactions with surrounding fields and particles. However, despite the power and the insights that Chandra and his associates and many other researchers were eventually able to provide, the results of this work remained inconclusive. Up to now, the problem of the ultimate fate of a collapsing star remains unresolved.

In coincidence with the publication of his volume on black holes, Chandra was awarded the 1983 Nobel Prize in Physics "*for his theoretical studies of the physical processes of importance to the structure and evolution of the stars*". He shared the Prize with William Fowler, who had done extensive work during the 1950s on theoretical and experimental studies of the nuclear reactions of importance in the formation of the chemical elements in the universe.

Besides his great commitment to research, Chandra had a deep and abiding interest in literature and classical music. He cultivated them with the same degree of thoroughness and intensity as his science. After the book on black holes was published, Chandra lectured and wrote about the works of Shakespeare and Beethoven and Shelley, and about the relationship between art and science. A collection of his lectures for the general public was published in 1987 with the title *Truth and Beauty*. During the years of his retirement, he spent much of his time working his way through Newton’s *Principia*. He decided that rather than assessing Newton secondhand, through commentaries, he would absorb the *Principia* unmediated. More specifically, he would read a proposition and then, before going on to Newton's proof, would try to derive his own. Chandra reconstructed every proposition and every demonstration, translating the geometrical arguments of Newton into the algebraic language familiar to modem scientists. The results of his historical research were published in 1995, shortly before his death in his last book, Newton’s *Principia for the Common Reader*, where Chandra transformed the Newtonian Mathematics into modern idioms and thus made it much more accessible to a wider audience. To explain why he wrote the book, he said, «I am convinced that one’s knowledge of the Physical Sciences is incomplete without a study of the *Principia* in the same way that one’s knowledge of Literature is incomplete without a knowledge of Shakespeare.»

In the summer of 1999, about 40 years after its conception in a seminal paper by Riccardo Giacconi and Bruno Rossi, an X-ray telescope was launched into space by the Space Shuttle Columbia. This Observatory was built to explore the high energy Universe, which features such exotic objects as neutron stars and black holes.

NASA conducted an international contest for naming the Observatory. There were more than 6000 entries from 61 countries. The winners were a high school student from Idaho, Tyrel Johnson, and a high school teacher from California, Jatila van der Veen. These two submitted the winning essays that selected Chandra as the name of this great space observatory, in honour of Subrahmanyan Chandrasekhar.

The success of *Chandra* has been enormous and covers all fields of X-ray astrophysics. This powerful mission was joined in orbit in December 2000 by the European Space Agency's Newton Observatory. Both *Chandra* and *Newton* took X-ray astronomy and high-energy astrophysics into a new era.

**Bibliography**

Wali K. C. (1991) Chandra: A Biography of S. Chandrasekhar, U. Chicago Press, Chicago

Wali K. C. ed. (2010) A Scientific Autobiography: S. Chandrasekhar,World Scientific, Hackensack, NJ

Saikia D. J. and V.Trimble eds. (2011) Fluid flows to black holes. A tribute to S. Chandrasekhar on his birth centenary. World Scientific

R. J. Tayler (1996) Biographical Memoirs of Fellows of the Royal Society 42: 80-94