Chandrasekhar, Subrahmanyan

(1910-1995), applied mathematician and astrophysicist

by Leon Mestel

© Oxford University Press 2004 All rights reserved

Chandrasekhar, Subrahmanyan (1910-1995), applied mathematician and astrophysicist, was born on 19 October 1910 in Lahore, India, the eldest of four sons and third of the ten children of C. Subrahmanyan Ayyar (1885-1960), assistant auditor to the Northwest Railways, and his wife, Sitalaksmi (1891-1931), daughter of Rao Baladur Balakrishnan Aiyar (1891-1931). His paternal ancestors were Brahmans and small landowners in Madras, where the family returned when he was still young. Chandra (as he was known to all generations) came from the intellectual élite of India. His father put pressure on his brilliant son to follow him into Indian government service, but with the gentle support of his mother, he was able to persist in his choice of a career in pure science, following rather the example of his father's brother, Sir (Chandrasekhara) Venkata Raman, who was to achieve fame and win a Nobel prize for his discovery of what became known as the Raman effect. While still an undergraduate at Presidency College, Madras, Chandrasekhar had already published his first paper, submitted to the Proceedings of the Royal Society by R. H. (Sir Ralph Howard) Fowler. In 1930 he departed for England on a scholarship from the Indian government, and said goodbye for the last time to his ailing mother.

Chandrasekhar was a research student at Trinity College, Cambridge, from 1930 to 1933, and a research fellow from 1933 to 1937. In 1936 he returned to India to see his family and to marry, on 11 September 1936, his fiancée, Lalitha Doraiswamy (b. 1910), daughter of a neighbouring family in Madras and a fellow student of physics at Presidency College. Their marriage, exceptionally, was by mutual choice rather than by arrangement. Lalitha's family was also very interested in education, and before her marriage she worked as a school headmistress. She was an ever-present support for Chandrasekhar during their fifty-nine years together. There were no children of the marriage. After a short period in Cambridge they moved to the USA, where they settled. For most of the time Chandrasekhar was on the staff of the University of Chicago, originally at Yerkes Observatory in Wisconsin and then at the city campus. For a while after the Second World War he would almost certainly have accepted the offer of a vacant chair in Oxford or Cambridge, but other appointments were made. In 1952 he was appointed Morton D. Hull distinguished service professor at Chicago, and in 1953 both he and Lalitha took out American citizenship. In 1964, by which time he had become inextricably part of the American scene, he cabled by return his refusal of the offer of a chair at Cambridge. He retired in 1980, becoming emeritus professor at the University of Chicago in 1985.

It was while travelling to England that Chandrasekhar (independently of E. C. Stoner and W. Anderson) made the discovery for which he is probably best known in the general scientific world. Some years earlier Fowler had applied the newly enunciated Pauli exclusion principle to infer that white dwarf stars--faint collapsed bodies of stellar mass but with planetary radii, and so with densities of about a ton to the cubic inch--constitute the natural graveyard towards which all normal stars such as the sun would evolve once all nuclear energy sources had been exhausted. Chandrasekhar showed that as a consequence of Einstein's special relativity, the pressure of the cold, 'degenerate' electron gas would be able to balance the enormous gravitational force only for stars of mass less than a critical value--'Chandrasekhar's limit'. However, this conclusion was resisted strongly by his Trinity colleague Sir Arthur Eddington, Plumian professor and author of The Internal Constitution of the Stars, who described Chandrasekhar's work as 'almost a reductio ad absurdum of the relativistic degeneracy formula' (Tayler, 85). Although other leading theoretical physicists assured Chandrasekhar privately that his theory was correct, they appear to have been unwilling to become involved in controversy with Eddington, who remained convinced to the end of his life that 'there is no such thing as relativistic degeneracy' (ibid.). There is now no doubt that Chandrasekhar was right. Relativistic degeneracy is an essential feature of our picture of stellar evolution, ensuring that stars above the Chandrasekhar limit contract to states of such high density and temperature (the 'hotter place' demanded by Eddington himself in a famous riposte) that one can account for the synthesis of the more massive elements, the occurrence of supernovae, and the formation of neutron stars, observed as radio and X-ray pulsars.

Chandrasekhar's work had indeed revived a ghost that Eddington thought had been finally laid by Fowler: what would be the fate of a star that ended its life with a mass too great to be able to settle down as a cold, dying body--either a white dwarf or a (subsequently studied) neutron star? It is now believed that such a massive body ends its days as a black hole, discovered by Karl Schwarzschild to be a solution of Einstein's general relativistic field equations. Decades later Chandrasekhar in characteristic style began a systematic study of some areas in general relativity which culminated in his penultimate treatise on the theory of black holes; this was devoted largely to the properties of R. P. Kerr's remarkable generalization for a rotating black hole of the Schwarzschild solution. By then, the opposition of the long-departed Eddington was part of history. Despite that controversy, however, Eddington's seminal contributions to astronomy were recalled by Chandrasekhar in his centenary lectures, Eddington: the most Distinguished Astrophysicist of his Time (1983), in which he paid him generous tribute. Earlier, Eddington had played a leading part in securing Chandrasekhar's 1944 election to the Royal Society.

Chandrasekhar's style of work was unique, and his output phenomenal. He would move into a new area, master the basic physics and its mathematical formulation, and proceed to make important--often outstanding--contributions to its mathematical development. A series of monographs told the story of his scientific life: An Introduction to the Study of Stellar Structure (1939); Principles of Stellar Dynamics (1942); Radiative Transfer (1950); Plasma Physics (1960); Hydrodynamic and Hydromagnetic Stability (1961); Ellipsoidal Figures of Equilibrium (1969); The Mathematical Theory of Black Holes (1983); and Newton's Principia for the Common Reader (1995). There were in addition six published volumes of selected papers containing material subsumed into the monographs but also much other material. Chandrasekhar's readership was not confined to the astronomical world; for example, the volume on radiative transfer became essential reading for those concerned with neutron diffusion in nuclear reactors.

Chandrasekhar's driving motivation was the opportunity to deploy his mathematical prowess. Sometimes he derived results whose importance was not appreciated by the astronomical community until later. Thus once the basis of magnetohydrodynamics had been established, it was inevitable that he would explore some of the consequences in mathematical detail. He was the first to derive general, exact, steady-state integrals for a rotating system with a magnetic field symmetric about the rotation axis; but it was left to others to re-derive the integrals and to show how they could describe the rotational history of the sun and other solar-type stars, with possible spin-off regarding the origin of planetary systems. Again, in his volume on hydrodynamic stability, there was a result that confirmed that the presence of a magnetic field would transform the whole stability problem for a rotating disc of gas surrounding a star. This result is now the starting point of a veritable 'accretion disc' industry. The study of the equilibrium and stability of rotating, self-gravitating ellipsoids goes back to Newton, and over the centuries it has attracted the attention of a long and distinguished series of astronomers and mathematicians. With characteristic insight, Chandrasekhar saw that the elaborate formalism developed by previous workers had made the subject unnecessarily complicated, and that the more important results could be obtained in Cartesian coordinates. It is gratifying that the twentieth century produced Chandrasekhar and his Chicago collaborator Norman Lebovitz, who responded to an inherited challenge with such éclat, correcting errors and populating completely the parameter space.

Chandrasekhar next moved into general relativity. His development of the post-Newtonian approximation for dealing with Einstein's non-linear equations was opportune, for the discovery of the first pulsar--a rotating, magnetic neutron star--that is also a member of a binary system had opened a laboratory for studying the implications of Einstein's theory. The predicted analogue of the perihelion advance--observed in the solar system as a mere 43 seconds of arc for the planet Mercury--is 4 degrees per year, and other characteristic general relativistic effects are similarly scaled up. In particular, the spin-up of the orbital motion due to energy loss through gravitational radiation has been monitored to astonishing accuracy by Joe Taylor and colleagues. Chandrasekhar's work, together with that by Hermann Bondi, Andrej Trautman, Kip Thorne, and others, laid to rest the lingering doubts about whether gravitational radiation is indeed a consequence of general relativity.

After his heroic efforts on the theory of black holes, Chandrasekhar returned to Newtonian gravitation. As outlined in the prologue to his volume Newton's Principia, his approach was to read the enunciation of the different propositions and then to construct proofs for them independently ab initio. He then presented Newton's proofs, but set them out in 'a linear sequence of equations and arguments, avoiding the need to unravel the necessarily convoluted style of Newton's prose. With the impediments of language and syntax thus eliminated, Newton's physical insight and mathematical craftmanship come sharply into focus' (Chandrasekhar, Newton's Principia, 1995, Prologue). This volume has in fact been criticized by some other students of Newton's legacy, but for one 'common reader' the book succeeded in its aim: it will be a continuing source of pleasure, and a permanent reminder of its author.

Parallel with his unrivalled productivity, Chandrasekhar undertook for nearly twenty years the herculean task of editing the Astrophysical Journal. He played a decisive role in its transformation from a private journal of the University of Chicago into the national journal of the American Astronomical Society. His draconian editorial style ensured that the journal retained and indeed greatly enhanced its worldwide reputation.

Chandrasekhar shared the 1983 Nobel prize for physics specifically for his work on white dwarfs and black holes. This was followed in 1984 by the Royal Society's highest award, the Copley medal. Chandrasekhar's many other awards included the Bruce medal of the Astronomical Society of the Pacific, the Henry Draper medal of the National Academy of Sciences, and the gold medal of the Royal Astronomical Society. In Roger Tayler's words, he 'was a classical applied mathematician whose research was primarily applied in astronomy and whose like will probably never be seen again' (Tayler, 91). His approach was to rewrite from first principles nearly every subject into which he entered, transforming it profoundly and triggering an era of new insights and discoveries by himself and others. The younger generation who wish to solve those problems which he has left for them will not attempt to compete with his analytical skills and his ability to perform complicated algebraic manipulation with minimal mistakes; instead they will use algebraic computing techniques.

Chandrasekhar died in Chicago from heart failure on 21 August 1995. He was survived by his wife Lalitha, and was buried in Chicago. Coming so soon after the completion of his last treatise, his death seemed symbolic, for he had stated that this would be his last scientific work. At the end of his biography, K. C. Wali notes that Chandrasekhar did question the single-minded pursuit of knowledge that had dominated his life; however, one could not imagine him ceasing to be creative, just being content to relax with Beethoven and Shakespeare, whom he coupled with Newton in a lecture entitled, 'Patterns of creativity'.

LEON MESTEL

Sources  
K. C. Wali, Chandra (1991)
K. C. Wali, ed., S. Chandrasekhar: the man behind the legend (1997)
R. J. Tayler, Memoirs FRS, 42 (1996), 81-94
K. Singh, Two essays on Professor S. Chandrasekhar (1971)
The Times (24 Aug 1995)
The Independent (24 Aug 1995)
WWW, 1991-5
personal knowledge (2004)
private information (2004) [Mrs Lalitha Chandrasekhar and others]

Archives  
University of Chicago, Joseph Regenstein Library, MSS |  Trinity Cam., corresp. with Harold Davenport

Likenesses  
photograph, 1950, repro. in Tayler, Memoirs FRS, 80
photograph, repro. in The Times
photograph, repro. in The Independent
photographs, repro. in Wali, ed., S. Chandrasekhar


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