Subrahmanyan Chandrasekhar, 19 October 1910 -...

1910 - 21 August 1995Subrahmanyan Chandrasekhar, 19 October

R. J. Tayler, F. R. S.

1996, 80-94, published 1 November421996 Biogr. Mems Fell. R. Soc.

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SUBRAHMANYAN CHANDRASEKHAR19 October 1910-21 August 1995

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SUBRAHMANYAN CHANDRASEKHAR

19 October 1910-21 August 1995

Elected F.R.S. 1944

B y R.J. T a y l e r , F.R.S.

Astronom y Centre, University o f Sussex, Faimer, Brighton BN1 9QH, UK

In t r o d u c t io n

In August 1930 Subrahmanyan Chandrasekhar arrived in London at the age of 19 years and 10 months with the aim of studying for a doctorate at Cambridge. He had already published several papers, including one which had been communicated to the Royal Society by R.H. (later Sir Ralph) Fowler, F.R.S. During his sea journey he had made considerable progress towards the solution of the problem of the maximum mass of a white dwarf star, which was a key topic in the award of the Nobel Prize for Physics to him in 1983. How could he have done so much at such a young age?

Although Chandrasekhar (known to all of his friends and colleagues as Chandra) was born in Lahore, in what is now Pakistan, his paternal ancestors were brahmins and small landowners in the Madras Presidency in south India. His grandfather, Ramanathan Chandrasekhar, was educated in an English school and subsequently obtained college degrees while working as a teacher; he eventually became a college vice-principal. The two oldest of his eight children were Chandra’s father, C. Subrahmanyan Ayyar and C. Ventakaraman (later Sir C.V. Raman, F.R.S. and Nobel Laureate). They were brilliant students who entered government service as accountants and auditors. Raman’s interest in science later led him to give up his secure employment to take up full-time research. Chandra’s father was assistant auditor to the Northwest Railways when Chandra was born on 19 October 1910. He was the third child and first son of C.S. Ayyar and his wife Sitalaksmi and he was to have three younger brothers and four younger sisters. In 1912 Chandra’s family moved to Lucknow and then his father became deputy accountant general in Madras, which meant that Chandra grew up where his family had its roots.

81 © 1996 The Royal Society



82 Biographical Memoirs

E a r l y l if e

Chandra was educated at home until he was 11. His parents knew that they had a very able pupil and when he entered high school he was placed immediately in the third form. He completed high school aged 15 and entered Presidency College, Madras. Meanwhile his father had built a large house in a prestigious suburb of Madras and one of their neighbours was Mrs Savitra Doraiswamy, one of whose daughters was Chandra’s future wife, Lalitha. After two years in college, Chandra wished to specialize in mathematics, not only because of his ability but because of his fascination with the legendary work of S. Ramanujan, F.R.S. His father wished him to study physics and to join the Indian Civil Service. Chandra was happy to study physics but he was intent on becoming a scientist; he wished to follow Ramanujan and Raman and in this he received some encouragement from his mother. 1928 saw the discovery of the Raman effect and speculation that this was so important that Raman would receive the Nobel Prize.

In late 1928 Arnold Sommerfeld, For. Mem. R.S., visited Presidency College on a lecture tour. Chandra had read Sommerfeld’s Atomic Structure and Spectral Lines and he managed to meet Sommerfeld. He was told that the book had been completely superseded by the new quantum mechanics. Sommerfeld gave Chandra a copy of the proofs of a paper on the electron theory of metals, which was an early application of Fermi-Dirac statistics. This stimulated Chandra to do original research and he wrote his first major paper ‘Compton scattering and the new statistics’ (1)*. He was confident that this would merit publication in an international journal but he needed to find someone to communicate it. Having seen a paper by R.H. Fowler on the application of Fermi-Dirac statistics to white dwarf stars, Chandra sent his paper to Fowler. After Fowler and N.F. Mott (later Sir Nevill, F.R.S.) made some suggestions for minor improvements, it was published in Proceedings o f the Royal Society while Chandra was still only 18.

He completed his undergraduate studies in 1929-30. He had two further papers published in the Philosophical Magazine in that year (2, 3) and he also had valuable scientific discussions with W. Heisenberg (later For.Mem.R.S.) and M.N. Saha, F.R.S. As a result of his studies and researches, he was offered a Government of India Scholarship for research in England. He was supposed to serve in the Madras State Service or at Presidency College on his return to India. There was one serious doubt about his acceptance of the scholarship. His mother had been seriously ill for some time and it was doubtful whether he would see her alive again. She was insistent that he should go and that settled it. One problem remained. Chandra wished to study with Fowler at Trinity College, Cambridge, but the High Commissioner for India said that was not possible and that he should join University College, London. Chandra sailed from Bombay on 31 July 1930 with the hope that he could persuade Cambridge to have him.

C a r e e r o u t l in e

Chandra was a research student at Cambridge from 1930 to 1933 and a Fellow of Trinity College from 1933 to 1937. While he was at Cambridge he made extended research visits to Copenhagen and to Harvard. In 1936 he returned to India to see his family and to marry Lalitha. His mother was not there to meet him. Her illness proved fatal and to his great sorrow

*Numbers in this form refer to the bibliography at the end of the text.



Subrahmanyan Chandrasekhar 83

she had died in May 1931, during his first year in Cambridge. The marriage to Lalitha was one of their own choosing and not the more conventional arranged marriage. Her family was, like his, very interested in education and particularly in education for their daughters. Lalitha also studied physics at Presidency College and she was a school headmistress before their marriage.

By 1936 Chandra’s future in Cambridge was unclear. His fellowship at Trinity would soon end and, because of a controversy with Sir Arthur Eddington, F.R.S., about the structure of white dwarf stars, it seemed unlikely that he would obtain a permanent post. He (and his father) still expected him to return to India in due course, but he turned down an offer from Raman as he did not wish to work in his uncle’s shadow. He did not apply for another attractive Indian post because one of his best friends was a candidate and he decided to broaden his experience by accepting an invitation from Otto Struve (later For.Mem.R.S.) to become a research associate at the Yerkes Observatory of the University of Chicago at Williams Bay, Wisconsin, in 1937. As a result, Lalitha and he started their married life in the American mid-west.

At this stage they little thought that he would be associated with the University of Chicago for the rest of his life. He became an associate professor in 1942, a full professor in 1944 and finally Morton D. Hull Distinguished Service Professor in 1952, becoming Emeritus Professor in 1985. Return to India seemed probable in the early years but no really appropriate opportunity arose. I understand that he allowed his name to be considered for vacant chairs at Cambridge and Oxford, but other appointments were made. Eventually in 1953, when it seemed very likely that they would be staying in the United States, he and Lalitha took out U.S. citizenship. They wished to have the freedom to participate more actively in the life of their adopted country. Chandra’s father was upset by what he considered a betrayal of India.

T he A stro ph y sic a l Jo u rn a l

In the early 1950s, two significant events occurred in Chandra’s scientific life. As a result of changes at the Yerkes Observatory, Chandra accepted an invitation from Enrico Fermi (For.Mem. R.S.) to be more closely associated with the main university campus in Chicago. Although he and Lalitha continued to live in Williams Bay until 1964, his main researches and teaching became concentrated in Chicago. In 1952 he became Managing Editor of the Astrophysical , a postwhich he retained until 1971. This was a period of great growth for the journal and Chandra was a very autocratic editor. He demanded the same high standards from other authors that he had himself. As far back as 1936, E.A. Milne, F.R.S., had written to Chandra: ‘In my opinion your papers are clearer and offer more pleasure in the reading than those of any contemporary astrophysicist.’ On one occasion Chandra wrote to an author: ‘Your paper is scientifically correct but I wish you would ask your colleague in the English Department to read it.’

While he was editor, his own scientific work did not slow down. It is difficult to imagine how he managed to achieve all that he did. He worked long hours and, as far as his research was concerned, he had the enviable ability to get complicated calculations right first time. He also organized his time very carefully. I am told that Astrophysical Journal business had to be over by 10 a.m. each day and that he would not discuss papers with authors after that hour. He was decisive and was not afraid to reject papers. This led to some tensions between him and the astronomical community. He said that there was some tendency for astronomers to avoid him.

When he took over the editorship the Astrophysical Journal was a private journal of




the University of Chicago. Because of the rapid growth of astronomy in the United States and Chandra’s high editorial standards, by the time he retired it was clearly the premier journal in astronomy and astrophysics. It seemed appropriate that it should become a national journal. After difficult negotiations, it was arranged for it to be taken over by the American Astronomical Society, although publication continued with the University of Chicago Press.

W id e r in t e r e s t s a n d f a m il y l if e

I have already mentioned Chandra’s high standards as an editor. These were related to his respect for the English language and to his great interest in literature and art. The connection between scientific and artistic creativity was explored in his 1975 Ryerson Lecture on Shakespeare, Newton and Beethoven. It also resulted in his 1987 book Truth and Beauty: Aesthetics and Motivations in Science (58). Chandra was certainly a scientist for whom the aesthetic qualities of his work ranked in importance with its practical importance. He regarded Newton as the greatest scientist ever and he compared reading Newton to equally awe- evoking experiences such as gazing at the ceiling of the Sistine Chapel, watching Sir John Gielgud play Hamlet or hearing Toscanini conduct Beethoven’s ninth symphony.

In 1980 Chandra’s respect for the genius of Ramanujan involved him in a project to have a bust made of him, so that his widow, who was old and living in reduced circumstances, could have one. Four busts were made, one of which was presented to Mrs Ramanujan in 1983, and two were acquired by Chandra and Lalitha. Chandra presented one to the Royal Society in May 1994 and the then President, Sir Michael Atiyah, placed it in his office.

Chandra and Lalitha had no children but K. Wali in his biography of Chandra (1991) brings out their warm feelings towards the children of their friends and colleagues and the good relationships which they had with them. Mrs M. Weston Smith, Milne’s daughter, tells me of the great kindnesses which she and her sister and brother received from Chandra and Lalitha including an offer to have them at Williams Bay during the World War II.

Raman and Chandra were not the only distinguished scientists in their immediate family. Raman’s son, Dr V. Radhakrishnan, is a distinguished radio astronomer, who succeeded his father as Director of the Raman Research Institute, Bangalore. Another of Chandra’s cousins is Professor Sivaramakrishna Chandrasekhar, F.R.S. and Royal Medallist, Director of the Centre for Liquid Crystal Research, Bangalore.

I l l n e s s a n d d e a t h

Chandra had heart trouble in late 1973 and then more seriously in September 1974. In 1976 he required major heart surgery. Although this slowed him down for a time, he was eventually able to return to his researches, which by that time were concentrated on the mathematical theory of black holes. His share of the 1983 Nobel Prize gave great pleasure to his many friends and admirers. He continued with research and scholarship almost to the time of his death, with his final book on Newton’s Principia (59) appearing in early 1995. He died of heart failure on 21 August 1995 after almost 59 years of very happy marriage.




S c ien tific w o rk at C a m b r id g e , 1930-36

Chandra’s period at Cambridge was scientifically very productive but what he did there has been overshadowed by his controversy with Eddington concerning relativistic degeneracy and the maximum mass of white dwarf stars. Chandra worked towards his definitive paper slowly and Eddington was not initially roused. A 1931 paper in the Astrophysical Journal on the maximum white dwarf mass, based on the work done on his journey to England, gave a value which was not precisely his final value. In 1934 a further paper in the Observatory Magazine gave the correct value but Chandra himself wrote of the implied infinite density: ‘but it is doubtful if the result has any particular significance’. All doubt had gone in January 1935 when Chandra read a paper (4) to the Royal Astronomical Society in which he gave the full discussion of what became known as the Chandrasekhar limit.

Eddington could not accept this result. He was, of course, entitled to his views, which were based partly on common sense that all stars must die quietly and partly on his own theories of the nature of matter, which were later summed up in his books The Relativity Theory of Protons and Electrons and the (posthumous) Fundamental Theory. There is, however, dispute about the manner in which he handled the R.A.S. meeting. He gave Chandra no advance warning of his criticisms. There is a majority view that this was unkind and a minority view, strongly supported by Sir William McCrea, F.R.S., that Eddington wished to give Chandra an opportunity to present his argument without the shadow of refutation hanging over him.

The Observatory Magazine carries an account of the meeting with the following statements. Chandra: ‘There exists a critical mass M. If the star’s mass is greater than M the star cannot have a collapsed core.’ Eddington: ‘I do not know whether I shall escape from this meeting alive but the point in my paper is that there is no such thing as relativistic degeneracy. Dr Chandrasekhar has got this result before, but he has rubbed it in in his last paper; and when discussing it with him I felt driven to the conclusion that this was almost a reductio ad absurdum of the relativistic degeneracy formula.’

Eddington’s status in British Astronomy was as that time supreme. Both Milne and Sir James Jeans, F.R.S., had disagreed with him about stellar structure but he had won the argument. There were few professional astronomers in the R.A.S. and most of those were observers who instinctively believed Eddington. This was a great disappointment to Chandra who felt seriously bruised by the experience. He regarded Eddington as one of the great men of science and he retained this regard as was shown by his address at the Eddington centenary in 1982 (57). However, he had made what proved to be a very important discovery and Eddington refused to accept it and as a result delayed its general acceptance. Chandra was in contact with theoretical physicists, who privately assured him that his theory was correct, but they had no wish to be involved in controversy with Eddington. P.A.M. Dirac, F.R.S., R. Peierls (later Sir Rudolf, F.R.S.) and M.H.L. Pryce (later F.R.S.) published a paper in 1942 criticizing Eddington’s treatment of relativistic quantum theory without mentioning Chandrasekhar’s result. Eddington’s views were emphatically put before a wider audience at the International Astronomical Union meeting in Paris in 1935, and in a conference on white dwarfs also in Paris in 1939.

One result of this disagreement with Eddington is that Chandra did not pursue the fate of stars which end their lives above the critical mass. Already in his 1934 paper he had made the remark: ‘It is conceivable for instance that at a very high critical density the atomic nuclei




come so near one another that the nature of the interaction might suddenly change and be followed by a sharp alteration in the equation of state in the sense of giving a maximum density of which matter is capable. However we are now entering a region of pure speculation.’ With encouragement he might have discussed realistic models of neutron stars and have considered the possible existence of black holes some years before J.R. Oppenheimer (later For.Mem.R.S.) did so.

Stellar structure and stellar atmospheres were the main focus of Chandra’s research in his Cambridge years. In his research on stellar atmospheres he enjoyed fruitful collaboration and friendship with Milne. After only a short time in Cambridge, Chandra was surprised to answer a knock on the door of his lodgings to find Milne standing there. An Oxford professor was seeking out a mere research student to tell him that he liked one of his papers on stellar absorption coefficients and that he was communicating it to the Royal Society. Milne also encouraged Chandra’s work on degenerate zones in normal stars. Chandra’s researches in this case did not support Milne’s views. A major series of papers, which were included in his Ph.D. thesis, was on the equilibrium structure of the idealized models of stars known as polytropes, in which he studied successively the structure of a single rotating star, the tidal distortion of a star by a companion and the full double star problem.

Y e r k e s O b se r v a t o r y a n d t h e U n iv e r s it y o f C h ic a g o , 1937-95

Chandra and his new bride Lalitha arrived at the Yerkes Observatory in December 1936. At that time it was one of the major observatories in the world. Its Director, Otto Struve, was now intent on making it strong in theoretical astronomy as well. To quote Martin Schwarzschild, For.Mem.R.S.: ‘Yerkes became a leading institution in every respect including the development of one of the most outstanding if not the outstanding graduate school in astronomy and astrophysics in the country. Chandra was by far the most active member of the group. He just loved to give lectures and was very demanding of his students, many of whom felt enormous loyalty to him’ (in Wali, 1991).

At Yerkes, his first research priority was the completion of his book An Introduction to the Study o f Stellar Structure (6) 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 o f the Stars. It contained almost everything that could be learnt about stellar interiors without the aid of a powerful computer. After he had completed the book, he carried out very few further researches on stellar structure, although he did some preliminary work on red giants stars and also demonstrated the existence of the Schonberg-Chandrasekhar limit, which is the maximum mass of a non-degenerate isothermal core in a star. In essentially ceasing to work on stellar structure, Chandra was starting a pattern which would continue for most of the rest ol his career. For a period he would work mainly but not exclusively in one research field at the end of which he would write a monograph summarizing his researches and then move on to another field.




S t e l l a r d y n a m ic s

The realization 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. This field of stellar dynamics was Chandra’s main field of research until 1943, starting with two papers in the Astrophysical Journal in 1939 and 1940 (5, 7), which contained a total of more than 350 pages. He worked on all aspects of the problem but his work on relaxation in stellar systems was a landmark in the discussion of the evolution of star clusters and galaxies as was the closely related work by L. Spitzer, For.Mem.R.S., on the relaxation in plasmas, with the similar force law but two signs of charge.

In the case of stellar dynamics, Chandra wrote his monograph Principles o f Stellar Dynamics (9), which appeared in 1942, somewhat prematurely as some of his most important work on the effect of dynamical friction on the motion of stars in a stellar system was published after the book had appeared. When a Dover reprint of the book appeared in 1960, the opportunity was taken to include in it three papers on dynamical friction, which appeared in the Astrophysical Journal in 1943 (11-13) and a further paper, ‘New Methods in Stellar Dynamics’, from the Annals o f the New York Academy o f Sciences (15). A very influential paper which is not in the Dover reprint is his 1943 article in Reviews o f Modern Physics on stochastic problems in physics and astronomy (14); also missing are two joint papers with J. von Neumann on fluctuations in the gravitational field due to a random distribution of stars (8, 10).

In 1944 Chandra was elected to Fellowship of the Society. The names of those nominating him make interesting reading. He was appropriately proposed by Raman with Milne as seconder, and other names include Fowler, Jeans, Eddington, E.T. Whittaker and H. Jeffreys. Despite their continuing disagreement concerning relativistic degeneracy, Eddington recognized that Chandra had done much outstanding work. I have seen an extract from a letter from Milne to Chandra in which he says that Eddington was particularly anxious that Chandra should be elected in 1944.

R a d ia t iv e t r a n s f e r

That year also saw the next change in direction of his researches which turned to radiative transfer and stellar atmospheres. He had first worked on stellar atmospheres in the early 1930s. Between 1944 and 1948 he published a series of 25 papers entitled ‘On the Radiative Equilibrium of a Stellar Atmosphere’ in the Astrophysical Journal (16-40). In addition he wrote papers on the negative hydrogen ion and other negative ions and on radiative equilibrium in expanding atmospheres. His own research productivity was remarkable but the pages of the Astrophysical Journal for those years also contain a large number of papers whichwere inspired by him but which do not carry his name; papers by students and junior colleagues. When it is remembered that he was also carrying a very large teaching load, it is remarkable what he managed to do. It also needs to be noted that during the war, while he was completing his work on stellar dynamics and starting that on radiative transfer, he worked hard




on weapons developments at the Army Ballistic Research Laboratory at Aberdeen, Maryland. He used to spend three weeks at Aberdeen and then three weeks at Yerkes.

His work on radiative transfer is notable for the introduction of new techniques or the considerable development of existing techniques for solving the equation of transfer. Chandrasekhar developed the principle of invariance first introduced into radiative transfer by V.A. Ambartsumian, For.Mem.R.S., which also followed from some early work of Lord Rayleigh, P.R.S., and H. von Helmholtz, For.Mem.R.S. The principle of invariant embedding which Chandra pioneered in his work has found later application in other fields. In his book Radiative Transfer (43) published in 1950 he stressed that his techniques had much wider use than in astronomy alone. Indeed the development of nuclear power stations led to major work on neutron diffusion, which is a closely similar mathematical problem. Because of this wider interest, Radiative Transfer was the book by Chandra with the largest sales.

I cannot do better than quote from his own preface: ‘In this book I have attempted to present the subject of radiative transfer in plane parallel atmospheres as a branch of mathematical physics with its own characteristic methods and techniques. On the physical side the novelty of the methods used consists in the employment of certain general principles of invariance which on the mathematical side leads to the systematic use of non-linear equations and the development of the theory of a special class of such equations. On these accounts the subject would seem to have an interest which is beyond that of the specialist alone: at any rate that has been my justification for writing this book. However, my own partiality has led me to include two chapters which are probably only of interest to the astrophysicist.’

H y d r o d y n a m ic a n d h y d r o m a g e n t ic s t a b il it y

Although he did further limited work on radiative transfer after completing his book, for the next ten years the main thrust of his research was in hydrodynamics and what he called hydromagnetics; the more clumsy word magnetohydrodynamics has now become generally accepted. There was an important exception to this, the series of five papers with Guido Munch on the theory of fluctuations in brightness of the Milky Way (41, 42, 44-46). He contributed to the theory of turbulence, starting with a critique of Heisenberg’s theory and following with a theory of his own, particularly in the presence of a magnetic field. Turbulence is one of those fields in which progress has been painfully slow. Astronomers have been waiting for 60 years for a better treatment of fully developed convection in stars than the one which was developed by L. Biermann and his colleagues in the 1930s. Chandra perhaps wisely limited his work in this field and instead concentrated on linear stability problems.

Chandra’s text on Hydrodynamic and Hydromagnetic Stability (53) which appeared in 1961 was different from his other research monographs in that much of its contents were originally due to other authors. Chandra’s own contributions were of course very important but a major task which he set himself was the reworking of what had been done before and converting it all into one clear notation. He provided a particularly complete treatment of conditions for the onset of convection. The classical Benard problem of a plane parallel fluid heated from below was modified by the introduction of rotation and of a magnetic field and then by their simultaneous presence. Convection in spheres and spherical shells was discussed but the possible geophysical and astrophysical interest scarcely touched upon. Another topic to which



Subrahmanyan 89

he made important contributions was the stability of flow between rotating cylinders; once again he considered the problem with an impressed magnetic field.

In studies of hydrodynamic stability Chandra had close associates, including particularly W.H. Reid and he was ably assisted by Miss Donna Elbert, who carried out his calculations for many years. The work was unusual for him as it was amenable to experimental test. As he stated: ‘The experimental investigations of Drs D. Fultz, Y. Nakagawa and R.J. Donnelly in close association with the theoretical developments have been a source of constant encouragement; much of the experimental work summarised in the book is theirs.’ In 1956-57, Dr J.B. Sykes from A.E.R.E. Harwell worked with Chandra at Williams Bay and wrote a parody of a Chandra paper, ‘On the imperturbability of elevator operators LVII by S Candlestickmaker’. John Sykes caught enough of Chandra’s style for Chandra to have the paper printed as if it had appeared in the Astrophysical Journal. Candlestickmaker’s calculation were performed by Miss Canna Helpit.

It is not surprising that Chandra’s help and encouragement was sought with work on controlled thermonuclear reactions, with the associated problems of hydromagnetic equilibrium and stability. Chandra communicated to the Royal Society the first U.S. theoretical paper which was allowed to be published: ‘Some instabilities of a completely ionized plasma’ by M. Kruskal and M. Schwarzschild. With A.N. Kaufman and K.M. Watson he wrote three papers directly concerned with thermonuclear research including one on the stability of the pinch (49-51). A course of lectures which he gave on plasma physics was converted into a book by a former student S.K. Trehan (52).

It was during this period that Chandra wrote two papers with Enrico Fermi on magnetic fields in spiral arms of galaxies (47) and on problems of gravitational stability in the presence of a magnetic field (48). Their work on magneto-gravitational stability was a forerunner of much subsequent work on both stars and galaxies. Magnetic models of spiral structure have never received much support although they are revived periodically.

R o t a t in g l iq u id m a s s e s

In about 1960 he again changed his field of research, albeit to one which was not greatly removed from the previous one, the equilibrium and stability of rotating liquid masses. His researches, largely carried out in collaboration with Norman R. Lebovitz, were stimulated by the invitation to give the Sillman Memorial Lectures at Yale in 1963. As he had started work in the field, he agreed to lecture on ‘Rotation of Astronomical Bodies’. Giving the lectures made him realize how much he did not understand. Instead of his writing a short book, he and Lebovitz, with the assistance of Donna Elbert, spent five further years in research leading to yet another monograph in 1969, Ellipsoidal Figures (54).

The topic already had a long and distinguished history with important contributions by Newton, Maclaurin, Jacobi, Dirichlet, Dedekind, Riemann, Poincare and Darwin amongst others. Chandra and Lebovitz were able to expose lack of clarity, errors and incompleteness in the existing studies and between 1960 and 1969 Chandra, Lebovitz and his students published a total of 40 papers. He demonstrated the considerable power of the virial equations of various orders, which are moments of the equations of motion, to give solutions to complex problems. For example, he showed that the second order virial equations provide all the




information required for the equilibrium and stability of the allowed ellipsoidal figures in Dirichlet’s problem; a homogeneous, rotating, self-gravitating fluid mass with internal motions a linear function of position.

In his work he clarified such matters as the points of bifurcation from spheroidal to ellipsoidal and then to pear-shaped figures and the role of secular and dynamical instability. Some of the results were already well known but some were not. In particular Chandra and Lebovitz demonstrated that Riemann had made errors in his study of triaxial configurations with internal motions and demonstrated new instabilities in the Roche problem, ellipsoids subjected to the tidal influence of a secondary

At the end of his book Chandra says: ‘Except for Chapter 2 the present book has been concerned exclusively with homogeneous liquid masses. A critic might be inclined to side with Eddington and say “It is not enough to deal with theoretical liquid masses. The astronomer want to know how these results are maintained when we take into account the non- homogeneous or gaseous condition of actual stars.’” Chandra counters this by stressing that the subject is not only interesting in its own right but that the mathematical techniques developed can have much wider applicability.

G e n e r a l r e l a t iv it y a n d b l a c k h o l e s

Chandra’s next research field was general relativity. Although this had been widely accepted as the best available theory of gravitation since the 1920s and had been applied to cosmology, there was little progress in relativistic astrophysics until the discoveries of quasars and pulsars in the 1960s. It was then accepted that neutron stars existed and that black holes probably did. Chandra started by extending his work on rotating liquid masses to the post-Newtonian approximation; the first effects of general relativity. He continued this work in the 1970s with particular interest on the role of energy loss through gravitational radiation on the evolution of the systems and he also studied further relativistic stability problems. His 1972 Halley Lecture was entitled ‘The Increasing Role of General Relativity in Astronomy’ (55). It was in the mid-1970s that he focused his main research interests on the properties of black holes.

Chandra had been excited by the 1963 discovery by R.R Kerr of the exterior metric to a rotating black hole and his researches were largely concentrated on the mathematical properties of rotating and charged black holes. One of his particular achievements was the separation of the Dirac equation for spin 1/2 particles in Kerr space-time. In this his research career came full circle because his earliest researches were concerned with applications of Fermi-Dirac statistics. It is clear that much of his work on black holes was done for his own satisfaction. As he explains in the preface to The Mathematical Theory o f Black Holes (56): ‘Since the entire subject matter (including the mathematical developments) has been written (or worked out) ab , independent of the origins, the author has not made any serious search of the literature.’ Only a Chandrasekhar could dare to approach research in that manner in the 1980s.

Chandra’s researches did not end there. He continued his researches on general relativity until not long before his death. In 1991 alone he had five papers in Proceedings o f the Royal Society and his final paper in the journal appeared in the month of his death. At the same time he was writing his expository book on Newton’s Principia (59). Here he used the methods available to Newton to solve the problems which Newton had solved and then compared his




proofs with those of Newton, often to his own disadvantage he admitted. Also in his final years six volumes of his selected papers were published (60); these were those papers not included in any of his books.

C o n c l u s io n

Chandra was a classical applied mathematician whose research was primarily applied in astronomy and whose like will probably never be seen again. Although he did not initiate any totally new fields of research, he transformed those on which he did work. 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. In discussing his career undue emphasis is often placed on his early work on white dwarfs and on his controversy with Eddington. He certainly thought so. In a letter to me shortly after the biography by Wali had appeared he said that he sometimes felt that his past 50 years’ work counted for nothing. Here he was abundantly wrong.

P r in c ip a l h o n o u r s a n d a w a r d s

1944 Fellow of the Royal Society.1947 Adams Prize, Cambridge University.1949 Henry Norris Russell Lecture, American Astronomical Society.1952 Bruce Gold Medal, Astronomical Society of the Pacific.1953 Gold Medal, Royal Astronomical Society.

George Darwin Lecture, Royal Astronomical Society.1955 Member of the National Academy of Sciences.1957 Rumford Medal, American Academy of Arts and Sciences.1962 Royal Medal, Royal Society.

Srinivasa Ramanujan Medal, Indian National Science Academy. 1966 National Medal of Science, United States.1968 Padma Vibhushan Medal, India.

Second Nehru Memorial Lecture.1971 Henry Draper Medal, National Academy of Sciences.1972 Halley Lecture, University of Oxford.1973 Smoluchowski Medal, Polish Physical Society.1974 Dannie Heinemann Prize, American Physical Society.1979 Milne Lecture, Oxford.1983 Nobel Prize for Physics.1984 Dr Tomalla Prize ETH, Zurich.

Copley Medal, Royal Society.R.D. Birla Memorial Award, Indian Physics Association.

1985 Vainu Bappu Memorial Award,Indian National Science Academy. 1991 Charles Greeley Abbot Award, American Solar-Energy-Society.




A c k n o w l e d g e m e n t s

I am grateful to many colleagues and friends, including particularly Lady Jeffreys, Professor D. Lynden-Bell, ER.S., Professor Sir William McCrea, F.R.S., Professor L. Mestel, F.R.S., Professor D. Osterbrock, Professor Sir Martin Rees, F.R.S., and Mrs M. Weston Smith, for helpful discussion and information. I found the biography by K.C. Wali a valuable source for Chandra’s early life.

The frontispiece photograph was given to the Royal Society in 1950 and is reproduced with the kind permission of the Fossum Studio, Wisconsin.

R e f e r e n c e s t o o t h e r a u t h o r s

Wali, K.C. 1991 Chandra: A biography of SChandrasekhar. University of Chicago Press.

B ib l io g r a p h y

The following publications are those referred to directly in the text. A full bibliography appears on the accompanying microfiche, numbered as in the second column. A photocopy is available from the Royal Society Library at cost.

(1) (2) 1929 The Compton scattering and the new statistics. Proc. R. Soc. Lond. A 125, 231-237.(2) (3) 1930 The ionization-formula and the new statistics. Phil Mag. IX, 292-299.(3) (4) On the probability method in the new statistics. Phil Mag. IX, 621-624.(4) (30) 1935 The highly collapsed configuration of Stella mass (second paper), Mon. Not. R. Astr.

Soc. 95, 207-225.(5) (61) 1939 The dynamics of stellar systems, I—VIII. Astrophys. J. 90, 1-154.(6) (63) An introduction to the study of stellar structure. University of Chicago Press, pp.

509.The dynamics of stellar systems, IX-XIV. Astrophys. J. 92, 441-642.(7) (64) 1940

(8) (73) 1942 (with J. von Neumann) The statistics of the gravitational field arising from a random distribution of stars, I. The speed of fluctuations. Astrophys. J. 95, 489-531.

(9) (76) Principles of stellar dynamics. University of Chicago Press, pp.251.GO) (77) 1943 (with J. von Neumann) The statistics of the gravitational field arising from a random

distribution of stars, II. The speed of fluctuations; dynamical friction; spatial correlations. Astrophys. J. 97, 1-27.

(U) (78) Dynamical friction, I. General considerations: the coefficient of dynamical friction. Astrophys. J 97, 255-262.

(12) (79) Dynamical friction, II. The rate of escape of stars from clusters and the evidence for the operation of dynamical friction. Astrophys. J. 97, 263-273.

(13) (80) Dynamical friction, III. A more exact theory of the rate of escape of stars from clusters. Astrophys. J. 98, 54-60.

(14) (82) Stochastic problems in physics and astronomy. Rev. Mod. Phys. 15, 1-89.(15) (83) New methods in stellar dynamics. Ann. N.Y. Acad. Sci. 45, 131-162.(16) (87) 1944 On the radiative equilibrium of a stellar atmosphere. Astrophys. J. 99, 180-190.(17) (89) On the radiative equilibrium of a stellar atmosphere, II. Astrophys. J. 100, 76-86.(18) (91) On the radiative equilibrium of a stellar atmosphere, III. Astrophys. J. 100, 117-127.(19) (93) (with C.U. Cesco & J. Sahade) On the radiative equilibrium of a stellar atmosphere,

IV. Astrophys. J. 100, 355-359.




(20) (96) 1945 On the radiative equilibrium of a stellar atmosphere, V. Astrophys. 101, 95-107.(21) (97) (with C.U. Cesco & J. Sahade) On the radiative equilibrium of a stellar atmosphere,

VI. Astrophys. J. 101, 320-327.(22) (98) On the radiative equilibrium of a stellar atmosphere, VII. Astrophys. J. 101,

328-347.(23) (99) On the radiative equilibrium of a stellar atmosphere, VIII. Astrophys. J. 101,

348-355.(24) (107) 1946 On the radiative equilibrium of a stellar atmosphere, IX. Astrophys. J. 103, 165-192.(25) (108) On the radiative equilibrium of a stellar atmosphere, X. Astrophys. J. 103, 351-370.(26) (109) On the radiative equilibrium of a stellar atmosphere, XI. Astrophys. J. 104, 110-132.(27) (111) On the radiative equilibrium of a stellar atmosphere, XII. Astrophys. J. 104,

191-202.(28) (115) 1947 On the radiative equilibrium of a stellar atmosphere, XIII. Astrophys. J. 105,

151-163.(29) (116) On the radiative equilibrium of a stellar atmosphere, XIV. Astrophys. J. 105,

164-203.(30) (117) On the radiative equilibrium of a stellar atmosphere, XV. Astrophys. J. 105, 424-434.(31) (118) (with F.H. Breen) On the radiative equilibrium of a stellar atmosphere, XVI.

Astrophys. J. 105, 435-440.(32) (119) On the radiative equilibrium of a stellar atmosphere, XVII. Astrophys. J. 105,

441-460.(33) (120) (with F.H. Breen) On the radiative equilibrium of a stellar atmosphere, XVIII.

Astrophys. J. 105, 461-470.(34) (121) (with F.H. Breen) On the radiative equilibrium of a stellar atmosphere, XIX.

Astrophys. J. 106, 143-144.(35) (122) On the radiative equilibrium of a stellar atmosphere, XX. Astrophys. J. 106,

145-151.(36) (123) On the radiative equilibrium of a stellar atmosphere, XXI. Astrophys. J. 106,

152-216.(37) (129) 1948 On the radiative equilibrium of a stellar atmosphere, XXII. Astrophys. J. 107, 48-72.(38) (130) On the radiative equilibrium of a stellar atmosphere, XXII (concluded). Astrophys.

J. 107, 188-215.(39) (131) (with F.H. Breen) On the radiative equilibrium of a stellar atmosphere, XXIII.

Astrophys. J. 107, 216-219.(40) (132) On the radiative equilibrium of a stellar atmosphere, XXIV. Astrophys. J. 108,

92-111.(41) (146) 1950 (with G. Munch) The theory of the fluctuations in brightness of the Milky Way, I.

Astrophys. J. 112, 380-392.(42) (147) (with G. Munch) The theory of the fluctuations in brightness of the Milky Way, II.

Astrophys. J. 112, 393-398.(43) (148) Radiative transfer. Oxford: Clarendon Press, pp. 393.(44) (155) 1951 (with G. Munch) The theory of the fluctuations in brightness of the Milky Way, III.

Astrophys. J. 114, 110-122.(45) (158) 1952 (with G. Miinch) The theory of the fluctuations in brightness of the Milky Way, IV.

Astrophys. J. 115, 94-102.(46) (159) (with G. Munch) The theory of the fluctuations in brightness of the Milky Way, V.

Astrophys. J. 115, 103-123.(47) (171) 1953 (with E. Fermi) Magnetic fields in spiral arms. Astrophys. J. 118, 113-115.(48) (172) (with E. Fermi) Problems of gravitational stability in the presence of a magnetic

field. Astrophys. J. 118, 116-141.(49) (210) 1957 (with A.N. Kaufman & K.M. Watson) Properties of an ionized gas of low density in

a magnetic field, III. Ann. Phys. 2, 435-470.




(50) (216) 1958

(51) (222)

(52) (233) 1960(53) (240) 1961

(54) (295) 1969(55) (313) 1972

(56) (358) 1983(57) (359)

(58) (377) 1987

(59) (408) 1995(60) 1989-91

(with A.N. Kaufman & K.M. Watson) The stability of the pinch. Proc. R. Soc. Lond. A 245, 435-455.(with A.N. Kaufman & K.M. Watson) Properties of an ionized gas of low density in a magnetic field, IV. Ann. Phys. 5, 1-25.Plasma physics (compiled by S.K. Trehan). University of Chicago Press, pp. 217. Hydrodynamic and hydromagnetic stability. Oxford: Clarendon Press, pp. 654 (reprinted 1968).Ellipsoidal figures of equilibrium. Yale University Press, pp. 253.The increasing role of general relativity in astronomy (Halley Lecture). Observstory 92, 160-174.The mathematical theory of black holes. Oxford: Clarendon Press, Oxford, pp. 646. Eddington: the most distinguished astrophysicist of his time. Cambridge University Press, pp. 64.Truth and beauty: aesthetics and motivations in science. University of Chicago Press, pp. 170.Newton’s principia for the common reader. Oxford: Clarendon Press, pp. 595.Selected papers of S.Chandrasekhar (six volumes), University of Chicago Press.



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