CHANDRASEKHAR, SUBRAHMANYAN

(b. Lahore, Punjab, British India [later Pakistan], 10 October 1910;

d. Chicago, Illinois, 21 August 1995), physics, astrophysics, applied mathematics.

A Nobel Laureate honored for his extraordinarily wide-ranging contributions to physics, astrophysics, and applied mathematics, Chandrasekhar is well known for his discovery of the limiting mass (Chandrasekhar limit) of a star that could become a white dwarf.

Career . Chandrasekhar, known simply as “Chandra” in the scientific world, was one of ten children of Chandrasekhara Subrahmanyan Ayyar and Sitalakshmi Balakrishnan. Ayyar was an officer in the British government services. Sitalakshmi, a woman of great talent and self-taught intellectual attainments, played a pivotal role in her son’s career. Chandrasekhar’s uncle Sir Chandrasekhara Venkata Raman was the recipient of a Nobel Prize for the celebrated discovery concerning the molecular scattering of light known as the “Raman Effect.”

Chandrasekhar’s early education took place under the tutelage of his parents and private tutors. When he was twelve, his family moved to Madras, where he began his regular schooling at the Hindu High School in Triplicane, which he attended from 1922 to 1925. Chandrasekhar then received his university education at Presidency College in Madras and earned a bachelor’s degree with honors in 1930. He was awarded a three-year Government of India scholarship for graduate studies at Cambridge in England.

Chandrasekhar left India for England in July 1930 to undertake research under the supervision of the pioneering theoretical astrophysicist Ralph Howard Fowler. He spent the third year of his graduate scholarship in Copenhagen, Denmark, at Niels Bohr’s Institute of Theoretical Physics before completing his work on his Cambridge PhD in the summer of 1933. In October he was elected a fellow of Trinity College, Cambridge, a position he held from 1933 to 1937. He visited the United States for the first time from January to March 1936 at the invitation of Harlow Shapley, the director of the Harvard College Observatory at Harvard University. In the late summer of 1936, Chandrasekhar returned to India for a short visit to marry Lalitha Doraiswamy, whom he had met while both were undergraduate students at the Presidency College. They wed on 11 September 1936.

In January 1937, Chandrasekhar joined the faculty of the University of Chicago at the Yerkes Observatory, Williams Bay, Wisconsin. Chandrasekhar and Lalitha lived in Williams Bay for the next twenty-seven years. In 1964, they moved to Chicago, living in the Hyde Park neighborhood near the university. Elected a Fellow of the Royal Society of London and named the Morton D. Hull Distinguished Service Professor in 1946, Chandrasekhar remained at the University of Chicago until his death. Chandrasekhar and Lalitha became U.S. citizens in 1953.

Chandrasekhar is known for a distinctive pattern of research that encompassed diverse areas, each of which occupied a period of five to ten years. Each period of study resulted in a series of long papers and ended with a monograph. Speaking of his monographs and his motivation for research, Chandrasekhar, in the autographical account published with his Nobel lecture, said:

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.

Thus Chandrasekhar’s researches, principally motivated by a quest after perspectives, a quest after attaining a complete understanding of an area and internalizing it, covered a wide range of investigations that are summarized here chronologically.

Stellar Structure, White Dwarfs (1929–1939) . Chandrasekhar’s scientific career began while he was still an undergraduate at Presidency College, when he published his first paper, “The Compton Scattering and the New Statistics,” in 1929. The new statistics refers to the Fermi-Dirac quantum statistics that he was made aware of in a dramatic encounter with Arnold Sommerfeld during the latter’s visit to Presidency College in the fall of 1928. The new quantum mechanics, which had stunned Europe, had not yet made its way to India. Sommerfeld was invited to speak to the science students and Chandrasekhar, who was among them, made arrangements to see him the following day in his hotel room.

Chandrasekhar had mastered the atomic theory as laid out in Sommerfeld’s classic book on old quantum

theory, Atomic Structure and Spectral Lines. He approached Sommerfeld with the brash confidence of a young undergraduate to impress upon the master his knowledge as well as his intense desire to pursue a research career in physics. But Sommerfeld shocked him by telling that the old quantum theory in his book was no longer of any use. It was replaced by the revolutionary new quantum mechanics due to the work of Erwin Schrödinger, Werner Heisenberg, Paul M. Dirac, and others. While Chandra had also studied on his own the classical Maxwell-Boltzmann statistics, Sommerfeld told him that too had undergone a fundamental change in the light of the new quantum mechanics. Seeing a crestfallen young student facing him, Sommerfeld offered Chandra the galley proofs of his as yet unpublished paper that contained an account of the new Fermi-Dirac quantum statistics and its application to the electron theory of metals.

Chandrasekhar would later characterize this encounter as the “single most important event” in his scientific career. He immediately embarked on a serious study of the new developments in atomic theory. Sommerfeld’s paper was sufficient for him to learn about Fermi-Dirac statistics and write, within a few months, his first paper. He sent it for publication in the Proceedings of the Royal Society of London to be communicated through Ralph H. Fowler in Cambridge, England. Fowler had published a pioneering paper on the theory of white dwarfs (dense collapsed configurations of stars, with planetary dimensions but as massive as the Sun, in their terminal stages) that contained still another application of the new statistics to the stellar matter in the form of degenerate electrons in white dwarfs and solved a long-standing problem about their equilibrium structure. So for Chandra, at the time, Fowler was someone who knew Fermi-Dirac statistics and consequently someone who could understand his paper and support its publication. The paper was indeed published in the Proceedings. However, this chance circumstance was to have a profound influence on Chandra’s future scientific career. The following year, when he was unexpectedly offered the Government of India scholarship to continue his research in England after his graduation, he did not have to think hard before choosing Cambridge University and Fowler as his thesis advisor.

In studying Fowler’s paper, Chandrasekhar discovered that Fowler’s pressure-density relation in the white dwarf configuration, when combined with conditions for it to be in equilibrium under its own gravity, led to some far-reaching conclusions: (i) the radius of a white dwarf was inversely proportional to the cube root of the mass— implying thereby that every finite-mass star has a finite radius; (ii) the density is proportional to the square of the mass; (iii) the central density would be six-times the mean density ρ_m.

Chandrasekhar prepared a paper to present to Fowler on his arrival in Cambridge. But on his long voyage to England, he began to ponder the implications of the last of the three conclusions that seemed to raise a number of key questions, which proved crucial to the subsequent theory of white dwarfs. If the central densities were so high, would not the electron energies, increasing as one moved away from the center of the Fermi sphere, reach magnitudes comparable to their rest masses? If they did, the special-relativistic variation of mass with velocity would be important and would have to be taken into account. What would be the consequences?

He made a quick calculation and found that relativistic effects were indeed important. In the extreme relativistic limit, the pressure-density relation changed from the nonrelativistic case in such a way that it was no longer true that a star of any mass could have a finite radius. The total mass of the equilibrium configuration (at the limiting zero radius) was uniquely determined in terms of fundamental atomic constants and mean molecular weight μ of the stellar matter. Using the known values of the atomic constants, the mass turned out to be 5.76/μ² solar masses. In 1930, the canonical value for μ was 2.5, giving a mass of 0.91 solar masses (which later became 1.44 solar masses when μ was revised to 2). This was the origin of the critical mass or Chandrasekhar limit.

Chandrasekhar brought two short papers with him to Cambridge. One dealt with the extension of Fowler’s non-relativistic degenerate configurations, the other with relativistic effects leading to the startling conclusion regarding the critical mass: If the mass was greater than the critical mass, the star would not become a white dwarf. It would continue to collapse under the extreme pressure of gravitational forces to reach a point of infinite mass density, clearly unphysical. After a few more years of hard work, he established the critical mass condition on a rigorous basis and reported his findings at the January 1935 meeting of the Royal Astronomical Society of London. His findings raised challenging, fundamental questions: What happens to the more massive stars when they continue to collapse? Are there terminal stages of stars other than the white dwarfs?

Astronomers’ appreciation of the importance of this discovery was withheld because of the objections of Arthur Stanley Eddington, an older, well-established, and renowned scientist. Soon after Chandrasekhar’s presentation at the meeting, Eddington ridiculed the whole idea of relativistic degeneracy. He characterized Chandrasekhar’s theory as amounting to reductio ad absurdum behavior of the star, tantamount to stellar buffoonery. For Eddington, white dwarf stage was the ultimate terminal stage for all stars irrespective of their masses. He found it disturbing that if the mass of a star was greater than a certain limit, the collapse will continue and the star will not rest in peace. It was contrary to his view of nature.

While eminent physicists with no exception agreed that Chandrasekhar’s derivations based on fundamental concepts of quantum mechanics and special relativity were flawless, Eddington’s authority prevailed among astronomers until observations confirmed the theory. It was a traumatic incident in young Chandrasekhar’s life. While he was convinced about the validity of his results and the challenge they presented to those interested in stellar evolution, he thought it better not to go on confronting and arguing with Eddington. He wrote the monograph An Introduction to the Study of Stellar Structure in 1939, giving a full account of the theory of white dwarfs, and passed on to a new area of research.

Stellar Dynamics: Stochastic and Statistical Approaches (1938–1943) . Stellar dynamics deals with the distribution of matter and motion in stellar systems such as the Milky Way, the galaxy which is the home of Earth’s solar system with the Sun as one of at least 200 billion other stars and their planets, and thousands of clusters and nebulae. The focus of stellar dynamics is the interpretation of the characteristic features of stellar systems in terms of the forces that govern motions of the individual stars.

In his monograph Principles of Stellar Dynamics, Chandrasekhar laid the foundations of the dynamical theory as a branch of classical dynamics—a discipline in the same general category as celestial mechanics. As in celestial mechanics, the forces that govern the motion of stars in a stellar system are principally gravitational. The motion of an individual star is then affected, first, by forces that are due to a smoothed-out distribution of matter in the system and, second, from the effect of chance encounters with neighboring stars. The continuous motion under the gravitational potential due to the smoothed-out distribution undergoes abrupt change due the chance encounters.

An important question from the point of view of what can be observed is how the cumulative effect of chance encounters affects the orbit of a star measured by what is called “time of relaxation” of the stellar system. Conventional wisdom assumed it could be theoretically calculated by considering the cumulative effect of a large number of two-body encounters. A closer analysis convinced Chandrasekhar that such an idealization did not provide a good approximation to the physical situation in the stellar system. The gravitational field fluctuated in space and time. New methods of treating the problem based on statistics were required. He laid the foundations of such new methods in one of his most celebrated and widely quoted papers, “Stochastic and Statistical Problems in Astronomy,” published in 1943. The probability methods reviewed in this paper have found application beyond astronomy in a wide variety of problems and fields as different as colloidal chemistry and stellar dynamics. A series of papers and the monograph Principles of Stellar Dynamics marked the end of this period and the beginning of a new subject.

Radiative Transfer (1943–1950) . Chandrasekhar used to say that 1943 through 1948 were some of the happiest and most satisfactory years of his scientific life. His researches culminating in the monograph Radiative Transfer produced a series of papers in rapid succession. The subject evolved on its own, on its own initiative and momentum, and attained elegance and a beauty which, according to his own admission, was not to be found in any of his other work.

The subject of radiative transfer deals in a general way with the transport of energy in stellar atmospheres that absorb, emit, and scatter radiation as it emerges from the star. The characteristics of the emerging radiation, such as the variations in intensity over the stellar disc and the energy distribution over different wavelengths (spectral distribution) are the features that can be observed and measured. The latter are of extreme importance for an astrophysicist in his attempt to understand the constitution and structure of stellar atmospheres. The theoretical analysis of the transfer phenomena demanded new mathematical developments in the theory of integro–differential and functional equations. It demanded new approximation techniques to solve them to find the observed characteristics. Chandrasekhar’s pioneering effort during these years and his monograph provided the necessary foundation. His work also included a study of the formation of absorption lines due to scattering of light in moving atmospheres, a subject of great interest in astrophysics dealing with a variety of objects such as novae, Wolf-Rayet stars, planetary nebulae, solar corona, and solar prominences.

In a related subject, the explanation of the polarization of light by Earth’s atmosphere was a problem that had remained unsolved since the classic work of Lord Rayleigh in 1871. In explaining the blue color of the sky based on Maxwell’s equations, Rayleigh had made the approximation of a single scattering of the radiation and predicted nonvanishing polarization in all directions, except directly towards or away from the Sun. It was known, however, that there existed two, sometimes three, neutral points of zero polarization on the Sun’s meridian circle, called the Babinet, Brewster, and Arago points. Chandrasekhar, in a series of papers in 1946, formulated the scattering problem with polarization and found solutions for the sunlit sky exhibiting precisely the character of the observations, in particular the above-described neutral points.

Negative Hydrogen Ion (1944–1958) . The negative hydrogen ion (quantum mechanically, the bound state of a neutral hydrogen atom and an electron) was a subject of great astrophysical importance. Hans A. Bethe in 1929 and independently Egil A. Hylleraas in 1930 had demonstrated theoretically that such a stable configuration could exist, which in turn pointed to its possible existence in the Sun’s atmosphere, where there was an abundance of neutral hydrogen atoms as well as a supply of electrons due to the ionization of other elements. Theory anticipated that under such circumstances, there should be bound negative ions of hydrogen, and they should have an effect on the absorption spectrum of the Sun. Rupert Wildt in 1938 had indeed produced strong evidence for the presence of negative ions of hydrogen in sufficient quantities to be the principal source of continuous absorption in the solar atmosphere and in the atmospheres of certain types of stars.

After the pioneering work of Bethe and Hylleraas, several others tried to determine the electron affinity to the hydrogen atom (binding energy) with greater precision by trying out wave functions with more parameters than the original calculations of Bethe and Hylleraas. These efforts, however, had led to ambiguous results. Chandrasekhar realized that the form of the wave function used by the later authors, based upon an analogy with the wave function that was immensely successful in explaining the helium atom, was not appropriate for the physical situation in the case of the negative hydrogen ion. With a more general parameterization, he was able to obtain a more precise and stable value for the binding energy and subsequently the value for the continuous absorption coefficient of the negative hydrogen ion and the consequent cross-sections for radiative processes leading to its ionization. These results played an extremely important role in scientists’ understanding of the continuous spectrum of the sun and the stars.

Turbulence and Magneto-Hydrodynamics (1950–1960) . After completing the monograph Radiative Transfer Chandrasekhar embarked on a new area, the study of turbulence, a phenomenon widespread in nature in the flow of liquids and gases. It is a familiar fact that a steady linear flow of water in a tube persists for velocities below a certain limit and, when the velocity exceeds this limit, the steady flow ceases spontaneously. Complex, irregular, and fluctuating motion sets in. Similar phenomena in solar and stellar atmospheres are to be expected and have been found observationally.

The theory of turbulence has been and continues to be one of the most intractable subjects. Chandrasekhar’s work began with a closer analysis of Werner Heisenberg’s elementary theory of turbulence, which provided an easily visualizable picture of what takes place in a turbulent medium. Heisenberg had provided an equation for determining the “spectrum” of turbulence encoded in a function of wave numbers of the eddies in the turbulence. Chandrasekhar obtained an explicit solution to the equation in the case of statistically stationary turbulence and offered further simplifications of the equation making it amenable to solutions in a more general case.

The theory of turbulence and hydrodynamics needed a reconsideration of the fundamental problems concerning the adequacy of their formulation in the context of astrophysical problems or adequacy of their formulation when dealing with the physics of the stellar interiors. In the early 1950s, Chandrasekhar undertook such reconsideration and developed appropriate mathematical formulations, their relation to underlying physics and approximation schemes best suited to the problems. Of particular importance was the generalization of hydrodynamics to include magnetic fields whose all-pervasive character in astrophysical settings (especially on the galactic scale) was becoming of great importance. Along with Enrico Fermi, he wrote two seminal papers, one on the estimation of the magnetic field in the spiral arms of the our galaxy, and the other on the gravitational stability of cosmic masses of infinite conductivity in the presence of a magnetic field.

The methods and approximation schemes developed in the astrophysical context became equally useful in the applications to laboratory experiments concerning the stability of viscous flow in the presence of a magnetic field and the hydrodynamic stability of helium II between rotating cylinders. As usual, a series of papers on the subject ended with the monograph Hydrodynamic and Hydro-magnetic Stability.

Ellipsoidal Figures of Equilibrium (1960–1968) . As a consequence of his work with Fermi, it became clear to Chandrasekhar that stars with magnetic fields were unlikely to be spherical. In order to study the stability of such stars, methods used in radial oscillations of spherical stars were inadequate. The methods used in their work based on the so-called virial theorem needed to be generalized to be useful in the context of nonspherical rotating fluid masses. Chandrasekhar developed the needed theory and, along with Norman Lebovitz, applied the theory to the problem of oscillations of a class of historically well-known objects, the Jacobi ellipsoid and the Maclaurin spheroid and a wider class of ellipsoidal figures discovered by Richard Dedekind and Georg Friedrich Bernhard Riemann. The collaboration resulted in a series of classic papers, culminating in Chandrasekhar’s Ellipsoidal Figures of Equilibrium, acclaimed as one of the most elegant expositions on the subject.

Relativistic Astrophysics (1965–1975) . During and after the near completion of his work on hydrodynamic and hydromagnetic stability, Chandrasekhar began to think of turning to general relativity, a subject he was introduced to in his first year as a graduate student in Cambridge. Charmed though he was by Eddington’s exposition of relativity, full of fun and humor, he had shied away from a serious study of relativity for more than thirty years. This was partly because, at the time, relativity did not seem to be relevant for problems of stellar structure, internal constitution of stars, and other problems in astronomy.

The situation had changed by the 1960s. Rapid discoveries were taking place in astronomy. Quasars, pulsars, radio galaxies, cosmic x-ray sources, and cosmic microwave background radiation created a new arena of research for practical-minded relativists. On the theoretical side, a new discipline, relativistic astrophysics, was shaping up, dominated by youthful personalities that included Kip Thorne, Roger Penrose, James Hartle, James Bardeen, Stephen Hawking, Brandon Carter, and others. “Chandrasekhar (or Chandra, as he encouraged us to call him) was our young-at-heart co-worker,” says Kip Thorne, “as new to relativity as we. We had the flexibility of youth, the freedom from preconceived notions that is a modest compensation for lack of experience. Chandra had the wisdom of decades of research in fundamental, Newtonian physics and astrophysics—a wisdom that gave him guidance on what problems were worth studying and how to approach them” (in Chandrasekhar, Selected Papers, vol. 5, p. xii).

Once he decided to turn to general relativity, it was not long before he brought general relativity to its “natural home”—astronomy. It was a well-established fact that massive stars, during the course of their evolution, and when they have exhausted their nuclear source of energy, collapse into equilibrium configurations of finite dimensions (white dwarfs, neutron stars). The question arose concerning their stability. If one assumes that they are spherical, nonrotating gaseous masses, their stability against radial oscillations is governed by γ, where γ is the average ratio of specific heats. As long as γ > 4/3, Newtonian theory predicted that no matter what the mass of the star, it could be in a dynamically stable configuration with a radius that decreased with increasing mass, reaching zero only when the mass becomes infinite.

An appeal to quantum Fermi-Dirac statistics and degeneracy pressure, including special relativistic effects, did not alter this conclusion, except that the vanishing radius is reached at a finite limiting mass, the Chandrasekhar limit (1.44 solar masses in the case of white dwarfs and 2–3 solar masses in the case of neutron stars). The singular nature of the solution, namely, a star with finite mass shrinking to a point of zero radius, was clearly unphysical; it also contradicted observations, because white dwarfs and neutron stars existed in nature with finite radii. Such an unphysical solution, a consequence of relativistic degeneracy, had led Eddington in the thirties to characterize Chandrasekhar’s theory of white dwarfs as the reductio ad absurdum behavior of the stars.

In the mid-1960s, Chandrasekhar made a major discovery. He showed that this difficulty was no longer an issue within the framework of general relativity. In addition to γ, the stability depended upon the radius of the star as well. For any finite γ, dynamical instability always intervened and prevented the star collapsing to a singularity. If a massive star was to collapse into a stable configuration of a finite mass and a finite radius, it had to explode and eject a substantial fraction of material to interstellar space. Such a mass ejection could be a cataclysmic event, such as supernova explosion. If the remnant mass was in the narrow permissible range, it would then settle into a stable state of a white dwarf or a neutron star. A priori, it was highly unlikely that a massive star of several solar masses would always eject, in a violent explosion, just the right amount. It was more likely that the collapse would continue, leading to the formation of a black hole. Thus, if general relativity had a say in the matter, the existence of black holes had to be accepted as a reality.

After this major discovery, Chandrasekhar devoted himself to a systematic development of post-Newtonian approximation schemes stemming from general relativity. It marked the beginning of a correct description of radiation reaction and the discovery of a radiation-reaction-driven instability, conservation laws in general relativity, and how they are incorporated in successive post-Newtonian approximations.

Mathematical Theory of Black Holes, and Newton’s Principia (1975–1995) . After carrying out post-Newtonian approximation nearly as far as it could go, Chandrasekhar decided to undertake a systematic exploration of uniformly rotating stars within the framework of general relativity. In a series of papers with John Friedman, he developed a general formalism that paralleled Newtonian theory and revealed departures from it. In the process of studying the stability of such rotating stars under perturbations, their work led to the study of the physical situation outside a black hole (technically, the study of deformations of vacuum solutions external to a black hole).

Chandrasekhar’s study of black holes, which began with an analysis of the equations governing the perturbations of the Schwarzschild black holes, was to develop into a complete body of work of his own published in the form of a treatise, The Mathematical Theory of Black Holes. He was prompted to undertake this study because there was a great deal of mystery shrouding the subject with different sets of equations attributed to different authors (Zerilli equation, Bardeen–Press equation, Regge-Wheeler equation). Chandrasekhar’s coherent and self-contained account clarified the mystery and established the relations between the different sets of equations.

In the 1980s, during and after the completion of his book, Chandrasekhar had two young collaborators in Basilis Xanthopoulos and Valeria Ferrari. Together they discovered an underlying unity in the mathematical description of black holes and colliding gravitational waves. Earlier K. Khan and Roger Penrose had discovered the formation of a spacelike singularity in the collision of two plane gravitational waves. The nature of this singularity was very much like the one in the interior of the black hole. Subsequent extensions to more complicated waves and coupled gravitational and electromagnetic waves had led to problems that needed new ideas in the form of a rigorous mathematical theory of colliding waves patterned after the mathematical theory of black holes. With Ferrari and Xanthopoulos, Chandrasekhar formulated such a theory.

After the tragic, violent death of Basilis Xanthopoulos on 27 November 1990, Chandrasekhar continued to work with Ferrari on nonradial oscillations of stars in the framework of general relativity, until the end of his life. Concurrently, during the last decade of his life, he was devoted to the study of Sir Isaac Newton’s Principia(1687) and in 1995, just before he died of a heart attack, his monumental treatise Newton's Principia for the Common Reader was published.

BIBLIOGRAPHY

WORKS BY CHANDRASEKHAR

“The Compton Scattering and the New Statistics.” Proceeding of the Royal Society, A, 125 (1929): 231–237.

An Introduction to the Study of Stellar Structure. Chicago: University of Chicago Press, 1939. Reprinted New York: Dover Publications, 1967. Translated into Japanese and Russian.

“Stochastic Problems in Physics and Astronomy.” Reviews of Modern Physics15 (1943): 1–89. Reprinted in Selected Papers on Noise and Stochastic Processes, edited by Nelson Wax. New York: Dover Publications, 1954, 3–91.

Principles of Stellar Dynamics. Chicago: University of Chicago Press, 1943. Reprinted New York: Dover Publications, 1960.

Radiative Transfer. Oxford: Clarendon Press, 1950. Reprinted New York: Dover Publications, 1960. Translated into Russian.

Hydrodynamic and Hydromagnetic Stability. Oxford: Clarendon Press, 1961. Reprinted New York: Dover Publications, 1981. Translated into Russian.

Ellipsoidal Figures of Equilibrium. New Haven, CT: Yale University Press, 1968. Reprinted New York: Dover Publications, 1987. Translated into Russian.

The Mathematical Theory of Black Holes. Oxford: Clarendon Press, 1983. Translated into Russian.

“Autobiography.” In Les Prix Nobel: The Nobel Prizes 1983, edited by Wilhelm Odelberg. Stockholm: Nobel Foundation, 1984. Also available from http://nobelprize.org

Eddington: The Most Distinguished Astrophysicist of His Time. Cambridge: Cambridge University Press, 1983.

Truth and Beauty: Aesthetics and Motivations in Science. Chicago: University of Chicago Press, 1987.

Newton's Principia for the Common Reader. Oxford: Clarendon Press, 1995.

Selected Papers. 7 Volumes. Chicago: University of Chicago Press, 1989–1997. Chandrasekhar’s original papers.

A Quest for Perspectives: Selected Works of S. Chandrasekhar, with Commentary, edited by Kameshwar C. Wali. London: Imperial College Press, 2001. A subset chosen from the Selected Papers volumes.

OTHER SOURCES

Fowler, Ralph H. “On Dense Matter.” Monthly Notices of the Royal Astronomical Society 87 (1926): 114.

Wali, Kameshwar C. Chandra: A Biography of S. Chandrasekhar. Chicago: University of Chicago Press, 1992.

The following three books contain articles by various experts providing a grand tour of the colossal scientific edifice Chandrasekhar left behind and subsequent developments in their fields of expertise.

Srinivasan, G., ed. From White Dwarfs to Black Holes: The Legacy of S. Chandrasekhar. Chicago: University of Chicago Press, 1999.

Wald, Robert M. Black Holes and Relativistic Stars. Chicago: University of Chicago Press, 1998.

Wali, Kameshwar C., ed. S. Chandrasekhar: The Man behind the Legend. London: Imperial College Press, 1997.

Kameshwar C. Wali

Subrahmanyan Chandrasekhar

Subrahmanyan Chandrasekhar (1910-1995) worked on the origins, structure, and dynamics of stars and earned a prominent place in the annals of science. The Nobel Prize-winning physicist's most celebrated work concerns the radiation of energy from stars, particularly the dying fragments known as white dwarf stars.

Subrahmanyan Chandrasekhar was an Indian-born American astrophysicist and applied mathematician whose work on the origins, structure, and dynamics of stars secured him a prominent place in the annals of science. His most celebrated work concerns the radiation of energy from stars, particularly white dwarf stars, which are the dying fragments of stars. Chandrasekhar demonstrated that the radius of a white dwarf star is related to its mass: the greater its mass, the smaller its radius. Chandrasekhar made numerous other contributions to astrophysics. His expansive research and published papers and books include topics such as the system of energy transfer within stars, stellar evolution, stellar structure, and theories of planetary and stellar atmospheres. For nearly twenty years, he served as the editor-in-chief of the Astrophysical Journal, the leading publication of its kind in the world. For his immense contribution to science, Chandrasekhar, who died in 1995, received numerous awards and distinctions, most notably the 1983 Nobel Prize for Physics for his research into the depths of aged stars.

Chandrasekhar, better known as Chandra, was born on October 19, 1910, in Lahore, India (now part of Pakistan), the first son of C. Subrahmanyan Ayyar and Sitalakshmi nee (Divan Bahadur) Balakrishnan. Chandra came from a large family: he had two older sisters, four younger sisters, and three younger brothers. As the firstborn son, Chandra inherited his paternal grandfather's name, Chandrasekhar. His uncle was the Nobel Prize-winning Indian physicist, Sir C. V. Raman.

Chandra received his early education at home, beginning when he was five. From his mother he learned Tamil, from his father, English and arithmetic. He set his sights upon becoming a scientist at an early age, and to this end, undertook at his own initiative some independent study of calculus and physics. The family moved north to Lucknow in Uttar Pradesh when Chandra was six. In 1918, the family moved again, this time south to Madras. Chandrasekhar was taught by private tutors until 1921, when he enrolled in the Hindu High School in Triplicane. With typical drive and motivation, he studied on his own and steamed ahead of the class, completing school by the age of fifteen.

After high school, Chandra attended Presidency College in Madras. For the first two years, he studied physics, chemistry, English, and Sanskrit. For his B.A. honors degree he wished to take pure mathematics but his father insisted that he take physics. Chandra resolved this conflict by registering as an honors physics student but attending mathematics lectures. Recognizing his brilliance, his lecturers went out of their way to accommodate Chandra. Chandra also took part in sporting activities and joined the debating team. A highlight of his college years was the publication of his paper, "The Compton Scattering and the New Statistics." These and other early successes while he was still an eighteen-year-old undergraduate only strengthened Chandra's resolve to pursue a career in scientific research, despite his father's wish that he join the Indian civil service. A meeting the following year with the German physicist Werner Heisenberg, whom Chandra, as the secretary of the student science association, had the honor of showing around Madras, and Chandra's attendance at the Indian Science Congress Association Meeting in early 1930, where his work was hailed, doubled his determination.

Upon graduating with a M.A. in 1930, Chandra set off for Trinity College, Cambridge, as a research student, courtesy of an Indian government scholarship created especially for him (with the stipulation that upon his return to India, he would serve for five years in the Madras government service). At Cambridge, Chandra turned to astrophysics, inspired by a theory of stellar evolution that had occurred to him as he made the long boat journey from India to Cambridge. It would preoccupy him for the next ten years. He also worked on other aspects of astrophysics and published many papers.

In the summer of 1931, he worked with physicist Max Born at the Institut für Theoretische Physik at Göttingen in Germany. There, he studied group theory and quantum mechanics (the mathematical theory that relates matter and radiation) and produced work on the theory of stellar atmospheres. During this period, Chandra was often tempted to leave astrophysics for pure mathematics, his first love, or at least for physics. He was worried, though, that with less than a year to go before his thesis exam, a change might cost him his degree. Other factors influenced his decision to stay with astrophysics, most importantly, the encouragement shown him by astrophysicist Edward Arthur Milne. In August 1932, Chandra left Cambridge to continue his studies in Denmark under physicist Niels Bohr. In Copenhagen, he was able to devote more of his energies to pure physics. A series of Chandra's lectures on astrophysics given at the University of Liège, in Belgium, in February 1933 received a warm reception. Before returning to Cambridge in May 1933 to sit his doctorate exams, he went back to Copenhagen to work on his thesis.

Chandrasekhar's uncertainty about his future was assuaged when he was awarded a fellowship at Trinity College, Cambridge. During a four-week trip to Russia in 1934, where he met physicists Lev Davidovich Landau, B. P. Geraismovic, and Viktor Ambartsumian, he returned to the work that had led him into astrophysics to begin with, white dwarfs. Upon returning to Cambridge, he took up research of white dwarfs again in earnest.

As a member of the Royal Astronomical Society since 1932, Chandra was entitled to present papers at its twice monthly meetings. It was at one of these that Chandra, in 1935, announced the results of the work that would later make his name. As stars evolve, he told the assembled audience, they emit energy generated by their conversion of hydrogen into helium and even heavier elements. As they reach the end of their life, stars have progressively less hydrogen left to convert and emit less energy in the form of radiation. They eventually reach a stage when they are no longer able to generate the pressure needed to sustain their size against their own gravitational pull and they begin to contract. As their density increases during the contraction process, stars build up sufficient internal energy to collapse their atomic structure into a degenerate state. They begin to collapse into themselves. Their electrons become so tightly packed that their normal activity is suppressed and they become white dwarfs, tiny objects of enormous density. The greater the mass of a white dwarf, the smaller its radius, according to Chandrasekhar. However, not all stars end their lives as stable white dwarfs. If the mass of evolving stars increases beyond a certain limit, eventually named the Chandrasekhar limit and calculated as 1.4 times the mass of the sun, evolving stars cannot become stable white dwarfs. A star with a mass above the limit has to either lose mass to become a white dwarf or take an alternative evolutionary path and become a supernova, which releases its excess energy in the form of an explosion. What mass remains after this spectacular event may become a white dwarf but more likely will form a neutron star. The neutron star has even greater density than a white dwarf and an average radius of about .15 km. It has since been independently proven that all white dwarf stars fall within Chandrasekhar's predicted limit, which has been revised to equal 1.2 solar masses.

Unfortunately, although his theory would later be vindicated, Chandra's ideas were unexpectedly undermined and ridiculed by no less a scientific figure than astronomer and physicist Sir Arthur Stanley Eddington, who dismissed as absurd Chandra's notion that stars can evolve into anything other than white dwarfs. Eddington's status and authority in the community of astronomers carried the day, and Chandra, as the junior, was not given the benefit of the doubt. Twenty years passed before his theory gained general acceptance among astrophysicists, although it was quickly recognized as valid by physicists as noteworthy as Wolfgang Pauli, Niels Bohr, Ralph H. Fowler, and Paul Dirac. Rather than continue sparring with Eddington at scientific meeting after meeting, Chandra collected his thoughts on the matter into his first book, An Introduction to the Study of Stellar Structure, and departed the fray to take up new research around stellar dynamics. An unfortunate result of the scientific quarrel, however, was to postpone the discovery of black holes and neutron stars by at least twenty years and Chandra's receipt of a Nobel Prize for his white dwarf work by fifty years. Surprisingly, despite their scientific differences, he retained a close personal relationship with Eddington.

Chandra spent from December 1935 until March 1936 at Harvard University as a visiting lecturer in cosmic physics. While in the United States, he was offered a research associate position at Yerkes Observatory at Williams Bay, Wisconsin, staring in January 1937. Before taking up this post, Chandra returned home to India to marry the woman who had waited for him patiently for six years. He had known Lalitha Doraiswamy, daughter of Captain and Mrs. Savitri Doraiswamy, since they had been students together at Madras University. After graduation, she had undertaken a master's degree. At the time of their marriage, she was a headmistress. Although their marriage of love was unusual, as both came from fairly progressive families and were both of the Brahman caste, neither of their families had any real objections. After a whirlwind courtship and wedding, the young bride and groom set out for the United States. They intended to stay no more than a few years, but, as luck would have it, it became their permanent home.

At the Yerkes Observatory, Chandra was charged with developing a graduate program in astronomy and astrophysics and with teaching some of the courses. His reputation as a teacher soon attracted top students to the observatory's graduate school. He also continued researching stellar evolution, stellar structure, and the transfer of energy within stars. In 1938, he was promoted to assistant professor of astrophysics. During this time Chandra revealed his conclusions regarding the life paths of stars.

During the World War II, Chandra was employed at the Aberdeen Proving Grounds in Maryland, working on ballistic tests, the theory of shock waves, the Mach effect, and transport problems related to neutron diffusion. In 1942, he was promoted to associate professor of astrophysics at the University of Chicago and in 1943, to professor. Around 1944, he switched his research from stellar dynamics to radiative transfer. Of all his research, the latter gave him, he recalled later, more fulfillment. That year, he also achieved a lifelong ambition when he was elected to the Royal Society of London. In 1946, he was elevated to Distinguished Service Professor. In 1952, he became Morton D. Hull Distinguished Service Professor of Astrophysics in the departments of astronomy and physics, as well as at the Institute for Nuclear Physics at the University of Chicago's Yerkes Observatory. Later the same year, he was appointed managing editor of the Astrophysical Journal, a position he held until 1971. He transformed the journal from a private publication of the University of Chicago to the national journal of the American Astronomical Society. The price he paid for his editorial impartiality, however, was isolation from the astrophysical community.

Chandra became a United States citizen in 1953. Despite receiving numerous offers from other universities, in the United States and overseas, Chandra never left the University of Chicago, although, owing to a disagreement with Bengt Strömgren, the head of Yerkes, he stopped teaching astrophysics and astronomy and began lecturing in mathematical physics at the University of Chicago campus. Chandra voluntarily retired from the University of Chicago in 1980, although he remained on as a post-retirement researcher. In 1983, he published a classic work on the mathematical theory of black holes. Afterwards, he studied colliding waves and the Newtonian two-center problem in the framework of the general theory of relativity. His semi-retirement also left him with more time to pursue his hobbies and interests: literature and music, particularly orchestral, chamber, and South Indian.

During his long career, Chandrasekhar received many awards. In 1947, Cambridge University awarded him its Adams Prize. In 1952, he received the Bruce Medal of the Astronomical Society of the Pacific, and the following year, the Gold Medal of the Royal Astronomical Society. In 1955, Chandrasekhar became a Member of the National Academy of Sciences. The Royal Society of London bestowed upon him its Royal Medal seven years later. In 1962, he was also presented with the Srinivasa Ramanujan Medal of the Indian National Science Academy. The National Medal of Science of the United States was conferred upon Chandra in 1966; and the Padma Vibhushan Medal of India in 1968. Chandra received the Henry Draper Medal of the National Academy of Sciences in 1971 and the Smoluchowski Medal of the Polish Physical Society in 1973. The American Physical Society gave him its Dannie Heineman Prize in 1974. The crowning glory of his carer came nine years later when the Royal Swedish Academy awarded Chandrasekhar the Nobel Prize for Physics. ETH of Zurich gave the Indian astrophysicist its Dr. Tomalla Prize in 1984, while the Royal Society of London presented him with its Copley Prize later that year. Chandra also received the R. D. Birla Memorial Award of the Indian Physics Association in 1984. In 1985, the Vainu Bappu Memorial Award of the Indian National Science Academy was conferred upon Chandrasekhar. In May 1993, Chandra received the state of Illinois's highest honor, Lincoln Academy Award, for his outstanding contributions to science.

While his contribution to astrophysics was immense, Chandra always preferred to remain outside the mainstream of research. He died on August 21, 1995, at the age of 82 in Chicago. The respected physicist once described himself to his biographer, Kameshar C. Wali, as "a lonely wanderer in the byways of science." Throughout his life, Chandra strove to acquire knowledge and understanding, according to an autobiographical essay published with his Nobel lecture, motivated "principally by a quest after perspectives."

Further Reading

The Biographical Dictionary of Scientists, Astronomers, Blond Educational Company (London), 1984, pp. 36.

Chambers Biographical Encyclopedia of Scientists, Facts-on-File, 1981.

Goldsmith, Donald, The Astronomers, St. Martin's Press, 1991.

Great American Scientists, Prentice-Hall, 1960.

Land, Kenneth R. and Owen Gingerich, editors, A Sourcebook in Astronomy and Astrophysics, Harvard University Press, 1979.

Modern Men of Science, McGraw-Hill, 1966, p. 97.

Wali, Kameshwar C., Chandra: A Biography of S. Chandrasekhar, Chicago University Press, 1991. □

Subrahmanyan Chandrasekhar

Born: October 19, 1910
Lahore, India (now part of Pakistan)
Died: August 21, 1995
Chicago, Illinois
Indian-born American astrophysicist and mathematician

Subrahmanyan Chandrasekhar worked on the origins and structures of stars, earning an important place in the world of science. The Nobel Prize-winning physicist's most celebrated work concerns the radiation of energy from stars, particularly the dying fragments known as white dwarf stars.

Early years

Subrahmanyan Chandrasekhar, better known as Chandra, was born on October 19, 1910, in Lahore, India (now part of Pakistan), the first son of C. Subrahmanyan Ayyar and Sitalakshmi (Divan Bahadur) Balakrishnan. Chandra came from a large family—he had six brothers and three sisters. As the firstborn son, Chandra inherited his paternal grandfather's name, Chandrasekhar. His uncle was the Nobel Prize-winning Indian physicist, Sir C. V. Raman (1888–1970).

Chandra received his early education at home, beginning when he was five. From his mother he learned Tamil (a language spoken in India), from his father, English and arithmetic. He set his sights upon becoming a scientist at an early age, and to this end, undertook some independent study of calculus and physics. Private tutors taught Chandra until 1921, when he enrolled in the Hindu High School in Triplicane, India. With typical drive and motivation, he studied on his own and rose to the head of the class, completing school by the age of fifteen.

After high school Chandra attended Presidency College in Madras, India. For the first two years he studied physics, chemistry, English, and Sanskrit. For his bachelor's honors degree he wished to take pure mathematics but his father insisted that he take physics. Chandra registered as an honors physics student but attended mathematics lectures, where his teachers quickly realized his brilliance. Chandra also took part in sporting activities and joined the debating team. A highlight of his college years was the publication of his paper, "The Compton Scattering and the New Statistics." These and other early successes while still an eighteen-year-old undergraduate only strengthened Chandra's determination to pursue a career in scientific research, despite his father's wish that he join the Indian civil service.

Upon graduating with a master's degree in 1930, Chandra set off for Trinity College in Cambridge, England. As a research student at Cambridge he turned to astrophysics, inspired by a theory of stellar (stars) evolution that had occurred to him as he made the long boat journey from India to Cambridge. In the summer of 1931 he worked with physicist Max Born (1882–1970) at the Institut für Theoretische Physik at Göttingen in Germany. In 1932 he left for Copenhagen, Denmark, where he was able to devote more of his energies to pure physics. A series of Chandra's lectures on astrophysics given at the University of Liège, in Belgium in February 1933 received a warm reception.

White dwarfs

During a four-week trip to Russia in 1934—where he met physicists Lev Davidovich Landau (1908–1968), B. P. Geraismovic, and Viktor Ambartsumian—he returned to the work that had led him into astrophysics to begin with: white dwarfs. Upon returning to Cambridge, he took up researching white dwarfs again.

As a member of the Royal Astronomical Society since 1932, Chandra was entitled to present papers at its twice monthly meetings. It was at one of these that Chandra, in 1935, announced the results of the work that would later make his name. As stars evolve, he told the assembled audience, they release energy generated by their conversion of hydrogen into helium and even heavier elements. As they reach the end of their life, stars have less hydrogen left to convert so they release less energy in the form of radiation. They eventually reach a stage when they are no longer able to generate the pressure needed to maintain their size against their own gravitational pull, and they begin to shrink, eventually collapsing into themselves. Their electrons (particle with a negative charge) become so tightly packed that their normal activity is shut down and they become white dwarfs, or tiny objects of enormous density.

The Yerkes Observatory

In 1937 Chandra returned home to India to marry Lalitha Doraiswamy. The couple settled in the United States. A year later Chandra was charged with developing a graduate program in astronomy and astrophysics and with teaching some of the courses at the University of Chicago's Yerkes Observatory. His reputation as a teacher soon attracted top students to the observatory's graduate school. He also continued researching stellar evolution, stellar structure, and the transfer of energy within stars.

In 1944 Chandra achieved a lifelong goal when he was elected to the Royal Society of London, the world's oldest scientific organization. In 1952 he became the Morton D. Hull Distinguished Service Professor of Astrophysics in the departments of astronomy and physics, as well as at the Institute for Nuclear Physics, at the University of Chicago's Yerkes Observatory. Later the same year he was appointed managing editor of the Astrophysical Journal, a position he held until 1971.

Chandra became a United States citizen in 1953. He retired from the University of Chicago in 1980, although he remained on as a post-retirement researcher. In 1983 he published a classic work on the mathematical theory of black holes. His semi-retirement also left him with more time to pursue his hobbies and interests: literature and music, particularly orchestral, chamber, and South Indian.

Chandra died in Chicago on August 21, 1995, at the age of eighty-two. Throughout his life Chandra strove to acquire knowledge and understanding. According to an autobiographical essay published with his Nobel lecture, he was motivated "principally by a quest after perspectives."

For More Information

The Biographical Dictionary of Scientists, Astronomers. London: Blond Educations Company, 1984, p. 36.

Goldsmith, Donald. The Astronomers. New York: St. Martin's Press, 1991.

Land, Kenneth R., and Owen Gingerich, eds. A Sourcebook in Astronomy and Astrophysics. Cambridge, MA.: Harvard University Press, 1979.

Wali, K. C. Chandra: a Biography of S. Chandrasekhar. Chicago: University of Chicago Press, 1991.

Chandrasekhar, Subrahmanyan (1910–95) US astrophysicist, b. India. He formulated theories about the creation, life and death of stars, and calculated the maximum mass of a white dwarf star before it becomes a neutron star; the Chandrasekhar limit. It equals 1.4 times the mass of the Sun. He shared the 1983 Nobel Prize in physics with William Fowler.

Subrahmanyan Chandrasekhar

1901-1995

Indian-born American astrophysicist who was awarded the 1983 Nobel Prize for Physics for theoretical studies of the structure and evolution of stars. Chandrasekhar showed that as stars exhaust their nuclear fuel they reach a stage where they no longer generate sufficient pressure to sustain their size and gravitational collapse occurs. Chandrasekhar calculated that stars of 1.4 solar mass (the "Chandrasekhar limit") or less collapse to white dwarfs, while stars of greater mass become supernovas, typically leaving neutron stars.