Chandrasekhar and the Stars
Early life
Subramanyam Chandrasekhar was born in 1910 in Lahore which is in Pakistan now. When he was six, the family shifted to Lucknow. After his father shifted to
Madras as Assistant Accountant General, the family stayed in Madras permanently.
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Chandrasekhar was educated at his home in Madras along with his 5 brothers and 4 sisters. His education proceeded in a very strict and regular manner. His
father saw that Chandra was brilliant and so appointed very good teachers. Chandra went to School only when he was eleven. He was admitted into the third form
(which is equivalent to the eighth grade) in the Triplicane Hindu School which was considered the best School in Madras.
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His education at home had avoided bookish knowledge that was an impediment to real education and had opened his mind. All this changed in the School and he did not like it. But in the fourth form he could learn Algebra and Geometry which increased his enthusiasm for studies. In the summer holidays he started learning these subjects on his own. He learnt much more than what was taught at School. In the next three summer holidays, he learnt Conic Sections, Analytical Geometry, Calculus, Differential Equations, Permutations and Combinations and Solution of Cubic Equations. All this, he learnt by himself during his School years. Later he was praised as next only to Lord Rayleigh who was regarded as the greatest mathematical physicist the world has seen. The foundation for that was already laid during Chandra's School years.
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Chandra studied in the Intermediate College in Presidency College during 1925-27. Since his mathematical proficiency was very high, he passed out with highest marks in the class. He got distinction in mathematics, physics and chemistry. He was attracted towards BSc Hons Mathematics. His father wanted him to do BSc Hons Physics, pass ICS and join Government service. But Chandra had other plans. Since he was also interested in Physics, he joined BSc Hons Physics.
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He studied Arnold Sommerfeld's Atomic Structure and Spectral Lines which was regarded as the Bible of Old Quantum Theory. The years 1927-30 that he spent in Presidency College saw two important events - the visits of Sommerfeld and Heisenberg. Sommerfeld was the teacher of many famous theoretical physicists. Heisenberg was a creator of Quantum Mechanics which revolutionized twentieth century physics. How Chandra encountered these two giants is described below.
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The first three research papers of Chandrasekhar were published in Indian Journal of Physics, Proceedings of Royal Society and Philosophical Magazine during 1928-30 even while he was a student of Presidency College.
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His brilliant academic career was brought to the attention of the Government of Madras. The British Government awarded a scholarship to Chandra for studying in Cambridge. His Professors in Presidency College, especially Prof Parameswaran and Principal Fyson helped him towards this. He sailed for Cambridge in July 1930.
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Meeting with Sommerfeld
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We describe this Chandra's own words:
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"I went and met him in his hotel. I told him of my interest in Physics and of my desire to talk with him. He asked me to come next day and see him. I went. He asked me how much I had read. I told him that I have read his book "Atomic Structure and Spectral Lines". He said that after that book was written, Physics has changed completely and told me about the discoveries of Schrodinger, Heisenberg, Pauli and Dirac. I felt very disappointed. He noticed that and asked what else did I know. I said that I have read a little about Statistical Mechanics. He said that there are changes in that subject too and gave me his article " Electrons in metals" in the proof form even before it was published."
We shall come back to the effect of this article on Chandra.
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Meeting with Heisenberg
Chandra was the Secretary of the Students' Physics Club. KS Krishnan, the famous physicist was visiting Madras at that time. He gave Chandra the responsibility of showing Heisenberg around Madras and neighborhood in a sight-seeing tour. In a rented car, Chandra took him to Kanchipuram and Mahabalipuram and showed him all the famous temples. In the evening, they went along the Marina beach. Being with such a famous scientist for one whole day was an exhilarating experience for Chandra. In a letter to his father, he says:
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"I was with him for the whole day until he left for Colombo in the Boat Mail. I discussed
my research articles with him. In one day, I learnt a whole world of physics from him."
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Fermi-Dirac Statistics and Degeneracy Pressure
When Sommerfeld visited Madras in 1928, Chandra learnt from him about Fermi-Dirac Statistics and how this controls the behavior of electrons in metals. This provided the seed for Chandra's famous research in Cambridge.
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R H Fowler had shown how the degeneracy pressure of electrons due to Fermi-Dirac statistics prevented the gravitational shrinking of dead stars called white dwarfs. Chandra discovered that if the electrons are relativistic, the degeneracy pressure is unable to prevent gravitational collapse of stars of mass above a critical limit. The thinking for this discovery started after he met Sommerfeld in Madras!
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Chandra joined Cambridge University in 1930 and got his PhD in 1933 under the guidance of R H Fowler. In 1937, he crossed the Atlantic and joined Chicago University in USA. He worked there in various capacities and continued as Morton D Hull Distinguished Service Professor during 1952 to 1986. He passed away on 21 August 1995.
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He got Nobel Prize in 1983 for his discovery of the upper limit to the mass of a star which was done in 1935! Why the Prize was given after almost 50 years, is an interesting story which will be described below.
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The six facets of Subramanyam Chandrasekhar
Chandra's scientific research spanned six areas: Internal Structure of Stars, Dynamics of Stars, Stellar Atmospherics, Fluids and Plasmas, Stability of gravitating
masses and Black Holes. These came out as 6 books:
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Introduction to the study of Stellar Structure (1937)
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Principles of Stellar Dynamics (1942)
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Radiative Transfer (1949)
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Hydrodynamic and Hydromagnetic Stability (1961)
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Ellipsoidal Figures of Equilibrium (1969)
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The Mathematical Theory of Black Holes (1983)
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Rajaram Nithyananda, in his lecture on Chandrasekhar, given at IMSc in 1995, lays special emphasis on Subramanyam in Chandra's name, referring to the six-faced Lord.
1. Internal Structure of Stars
We already mentioned about the limiting mass of stars discovered by Chandrasekhar. When the velocity of the electrons in the star is low, nonrelativistic quantum mechanics leads to the result that the degeneracy pressure is proportional to the 5/3 power of density. Chandrasekhar found that when the velocity increases and becomes relativistic, the power is reduced to 4/3. Thus, in the relativistic region, the degeneracy pressure is reduced. In this case, above a certain mass, pressure is not able to balance the inward gravitational force and hence the star starts shrinking. This critical mass is called Chandrasekhar limit.
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But the famous astronomer Sir Arthur Eddington did not agree with this conclusion. He said Chandrasekhar must have made some mistake in his calculation and ridiculed him. On the other hand neither Eddington nor anybody else could pinpoint the mistake.
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Chandrasekhar was very much affected by this controversy with Eddington. In his words, "I have to take an important decision. Should I spend my life in this fight? No. I will publish my research results in a book and start on a different piece of research."
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This is what he did. His first book on the internal structure of stars came out in 1937. In the end Chandrasekhar won. Many theoretical calculations and observational research on stars confirmed Chandra's results. In 1983 he got the Nobel Prize. "Chandrasekhar Limit" came to text books also. How a star of mass above Chandrasekhar limit shrinks and becomes a neutron star and beyond that it becomes a black hole - all this is now learnt by students.
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When we compare with the totality of Chandrasekhar's scientific research, his discovery of the limiting mass which got the Nobel Prize sits in a corner, especially if one considers the time and effort he took in that discovery. But surely it is a great discovery. Further it is his confrontation with Eddington that determined his scientific trajectory. In his words again, "5-10 years of intense research and calculations, in a book. After that go to a different area."
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2. Stellar Dynamics
He left the structure of stars and started his research on the collection of stars and galaxies. How do stars interact with distant stars and how do they collide? He found that stars in a galaxy move by diffusion, just like the molecules in a gas. It is during this research that his famous essay on Brownian Motion came out. It became a citation classic.
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3. The Atmospheres of Stars
This was Chandrasekhar's famous research on Radiative Transfer.
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In the outer layers of a star, the density is low. In this region, the mean free path of light (or photons) and their trajectories are calculated by integral equations. All
of Chandrasekhar's mathematical acumen was utilized in solving these equations. In this process, he made many discoveries.
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Earlier the Russian scientist Ambarstrumian had discovered the principle of invariance. Chandra extended this principle. As a climatic result, Chandra discovered how a slab conducts the heat due to polarized light. He also found that the earlier results by others were wrong. To calculate these correctly, he found Stokes parameters are the proper tools and using them he completed the calculation. This was something that was started by Lord Rayleigh 75 years ago and had remained incomplete!
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Another success of Chandra in this area concerns the hydride ion which has two electrons instead of the one-electron in the Hydrogen atom. This was a three-body problem in quantum mechanics. Due to his hard work, he solved this problem also and resolved a contradiction between quantum mechanics and the spectral lines in starlight.
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4. Fluids and Plasmas
When he attained great success with radiative transfer of heat, he was invited to deliver the famous Henry Norris Russell lecture. He chose to talk about turbulence which plays an important role in astronomy. The book that he wrote at that time "Hydrodynamic and Hydromagnetic Stability" received much accolade. Like his other books, this book also presents all the knowledge available in the subject in a systematic way. One of his discoveries is how neutron stars and black holes send their atmospheres inwards, as a result of which their speeds of rotation get reduced.
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5. Equilibrium of self-gravitating rotating bodies
In 1960 Chandra moved backwards and took up a problem that existed since Newton's time. What kind of shape does a body take due to rotation and self gravitation? His research article written with Lebovitz and his book describe the results obtained by the famous mathematicians Maclaurine, Jacobi, Riemann, Dirichlet, Dedekind and Poincare. But all these results are not correct. Chandra, with Lebovitz, used "Tensor Virial Theorems"
to find the correct results.
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It is at this stage that he found that the earlier research on gravitational waves was incomplete. Along with his students Nutku and Esposito, he used the full Einstein equations and correctly calculated the reaction due to the radiation of gravitational waves.
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His other researches: (a) He returned to his old limiting mass and found that if general relativity is used to calculate the gravitational pressure, then the limiting mass occurs even before the radius becomes zero. (b) He found that an axially symmetric object loses its stability by gravitational radiation and many other things. His research on these, with Friedman, continued even upto the time of his death.
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6. General Relativity and Black Holes
In the 1960's Chandrasekhar started learning General Relativity by giving a course on it to graduate students.(I was one of those students). He said he was giving this course because he wanted to learn it!
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He was very much attracted by General Relativity and finally entered it. His book "The Mathematical Theory of Black Holes came out in 1982. In that book, his ten-years' work enabled him to systematize all the results on this subject. He called Black Holes as the most perfect objects in the Universe!
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After that he started research on the collision of gravitational waves. Infact during his visit to Institute of Mathematical Sciences, Chennai in the early 1990's he gave a seminar on this subject.
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Final Remarks
High goals, deep involvement in scientific research, unbounded effort to discover the truth, ceaseless work until the end - these are the hallmarks of Chandrasekhar. In these respects, it is difficult to find his equal even among famous scientists. He is infact one of the Rishis (sages) that we read about, in story books.
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References
1. Chandra, by KC Wali, Viking, Penguin India (1990)
2. Talk by Rajaram Nithyananda at IMSc, 17 November 1995