On the afternoon of 31 July 1930, in a third-class cabin of the P. and O. steamer Pilsna, somewhere in the western Indian Ocean between Madras and Aden, an eighteen-year-old Indian physics student named Subrahmanyan Chandrasekhar finished the central calculation of a paper he had been working on, off and on, since the morning the ship cleared the Madras roadstead two weeks earlier.
He had been admitted to Trinity College, Cambridge, as a research student for the Michaelmas term of 1930, on the strength of the bachelor's degree he had taken, with first-class honours, at Presidency College in Madras the previous June. He was eighteen. He had never been outside India.
The cabin was small and not well ventilated. The voyage would take three weeks. He had brought with him a small stack of books, a slide rule, a fountain pen, several quires of paper, and the recent issues of the Monthly Notices of the Royal Astronomical Society in which Arthur Eddington and Edmund Stoner had been arguing about the equation of state of dense stellar matter.
The argument, briefly, was the following. White dwarfs were known, from Walter Adams's 1925 spectroscopic measurements of Sirius B, to be stars of stellar mass packed into volumes about the size of the Earth. The densities were of the order of a tonne per cubic centimetre.
At such densities, the electrons were degenerate. They were no longer bound to particular atomic nuclei. They formed a Fermi gas whose pressure was, at low temperatures, almost independent of temperature and almost entirely a function of density.
Eddington, in his 1926 book The Internal Constitution of the Stars, had treated the electron pressure non-relativistically. He had concluded that white dwarfs of any mass could be supported indefinitely by electron degeneracy pressure and that the configurations were stable.
Stoner, working at Leeds, had pointed out in 1929 that at the densities required to support the most massive white dwarfs, the electrons were moving at a substantial fraction of the speed of light. The correct treatment was relativistic. The relativistic equation of state was softer than the non-relativistic one. The implication was that there was a maximum mass beyond which electron degeneracy pressure could not support the star.
Stoner had estimated the maximum at about one solar mass, working with a simplified, uniform-density model.
Chandrasekhar, in the cabin of the Pilsna, redid the calculation for a realistic, polytropic stellar model. He arrived at a maximum of about 1.4 solar masses for a star of mean molecular weight two. The number was higher than Stoner's, because the polytropic model was more accurate. The conclusion was the same.
He wrote up the result, in pencil, in a small notebook over the remainder of the voyage. The notebook is preserved in the Chandrasekhar papers at the University of Chicago.
He arrived in Southampton in mid-August and travelled directly to Cambridge. He was assigned, at his own request, to work under Ralph Fowler, who had been the supervisor of Paul Dirac and who was, in 1930, the leading British authority on the statistical mechanics of dense matter.
Fowler read the cabin calculation, made several suggestions, and recommended publication. The paper, titled The Maximum Mass of Ideal White Dwarfs, appeared in The Astrophysical Journal in 1931. It is just under three pages long.
It received almost no immediate attention.
Chandrasekhar spent the following four years extending the calculation. He worked through the relativistic polytropic equations in their full generality. He computed mass-radius relations for white dwarfs across the range of permissible compositions. He prepared a long paper for the Royal Astronomical Society, which he intended to present at the society's monthly meeting on 11 January 1935.
He delivered the paper. It ran for about twenty minutes. The conclusion, presented to the meeting in his soft and careful voice, was that white dwarfs more massive than about 1.4 solar masses could not be in hydrostatic equilibrium. Beyond that limit, no static configuration existed.
The implication, which he did not fully draw out in the talk but which was implicit in the equations, was that a sufficiently massive stellar core, at the end of its nuclear-burning life, would collapse without limit.
Sir Arthur Eddington, who had been sitting in the front row of the meeting and who was, in 1935, the most authoritative British astrophysicist alive, rose to comment.
He spoke for almost as long as Chandrasekhar had. His comment, the text of which survives in the Monthly Notices for that month, was that Chandrasekhar's combination of relativity and non-relativistic statistical mechanics was inconsistent and that the result was, in consequence, physically meaningless.
He concluded with the sentence that has become, in retrospect, the most-quoted line of the encounter: I think there should be a law of Nature to prevent a star from behaving in this absurd way.
Chandrasekhar, who had not been warned that the comment was coming, sat through it without visible reaction. He left the meeting room afterward and walked, by his own later account, for several hours along the Embankment.
Eddington's objection was, by the standards of the physics community of 1935, technical rather than ad hominem. The leading physicists of the period took the objection seriously enough to ask their own quantum-mechanical colleagues about it. Léon Rosenfeld in Copenhagen, Wolfgang Pauli in Zurich, and Niels Bohr himself examined the question over the following year.
Their unanimous verdict, communicated to Chandrasekhar in correspondence preserved at Chicago, was that Eddington was wrong and Chandrasekhar was right. The combination of special relativity and Fermi-Dirac statistics that Chandrasekhar had used was the correct one. There was no inconsistency.
None of them said so in print. Eddington was Eddington. The British astrophysical community was small, and Eddington's authority within it was nearly absolute. The cost of a public correction was judged, by everyone in a position to make it, to be too high.
Chandrasekhar left Britain for the United States in 1936, joining the University of Chicago at the Yerkes Observatory in Wisconsin. He published the full long-form treatment of the white-dwarf result as a chapter of his 1939 monograph An Introduction to the Study of Stellar Structure, where it has been sitting, correctly, for nearly ninety years.
The limit is now universally known as the Chandrasekhar mass. The value, with modern equation-of-state corrections, is about 1.44 solar masses. It is the foundation of the modern theory of stellar evolution, the threshold above which a stellar core must collapse to a neutron star or a black hole, the trigger condition for Type Ia supernovae.
Chandrasekhar received the Nobel Prize in Physics in 1983, jointly with William Fowler, for his theoretical studies of the physical processes of importance to the structure and evolution of stars. He was seventy-three. The cabin calculation, fifty-three years earlier, was specifically cited.
He died on 21 August 1995, of heart failure, in Chicago. He was eighty-four.
His widow, Lalitha Chandrasekhar, preserved the cabin notebook, which had stayed with him through the move to America and through the moves to Yerkes and then to Hyde Park. The notebook is in the University of Chicago archives now. It is not on public display. It is, on inspection, a quite ordinary student notebook, with mathematics in a neat right-leaning hand and a small inkblot on the page where the limit first appears as a number.
