how we figured out big stars can't die as white dwarfs

The Mechanism

Subrahmanyan Chandrasekhar was born on 19 October 1910 in Lahore, then in British India, the eldest son in a Tamil Brahmin family; his father was a deputy auditor-general of the Northwestern Railways and his uncle, C. V. Raman, would win the 1930 Nobel Prize in Physics for the Raman effect. Chandra took his B.A. Honours in physics at Presidency College, Madras, in June 1930 at 19, having already published four papers as an undergraduate — one of them, on Compton scattering, in the *Proceedings of the Royal Society*. That summer, on the strength of a Government of India scholarship, he boarded the Lloyd Triestino steamer *SS Pilsna* at the Ballard Pier in Bombay on 31 July 1930 bound for Venice, en route to Trinity College, Cambridge, where he was to read for a Ph.D. under Ralph Fowler. He had two open questions on his mind. The first: R. H. Fowler had shown in 1926 that white dwarf stars — stars whose nuclear fuel is spent and which support themselves against gravity by a purely quantum-mechanical pressure called *electron degeneracy pressure* — could exist at any mass, in principle. The second: E. C. Stoner and Wilhelm Anderson had, in 1929–30, published brief calculations suggesting that if one included Einstein's special relativity, this pressure would soften at very high densities; but their treatments were approximate and no one had integrated the argument through the equation of state of a whole star. Chandrasekhar spent the eighteen-day voyage — as he later told S. G. Wagh and Kameshwar Wali — in a deck chair with his back against a life-preserver, working alone through the stellar-structure equations that Arthur Eddington had laid out in 1926 in *The Internal Constitution of the Stars*, with three books beside him: Eddington's monograph, Fowler's 1926 paper, and Sommerfeld's *Atomic Structure and Spectral Lines*. He treated the electron gas in the interior of a white dwarf relativistically — that is, he acknowledged that at densities of about a million grams per cubic centimetre, the electrons at the top of the Fermi sea are moving at a substantial fraction of the speed of light, so their momentum grows more slowly with density than the non-relativistic approximation predicts. The consequence, which fell out of his integrated *polytrope* equation as cleanly as any result in physics, was that the total mass of a stable relativistically-degenerate white dwarf converged to a single fixed number — a mass, in his final calculation, of about 0.91 solar masses (later, once the mean molecular weight per electron was refined, sharpened to about 1.44 solar masses). Above that number, no white dwarf could exist. When he handed his notebook to Fowler at Trinity in the autumn of 1930, Fowler was polite but unconvinced; his short first paper appeared in November 1931 in the *Astrophysical Journal* under the title *"The Maximum Mass of Ideal White Dwarfs,"* Volume 74, pages 81–82. He then spent five more years extending the calculation into a full stellar-structure theory and, on Friday 11 January 1935, at 27, presented the finished work to the Royal Astronomical Society in London under the title *"The Highly Collapsed Configurations of a Stellar Mass."* The moment he sat down, Arthur Eddington — the most powerful astrophysicist alive, then 52 — stood up, walked to the front, and mocked the result in front of the room. Eddington said he thought there must be a *reductio ad absurdum* somewhere, some undiscovered "law of Nature" that saved the star from becoming infinitely dense — that Chandra's calculation, if believed, meant that a sufficiently massive star's core, having exhausted its nuclear fuel, must go on collapsing without limit. In the audience Rosseland, Milne, Fowler, and others sat silent; no one wanted to publicly oppose Eddington. Chandra was devastated. He was 24 years old and a South Indian student in a room of English professors, and he had been publicly ridiculed by the most famous astrophysicist in the world. He never fought Eddington directly. He collected the full argument into his 1939 book *An Introduction to the Study of Stellar Structure*, left Cambridge, took a job at the Yerkes Observatory in Williams Bay, Wisconsin, and moved on. Vindication was slow. Robert Oppenheimer and Hartland Snyder's 1939 paper on continued gravitational collapse showed that Chandra's continuously-collapsing objects had to form what would in the 1960s be called black holes. In 1966 Freeman Dyson gave a talk at the Rutherford Centenary calling the Chandrasekhar limit "the most important limit in stellar physics." In 1983, at 72, Chandra shared the Nobel Prize in Physics with William Fowler for "his theoretical studies of the physical processes of importance to the structure and evolution of the stars"; the citation named the mass limit explicitly. Eddington, when he died in 1944, had never publicly conceded. Modern astrophysics is unambiguous: every neutron star ever detected is the corpse of a star whose iron core exceeded 1.44 solar masses; every black hole in the Milky Way is the corpse of a stellar core that exceeded a related (Tolman-Oppenheimer-Volkoff) limit above that. All the compact objects in the sky — pulsars, magnetars, X-ray binaries, the black hole at the centre of the galaxy — are downstream of a Fermi-sea calculation a 19-year-old did alone in a deck chair on the *SS Pilsna* between the last week of July and the third week of August 1930.