The Highly Collapsed Configurations of a Stellar Mass (Second Paper); Stellar Configurations with Degenerate Cores. [With:] EDDINGTON. On 'Relativistic Degeneracy'. [With:] MØLLER & CHANDRASEKHAR. Relativistic Degeneracy. [With:] CHANDRASEKHAR. Stellar Configurations with Degenerate Cores (Second Paper)

THE 'CHANDRASEKHAR LIMIT' - NOBEL PRIZE IN PHYSICS 1983. First edition, offprint issue, of the five papers of 1935 in which Chandrasekhar gave the exact theory of the limiting mass of white dwarf stars and Eddington denied that the physics behind it existed, the group inscribed and initialled by Chandrasekhar: his own January offprint carries 'With kindest regards' in his hand, and Eddington's attack carries his initials 'S.C.' in the same ink. The question the papers settle is what becomes of a star once its fuel is spent. Fowler had shown in 1926 that the electrons of a burnt-out star, packed to the density of a white dwarf, obey the new quantum statistics and hold the star up without any heat. Stoner and Anderson had seen by 1930 that at such densities the electrons move at speeds where relativity counts. Chandrasekhar, from a calculation made on the voyage from Madras to Cambridge in 1930, had found that the relativistic law allows no white dwarf above about nine-tenths of the mass of the Sun. The January papers replace that estimate with the exact theory. They reduce the whole degenerate star to a single differential equation and follow its solutions to the configuration of zero radius. The limit comes out at 5.728 divided by the square of the mean molecular weight, in solar masses, which for matter without hydrogen is a little over 1.4 suns. Eddington answered them at the Royal Astronomical Society on 11 January 1935 with the paper that is the second offprint here. Chandrasekhar and Møller answered him in June with the third, and Chandrasekhar carried the theory into the Hertzsprung-Russell diagram in the fourth. Chandrasekhar was twenty-four. He had read Fowler's paper as a student at Presidency College, Madras, after Sommerfeld, visiting India in 1928, had shown him the new statistics, and on the voyage to Cambridge in the summer of 1930 he had written two short papers, one on the non-relativistic white dwarf and one on what happened when the electrons went relativistic. Fowler accepted the first and doubted the second; so did Milne, to whom Fowler sent it. The note that resulted, two pages in the Astrophysical Journal for 1931, gave the maximum mass as 0.91 suns for a mean molecular weight of 2.5 and compared it with the earlier value Stoner had found from a star of uniform density. The priority is shared, though the January paper concedes it only in part: its appendix credits Stoner with the equation of state and notes that Landau had used its ultra-relativistic form, and it does not name Anderson. Anderson in Tartu had seen in 1929 that the electrons of a solar-mass white dwarf must be relativistic; Stoner had derived the correct equation of state and shown in 1930 that the mass of a uniform star reaches a maximum as its density goes to infinity; and Landau, in a paper written in 1931 and printed in 1932, reached the same limit apparently without knowledge of Stoner. What was Chandrasekhar's own was the exact theory of 1935, worked out at Trinity, where he had been elected a Fellow in 1933, with Eddington calling on him often that autumn to ask how the calculations went. The first paper is dated 1 January 1935 and the second 4 January, a week before the Society's January meeting. The first paper takes the exact relativistic equation of state and proves what Chandrasekhar had announced without proof in the Observatory in 1934: that every completely degenerate star is a solution of one equation with a single parameter, the central value of a quantity that measures how relativistic the electrons are. Ten numerical integrations, tabulated over two pages, run the sequence from the ordinary Emden polytrope of index 3/2 at low mass to the polytrope of index 3 at the limit, where the radius vanishes. The mass-radius curve of figure 2, on p. 219, is the exact statement of the relation and ends at a point marked A where the star has no size at all; the density distributions of figure 4, running continuously from the one polyt.…