‘Unaffected by Fortune, Good or Bad’: Context and Reception of Chandrasekhar's Mass–Radius Relationship for White Dwarfs, 1935–1965

Summary

The 1935 conflict on the nature of relativistic degeneracy that pitted Subrahmanyan Chandrasekhar against Arthur Stanley Eddington is part of astronomical lore. In recountings of the events surrounding the dispute, the complaint is frequently aired that Chandrasekhar, who faced the pre-eminent astrophysicist of his time, did not enjoy the support of the astronomical community, which opted to side instead with Eddington. We reconsider these statements in the light of the published record and argue that the reception of Chandrasekhar's ideas was, if anything, rather favourable and that any perceived lack of support may have been due in great part to the inability to distinguish, on an observational basis, between the predictions of the competing theories. We further argue that the observational situation improved little over the subsequent thirty years, but that this did not prevent Chandrasekhar's version of relativistic degeneracy, and associated theory of electron-degenerate stars, from gaining a central position within the realm of stellar structure and evolution. We briefly compare this status to that enjoyed by general relativity before 1960.

Acknowledgements

A talk on some of these issues given in 1984 by Volker Weidemann provided the stimulus for this investigation, undertaken nearly a quarter of a century later. Jay Holberg, Michael Nauenberg and Jean-Louis Tassoul kindly read earlier versions of the manuscript. I am grateful for the hospitality of the REHSEIS, where this work was carried out, and for the permission to quote from the archives of the Center for the History of Physics, granted by the American Institute of Physics.

Notes

¹S. Chandrasekhar, as quoted by K.C. Wali, Chandra: a biography of S. Chandrasekhar (Chicago, 1991), p. 145. Furthermore, the title of the paper is inspired from Chandrasekhar's quote of Edward Arthur Milne: ‘He really succeeds who perseveres according to his likes unaffected by fortune, good or bad’ (S. Chandrasekhar, oral history interview with Kevin Krisciunas (6 October 1987), archives of the Center for the History of Physics, American Institute of Physics, p. 40).

³Wali (note 1), p. 145. It is unclear whether the ‘boldness [ … ] to come out and say Eddington was wrong’ envisioned by Chandrasekhar was meant to include written or oral pronouncements, or both. Donald Osterbrock (note 2, p. 660) has expanded on Chandrasekhar's exhortation and stated that ‘his [Eddington's] prestige was so great that not one of them stood up at a meeting and said that the great man [ … ] no longer understood the subject in which he had earlier done so much important research’. This emphasis on a public rebuttal of Eddington may not have been everyone's favourite modus operandi. David DeVorkin has emphasized, in this context, Henry Norris Russell's preference for airing conflicts in private (D.H. DeVorkin, Henry Norris Russell (Princeton, 2000), p. 249). Others may have preferred heeding Chandrasekhar's own advice as Managing editor of The Astrophysical Journal: ‘It seems to me that the best thing one can do about a misguided paper is to ignore it’ (Wali, note 1, p. 221).

²The most complete treatments are those of Wali (note 1) and A. I. Miller, Empire of the Stars: Obsession, friendship, and betrayal in the quest for black holes (Boston, 2005). Shorter discussions are provided by A.V. Douglas, The Life of Arthur Stanley Eddington (London, 1956), p. 160–2; K.C. Wali, ‘Chandrasekhar vs. Eddington – an unanticipated confrontation’, Physics Today, 35, no. 10 (1982), 33–40; W. Israel, ‘Dark stars: the evolution of an idea’, in Three Hundred Years of Gravitation, edited by S.W. Hawking and W. Israel (Cambridge, 1987), 199–276, pp. 212–16; K. Thorne, Black Holes and Time Warps: Einstein’s outrageous legacy (New York, 1994), 140–63; C.W. Kilmister, Eddington's Search for a Fundamental Theory: A key to the universe (Cambridge, 1994), 103–4; W.H. McCrea, ‘Obituary. Subrahmanyan Chandrasekhar’, The Observatory, 116 (1996), 121–4; R.J. Tayler, ‘Subrahmanyan Chandrasekhar. 19 October 1910–21 August 1995’, Biographical Memoirs of Fellows of the Royal Society, 42 (1996), 79–94, pp. 85–6; D.S. Evans, The Eddington Enigma (Princeton, 1998), 139–48; D.E. Osterbrock, ‘Subrahmanyan Chandrasekhar (19 October 1910–21 August 1995)’, Proceedings of the American Philosophical Society, 142 (1998), 658–65, pp. 659–60; E.N. Parker, ‘Subrahmanyan Chandrasekhar 19 October 1910–21 August 1995’, Biographical Memoirs of the National Academy of Sciences, 72 (1997), 28–49, pp. 35–7; J.-L. Tassoul and M. Tassoul, A Concise History of Solar and Stellar Physics (Princeton, 2004), 116–18; L. Mestel, ‘Arthur Stanley Eddington: pioneer of stellar structure theory’, Journal of Astronomical History and Heritage, 7 (2004), 65–73, pp. 69–72; F. Dyson, ‘The death of a star’, Nature, 438 (2005), 1086; and K. Hufbauer, ‘Stellar structure and evolution, 1924–1939’, Journal for the History of Astronomy, 37 (2006), 203–27, pp. 215–16. Chandrasekhar's own recounting of these events can be found in S. Chandrasekhar, ‘The Richtmyer memorial lecture –– some historical notes’, American Journal of Physics, 37 (1969), 577–84, more succinctly in ‘The increasing role of general relativity in astronomy’, The Observatory, 92 (1972), 160–74, and in Eddington: The most distinguished astrophysicist of his time (Cambridge, 1983), 46–52.

⁴S. Chandrasekhar, ‘The increasing role of general relativity in astronomy’, The Observatory, 92 (1972), 160–74, pp. 165–6; Wali (note 1), p. 143 and Miller (note 2), p. 106.

⁵Israel (note 2), p. 221–3; W. Israel, ‘Imploding stars, shifting continents, and the inconstancy of matter’, Foundations of Physics, 26 (1996), 595–626, pp. 605–7.

⁶While the limited observational context is occasionally brought up (for example by Wali, note 1, p. 32 and 134, who states ‘There was no simple way to prove that Eddington was wrong, no direct observational test’), its importance tends to be overlooked. The absence of an observational component in the debate is an essential ingredient in Alex Ipe's analysis of the dynamics of the Chandrasekhar–Eddington controversy in terms of the ‘theoreticians’ regress’ concept (A.I. Ipe, ‘Plausibility and the theoreticians’ regress: constructing the evolutionary fate of stars’, Ph.D. thesis, Carleton University, 2001).

⁷In this paper, we identify the beginning of the astrophysical study of white dwarf stars with the publication of the spectral type of the companion of o₂ Eridani (known today as 40 Eri B) by Walter Adams (W. S. Adams, ‘An A-type star of very low luminosity’, Publications of the Astronomical Society of the Pacific, 26 (1914), 198). The spectrum revealed an early type, completely out of character with the faint absolute magnitude (M_V=10.3) of the star. For completeness, we note that the anomalous spectrum of o₂ Eridani B was already discussed by Henry Norris Russell and Edward Pickering as early as December 1910 (C. Payne-Gaposhkin, in In Memory of Henry Norris Russell, edited by A.G. Davis Philip and D.H. DeVorkin (Albany, 1977), 89–90, p. 90, especially the editors’ footnote). For a recent review, see J.B. Holberg, ‘The discovery of the existence of white dwarf stars: 1862 to 1930’, Journal for the History of Astronomy, 40 (2009), 137–54.

⁸Miller (note 2), p. 106.

⁹E.N. Parker, ‘Subrahmanyan Chandrasekhar’, Physics Today, 48, no. 11 (1995), 106–8.

¹⁰In his review of Miller's book, Silvan Schweber has called for a deeper analysis of the sociology of the various communities involved to account for the lack of weight carried by the opinion of physicists in the debate (S.S. Schweber, ‘Eddington, Chandra, et al.’, Jounal for the History of Astronomy, 38 (2007), 519–22).

¹¹Wali (note 1), p. 132.

¹²Ralph Fowler is perhaps the most difficult to classify, given the breadth of his interests. McCrea considers him, nevertheless, ‘one of the principal founders of modern astrophysics’ (‘Sir Ralph Howard Fowler, 1889–1944: a centenary lecture’, Notes and Records of the Royal Society, 47 (1993), 61–78).

¹³James Jeans had retired from Cambridge in 1912, but carried out original research until 1929 and still attended the RAS meeting in the thirties (S. Chandrasekhar, oral history interview with Spencer R. Weart (17 May–31 October 1977), archives of the Center for the history of physics, American Institute of Physics, p. 48).

¹⁴Rosseland to Chandrasekhar, dated 18 May 1935, as quoted in Wali (note 1), p. 134.

¹⁵Wali (note 1), p. 131.

¹⁶R. Peierls, Bird of passage – Recollections of a physicist (Princeton, 1985), p. 117–18.

¹⁷Miller (note 2), p. 136. The paper referred to is P.A.M. Dirac, R.F. Peierls and M.H.L. Pryce, ‘On Lorentz invariance in the quantum theory’, Proceedings of the Cambridge Philosophical Society, 38 (1942), 193–200. Miller's comment also applies to the earlier supportive work of R. F. Peierls, ‘Note on the derivation of the equation of state for a degenerate relativistic gas’, Monthly Notices of the Royal Astronomical Society, 96 (1936), 780–84.

²⁵Wali (note 1), p. 145–6.

¹⁸Wali (note 1), p. 132; Miller (note 2), p. 111.

¹⁹In his book Statistical Mechanics. The theory of the properties of matter in equilibrium, 2nd edition (Cambridge, 1936; reprinted 1955), p. 652, Fowler stated in a footnote that ‘It has recently been contended by Eddington [ … ] that [the relativistic expression for the kinetic energy of an electron] is invalid and does not apply to an electron in any stationary state in an enclosure, but only to electrons represented by progressive waves. If his contentions are correct then the formulae derived from [that expression] are meaningless [ … ]’. This formulation was criticized by Wali (note 1, p. 144–5) for not going far enough in its rebuttal of Eddington's contention.

²⁰McCrea to Wali, dated November 1979, as quoted in Wali (note 1), p. 134.

²¹‘1935 January 11 meeting of the Royal Astronomical Society’, The Observatory, 58 (1935), 33–41, p. 37–9.

²²Wali (note 1), p. 132.

²³Wali (note 1), p. 144.

²⁴Wali (note 1), p. 134.

²⁶Adams (note 7) and ‘The spectrum of the companion of Sirius’, Publications of the Astronomical Society of the Pacific, 27 (1915), 236–7.

²⁷W.S. Adams, ‘The relativity displacement of the spectral lines in the companion of Sirius’, Proceedings of the National Academy of Sciences, 11 (1925), 382–7; ‘The radial velocity of the companion of Sirius’, The Observatory, 49 (1926), 88. In a paper in press in the Journal for the History of Astronomy, J.B. Holberg discusses the relevant Adams–Eddington correspondence.

²⁸A.S. Eddington, The Internal Constitution of the Stars (Cambridge, 1926; reprinted 1988), p. 171.

²⁹H.N. Russell, R.S. Dugan and J. Q. Stewart, Astronomy; A revision of Young’s manual of astronomy, 2 (Boston, 1927), p. 740, 751.

³⁰J.H. Jeans, Astronomy and Cosmogony (Cambridge, 1928), p. 59.

³¹Jeans (note 30).

³²A. van Maanen, ‘Two faint stars with large proper motions’, Publications of the Astronomical Society of the Pacific, 29 (1917), 258–9; P.T. Oosterhoff, ‘Note on a star which probably is a white dwarf’, Bulletin of the Astronomical Institute of The Netherlands, 6 (1930), 39.

³³S. Chandrasekhar, ‘The density of white dwarfs’, Philosophical Magazine, 11 (1931), 592–7.

³⁴R.H. Fowler, ‘On dense matter’, Monthly Notices of the Royal Astronomical Society, 87 (1926), 114–22.

³⁵S. Chandrasekhar, ‘The maximum mass of ideal white dwarfs’, The Astrophysical Journal, 74 (1931), 81–2. The independent, and much overlooked, contribution of Edmund Stoner to the demonstration of the existence of a maximum mass for degenerate, relativistic configurations has been highlighted by Israel (note 2, p. 212–16), and has recently been reconsidered in detail by Michael Nauenberg (‘Edmund C. Stoner and the discovery of the maximum mass of white dwarfs’, Journal for the History of Astronomy, 39 (2008), 297–312).

³⁶L. Landau, ‘On the theory of stars’, Physikalische Zeitschrift der Sowjetunion, 1 (1932), 285–8. Reprinted in Collected papers of L.D. Landau, edited by D. Ter Haar (New York, 1967), 60–2.

³⁷W. Anderson, ‘Die ‘Entartung’ des Elektronengases im Innern einiger Sterne’, Zeitschrift für Physik, 50 (1928), 874–77; ‘Über die Grenzdichte der Materie und der Energie’, Zeitschrift für Physik, 56 (1929), 851–6.

³⁸E.C. Stoner, ‘The limiting density in white dwarf stars’, Philosophical Magazine, 7 (1929), 63–70; ‘The equilibrium of dense stars’, Philosophical Magazine, 9 (1930), 944–63; E.C. Stoner and F. Tyler, ‘A note on condensed stars’, Philosophical Magazine, 11 (1931), 986–95.

³⁹J. Frenkel, ‘Anwendung der Pauli-Fermischen Elektronengastheorie auf das Problem der Kohäsionskräfte’, Zeitschrift für Physik, 50 (1928), 234–48, pp. 244–8. See also J.I. Frenkel, Statistische Physik (Berlin, 1957), 636–40. V.Y. Frenkel (Yakov Ilich Frenkel. His work, life and letters (Basel, 1996), 138–9) provides some insight on the limited impact of his father's work in astrophysics.

⁴⁰E.A. Milne, ‘The analysis of stellar structure’, Monthly Notices of the Royal Astronomical Society, 91 (1930), 4–55.

⁴¹D.S. Kothari, ‘A note on the white dwarfs and the electrostatic correction’, Philosophical Magazine, 12 (1931), 665–76.

⁴²H. Siedentopf, ‘Zum Aufbau der weissen Zwergsterne. I’. Astronomische Nachrichten, 243 (1931), 1–4; R. C. Majumdar, ‘Die neue Statistik und die Ionisationsformel bei Berücksichtigung der relativischen Korrektionen’, Astronomische Nachrichten, 242 (1931), 145–54.

⁴³S. Suzuki, ‘The relative abundance of the chemical elements in white dwarf and its electrification’, Proceedings of the Imperial Academy (Tokyo), 7 (1931), 307–10.

⁴⁴A. Hnatek, ‘Über die Sternmodelle der weißen Zwerge aus völlig degenerierter Materie’, Astronomische Nachrichten, 252 (1934), 237–42; ‘Über relativistisch vollständig entartete Modelle weißer Zwerge mit vorgegebener Verteilung der Energiequellen’, Astronomische Nachrichten, 256 (1935), 93–100.

⁴⁵T. Araki, ‘Zur Theorie des inneren Aufbaues der weiβen Zwerge’, Zeitschrift für Astrophysik, 8 (1934), 358–69; ‘Zur Theorie des inneren Aufbaues der weiβen Zwerge. II’. Zeitschrift für Astrophysik, 9 (1934), 163–75.

⁴⁶Wali (note 1), pp. 117, 123.

⁴⁷S. Chandrasekhar, ‘The highly collapsed configurations of a stellar mass (Second paper)’, Monthly Notices of the Royal Astronomical Society, 95 (1935), 207–25.

⁴⁸As emphasized by Nauenberg (note 35), the non-relativistic and relativistic regimes had already been treated self-consistently in the investigation of Edmund Stoner (‘The equilibrium of dense stars’, Philosophical Magazine, 9 (1930), 944–63, and ‘The minimum pressure of a degenerate electron gas’, Monthly Notices of the Royal Astronomical Society, 92 (1932), 651–61).

⁴⁹The upper boundary depends slightly on the composition of the plasma, and is sometimes advertised as 2.1 instead of 2 for some compositions (e.g. A.S. Eddington, ‘The hydrogen content of white dwarf stars in relation to stellar evolution’, Monthly Notices of the Royal Astronomical Society, 99 (1939), 595–606, p. 597). This is an unnecessary complication, and we use here µ_e=2 as the relevant upper limit.

⁵⁰S. Chandrasekhar (note 47), p. 220. In this quote, the value of M₃ is 5.728 M_[odot] for µ_e=1 and 1.432 M_[odot] for µ_e=2. The value of M₃ for µ_e=2 is known today as the Chandrasekhar mass; its exact value has a slight dependence on the level of sophistication of the stellar model.

⁵¹J.L. Greenstein, oral interview with Rachel Prud'homme (25 February, 16 and 23 March 1982), Archives of the California Institute of Technology.

⁵²A.S. Eddington, ‘On ‘relativistic degeneracy’’, Monthly Notices of the Royal Astronomical Society, 95 (1935), 194–206; ‘The pressure of a degenerate electron gas and related problems’, Proceedings of the Royal Society of London. Series A, 152 (1935), 253–72; ‘Note on “relativistic degeneracy”’, Monthly Notices of the Royal Astronomical Society, 96 (1935), 20–1. Chandrasekhar's work, because it had clear implications for stellar evolution, suffered the brunt of Eddington's criticisms. However, the same expression for relativistic degeneracy had been used by Stoner (note 38), Hnatek (note 44), Araki (note 45), and Siedentopf (‘Der Polytropenindex im Sterninneren’, Astronomische Nachrichten, 244 (1932), 273–80) in their contributions.

⁵³Eddington, ‘On ‘relativistic degeneracy’’ (note 52), p. 195.

⁵⁴G.P. Kuiper, ‘Two new white dwarfs of large parallax’, Publications of the Astronomical Society of the Pacific, 46 (1934), 287–90.

⁵⁵H.N. Russell, ‘Double stars’, Scientific American, 153 (1935), 238–9, p. 239.

⁵⁶G.P. Kuiper, ‘A new white dwarf of large parallax’, Publications of the Astronomical Society of the Pacific, 47 (1935), 96–8.

⁵⁹H.N. Russell, ‘Impossible planets’, Scientific American, 153 (1935), 18–19, p. 19. For complete coherence, the order of the sentences ‘We should expect, too, … ’ and ‘This very striking … ’ in Russell's text should probably be inverted.

⁵⁷Miller (note 2), p. 50. See also DeVorkin, (note 3), p. 249.

⁵⁸S. Chandrasekhar (note 13), p. 63.

⁶⁰Milne (note 40), p. 4 and 38–9.

⁶¹W.H. McCrea, ‘The international astronomical union meeting in Paris 1935’, The observatory, 58 (1935), 257–65, p. 259.

⁶²Wali (note 1, p. 133–4), from which one is left with the definite impression that Chandrasekhar was gagged. McCrea's report also shows that Chandrasekhar intervened on other topics: ‘Dr. S. Chandrasekhar drew attention to some such curves recently calculated by him. Dr. Chandrasekhar went on to show the significance of the creation of positive and negative electron pairs in the central regions of massive stars. Further, he pointed out the theoretical importance of data on the masses of Wolf-Rayet stars, and on massive stars in general’ (W.H. McCrea, note 61, p. 260). The expression ‘drew attention’ is identical to that used by McCrea to discuss the contributions of Russell and Shapley. This suggests that these were lengthy interventions, perhaps a factor in Russell's decision not to grant further speaking time to Chandrasekhar.

⁶³McCrea (note 61), p. 260.

⁶⁴G.P. Kuiper, ‘The white dwarf A.C. +70°8247, the smallest star known’, Publications of the Astronomical Society of the Pacific, 47 (1935), 307–13.

⁶⁵Chandrasekhar to his father, 12 December 1935, as quoted in Miller (note 2), p. 121.

⁶⁶Kuiper to Struve, 7 January 1936, as quoted in S. O. Rebsdorf, ‘Bengt Strömgren: interstellar glow, helium content, and solar life supply, 1932–1940’, Centaurus, 49 (2007), 56–79, p. 60.

⁶⁷R.G. Aitken, ‘The white dwarf stars’, Astronomical Society of the Pacific Leaflets, 2 (1936), 145–48, p. 148.

⁶⁹H.N. Russell, ‘Model stars’, Bulletin of the American Mathematical Society, 43 (1937), 49–77, p. 55.

⁶⁸Russell to Struve, 3 January 1936, as quoted in Rebsdorf (note 66), p. 60.

⁷⁰Wali (note 1), p. 99–100.

⁷¹B. Strömgren, ‘Scientists I have known and some astronomical problems I have met’, Annual Reviews of Astronomy and Astrophysics, 21 (1983), 1–11, p. 3.

⁷²F. Hund, ‘Materie unter sehr hohen Drucken und Temperaturen’, Ergebnisse der exakten Naturwissenschaften, edited by F. Trendelenburg and F. Hund, 15 (Berlin, 1936), 189–228, p. 196–9.

⁷³Hund (note 72), p. 225–7.

⁷⁴B. Strömgren, ‘Die Theorie der Sterninnern und die Entwicklung der Sternen’, in Ergebnisse der exakten Naturwissenschaften, edited by F. Trendelenburg and F. Hund, 16 (Berlin, 1937), 465–534, p. 507.

⁷⁵Rebsdorf (note 66), p. 61.

⁷⁶S. Chandrasekhar, ‘The internal constitution of the stars’, Journal of the American Philosophical Society, 81 (1939), 153–87, p. 185–6.

⁷⁷Eddington returned to the topic in his book Relativity theory of protons and electrons (Cambridge, 1936), p. 234–55 and in the address he gave at the 1936 Harvard Tercentenary Conference of Arts and Sciences (‘Constitution of the stars’, The Scientific Monthly, 43 (1936), 385–95).

⁷⁸Mineur's maneuvering and Shaler's plea (Shaler to Chandrasekhar, 4 February 1939) are described by Miller (note 2, p. 129–30).

⁷⁹Besides Eddington, Chandrasekhar and Shaler, who would later make noteworthy contributions to physical metallurgy, the eleven other participants identified on the official photograph of the Paris colloquium (e.g. Tassoul and Tassoul, note 2, p. 119) were Frederick Stratton, Cecilia Payne-Gaposchkin, Henry Norris Russell, Sergei Gaposchkin, Carlyle Beals, Bengt Edlén, Pol Swings, Gerard Kuiper, Bengt Strömgren, Walter Baade, and Knut Lundmark. All of these can be readily considered classical astronomers in the sense previously defined.

⁸⁰G.P. Kuiper, ‘White dwarfs. Discovery, observations, surface conditions’, in Novae and White Dwarfs. III. White dwarfs, edited by A.J. Shaler (Paris, 1941), 201–37.

⁸¹J.H. Oort, ‘The mass of van Maanen's star’, Bulletin of the Astronomical Institute of The Netherlands, 6 (1932), 287.

⁸²The idea was taken up by Russell (‘Inside the white dwarf stars’, Scientific American, 164 (1941), 216–17), who called it ‘not wholly satisfactory [but] entirely reasonable’.

⁸³Kuiper (note 80), p. 233.

⁸⁴Kuiper (note 80), p. 235.

⁸⁶See Novae and White Dwarfs. III. White dwarfs (note 85), p. 267. What Eddington calls the ‘Stoner-Anderson’ formula is the relativistic degeneracy formulation included in Chandrasekhar's work. Today, the names of Edmund Stoner and Wilhelm Anderson are all but forgotten. See Nauenberg (note 35) for a recent reevaluation of the issues of priority and credit involved.

⁸⁵ Novae and White Dwarfs. III. White dwarfs, edited by A J. Shaler (Paris, 1941), p. 264.

⁸⁷Wali (note 1), p. 138.

⁸⁸S. Chandrasekhar, An Introduction to the Theory of Stellar Structure (Chicago, 1939). While the book can be considered as the endpoint of Chandrasekhar's involvement with white dwarf stars, the book was started in the spring of 1938 and completed by the end of that year (Chandrasekhar, note 13, p. 78). Its preface is dated 1938 December. The book was thus completed prior to the July 1939 colloquium on novae and white dwarfs held in Paris.

⁸⁹Chandrasekhar (note 13), p. 34.

⁹⁰Miller (note 2), p. 128.

⁹¹Note that the mass obtained in this way actually depends on the radius assumed, since the gravitational redshift depends on the combination M/R. Thus the mass published by Chandrasekhar for van Maanen's star (M = 3.4 M_[odot]) is larger than those cited by Kuiper (note 80), which were in the range 1.9–2.6 M_[odot], because the radius adopted was different (R = 0.0089 R_[odot] for Chandrasekhar, and a range 0.0055–0.0069 R_[odot] for Kuiper).

⁹²Chandrasekhar (note 88), p. 432.

⁹³Eddington (note 49), p. 605.

⁹⁴Eddington (note 49), p. 599.

⁹⁵A.S. Eddington, Fundamental theory (Cambridge, 1948), p. 91. The three white dwarfs mentioned are o₂ Eri B, Sirius B, and van Maanen's star, three objects he earlier described as stars ‘for which more or less satisfactory observational data are available’ (note 49, p. 597).

⁹⁶H.N. Russell, ‘What's inside the stars?’ Scientific American, 161 (1939), 334–5.

⁹⁷A.S. Eddington, ‘The physics of white dwarf matter’, Monthly Notices of the Royal Astronomical Society, 100 (1940), 582–94. An ultimate, and opinionated, reference to the controversy is included in Eddington's posthumous book (note 95, p. 87–92).

⁹⁸D. Reuyl, ‘The white dwarf stars’, The Scientific Monthly, 52 (1941), 131–8, p. 131.

⁹⁹E. Schatzman, ‘The desire to understand the world’, Annual Reviews of Astronomy and Astrophysics, 34 (1996), 1–35, pp. 18–20.

¹⁰⁰E. Schatzman, ‘Théorie du débit d’énergie des naines blanches’, Annales d’Astrophysique, 8 (1945), 143–209, p. 146.

¹⁰⁶C. Domb, ‘Fred Hoyle and naval radar 1941–5 ‘, Astrophysics and Space Science, 285 (2003), 293–302, p. 294. The conversation between Domb and Hoyle took place in 1941.

¹⁰¹G. Gamow, ‘Physical possibilities of stellar evolution’, Physical Review, 55 (1939), 718–25, p. 722–3.

¹⁰²R.E. Marshak, ‘The internal temperature of white dwarf stars’, The Astrophysical Journal, 92 (1940), 321–53.

¹⁰³Marshak (note 102), p. 336.

¹⁰⁴F. Hoyle, ‘The synthesis of the elements from hydrogen’, Monthly Notices of the Royal Astronomical Society, 106 (1946), 343–83.

¹⁰⁵E.E. Salpeter, ‘Neutron stars before 1967 and my debt to Chandra’, in From White Dwarfs to Black Holes. The legacy of S. Chandrasekhar, edited by G. Srinivasan (Chicago, 1997), 27–30, pp. 27–8). An opposing viewpoint is offered by an exchange of letters between Erwin Schrödinger and George Lemaître (Schrödinger to Lemaître, 1950, as quoted in A.V. Douglas, note 2, p. 162) that suggests that some doubts had not completely subsided as late as 1950. Douglas specifically states that the controversy was ‘still a live issue’.

¹⁰⁷F. Hoyle, ‘Note on equilibrium configuration for rotating white dwarfs’, Monthly Notices of the Royal Astronomical Society, 107 (1947), 231–36, pp. 233, 231, 235.

¹⁰⁸Hoyle (note 107), p. 235.

¹⁰⁹Eddington (note 49), p. 602.

¹¹²Hoyle (note 110), p. 257.

¹¹⁰F. Hoyle, ‘Note on the origin of white dwarfs’, Monthly Notices of the Royal Astronomical Society, 107 (1947), 253–9.

¹¹¹Eddington (note 49).

¹¹⁴Gamow and Crichtfield (note 113), p. 294.

¹¹³G. Gamow and C.L. Crichtfield, Theory of atomic nucleus and nuclear energy–sources (London, 1949), p. 289–94.

¹¹⁵This idea is further addressed by T.D. Lee, ‘Hydrogen content and energy-productive mechanism of white dwarfs’, The Astrophysical Journal, 111 (1950), 625–40, p. 636.

¹¹⁶H.N. Russell, ‘Notes on white dwarfs and small companions’, The Astronomical Journal, 51 (1944), 13–17, p. 15.

¹¹⁷W.J. Luyten, ‘The white dwarfs’, Astronomical Society of the Pacific Leaflets, 5 (1945), 17–24, pp. 23–4.

¹¹⁸Luyten (note 117), p. 22–3.

¹¹⁹S. Chandrasekhar, ‘The structure, the composition, and the source of energy of the stars’, in Astrophysics. A topical symposium, edited by J.A. Hynek (New York, 1951), 598–674, p. 659.

¹²⁰Gamow (note 101), p. 723.

¹²¹W.J. Luyten, ‘The spectra and luminosities of white dwarfs’, The Astrophysical Journal, 116 (1952), 283–90, p. 290.

¹²²W.J. Luyten, ‘White dwarfs and degenerate stars’, Vistas in Astronomy, 2 (1956), 1048–56, p. 1054.

¹²⁶Schatzman (note 123), p. 98.

¹²³E. Schatzman, White Dwarfs (Amsterdam, 1958), p. 68–73. The terminology used by Schatzman is identical to Eddington's (see note 86).

¹²⁴There is general agreement that some of Eddington's objections had merit. They were mostly concerned with the unification of relativity with quantum theory and with the appropriate description of relativistic electrons in a dense plasma. Some of these technical points are briefly discussed by Mestel (note 2, p. 71) and by Salpeter (note 105, p. 28). Eddington's objections concerning relativity and quantum theory had been addressed in earlier papers (note 17; C. M⊘ller and S. Chandrasekhar, ‘Relativistic degeneracy’, Monthly Notices of the Royal Astronomical Society, 95 (1935), 673–76), but those concerning dense plasmas had remained largely unanswered. To rebut them, Schatzman had solicited the opinion of David Bohm, who had completed a detailed analysis of Coulomb interactions in a degenerate electron gas (Schatzman to Bohm, 1953 December 10, Fonds Evry Schatzman, Ms 1086, Observatoire de Paris).

¹²⁵Schatzman (note 123), p. 98. The error was particularly unfortunate given that Schatzman had stated earlier (p. 12) that ‘With the exception of Sirius B and 40 Eri B [o₂ Eridani B], all masses found in the literature have been derived from the theoretical mass–radius relation of Chandrasekhar’. The error is reproduced by E. Schatzman, ‘Théorie des naines blanches’, in Handbuch der Physik, edited by S. Flügge (Berlin, 1958), 51, 723–51, p. 740, and by D.H. Menzel, P.L. Bhatnagar and H.K. Sen, Stellar Interiors (London, 1963), p. 234, but with two fewer stars. Luyten would, later on, make a particularly caustic comment on this circuitous inclusion (‘White dwarfs’, in Advances in Astronomy and Astrophysics, edited by Z. Kopal (New York, 1963), 199–218, p. 211; for a posthumous evaluation of Luyten's colourful approach to ‘truth in science’, see A. Upgren, ‘Willem Jacob Luyten’, Publications of the Astronomical Society of the Pacific, 107 (1995), 603–5).

¹²⁸Luyten (note 125), 211.

¹³⁰Mestel (note 129), p. 306–7.

¹³¹Mestel (note 129), p. 307.

¹³²Luyten (note 122), p. 1056.

¹²⁷J.L. Greenstein, ‘The spectra of the white dwarfs’, in Handbuch der Physik, edited by S. Flügge (Berlin, 1958), 50, 161–86, p. 183.

¹²⁹L. Mestel, ‘The theory of white dwarfs’, in Stars and Stellar Systems, edited by L.H. Aller and D.B. McLaughlin (Chicago, 1965), 297–325.

¹³³Wali (note 1), p. 146.

¹³⁴H. Schmidt, ‘The empirical white dwarf mass–radius relation and its possible improvement by Hipparcos’, Astronomy and Astrophysics, 311 (1996), 852–7. The problems encountered even today contrast with Wali's wildly optimistic statement that ‘Today, hundreds of white dwarfs are known, and the masses of those that are measured fall neatly without a single exception on the curve Chandrasekhar predicted’ (Wali, note 2, p. 40).

¹³⁵Wali (note 1), p. 145–6.

¹³⁶See, for example, J. Eisenstaedt, ‘La relativité générale à l’étiage: 1925–1955’, Archive for History of Exact Sciences, 35 (1986), 115–85.

¹³⁷P.G. Bergmann, Introduction to the Theory of Relativity (New York, 1942), p. 211.

¹³⁸R J. Trumpler, ‘Observational results on the light deflection and on the red–shift in star spectra’, in Fünfzig Jahre Relativitätstheorie, edited by A. Mercier and M. Kervaire (Basel, 1956), 106–13, p. 108.

¹³⁹R.H. Dicke, ‘Remarks on the observational basis of general relativity’, in Gravitation and relativity, edited by H.-Y. Chiu and W. F. Hoffmann (New York, 1964), 1–16, p. 1.

¹⁴⁰Chandrasekhar's argument that his theory of the mechanical support of white dwarf stars simply derives from a part of quantum mechanics that has been confirmed by laboratory experiments (Chandrasekhar, note 88, p. 432) is reminiscent of the argument that presents general relativity as a ‘logical extension of the special theory of relativity, for which there is very strong experimental evidence’ (E. Gerjuoy, ‘Feasibility of a nonrelativistic explanation for the advance of the perihelion of Mercury’, American Journal of Physics, 24 (1956), 3–6, p. 4).

¹⁴¹This is perhaps best illustrated by the revealing statement that ‘We can hope that further work on the Sirius B redshift, with higher precision than we could attain, will confirm the theoretical value (even though that theory needs no such confirmation [emphasis added])’ (Greenstein, Oke and Shipman, ‘On the redshift of Sirius B’, Quarterly Journal of the Royal Astronomical Society, 26 (1985), 279–88, p. 288).

¹⁴²C. Lanczos, ‘Stellung der Relativitätstheorie zu anderen physikalischen Theorien’, Die Naturwissenschaften, 20 (1932), 113–16, p. 115.