Editing Chandrasekhar limit (section)

==History==
In 1926, the British [[physicist]] [[Ralph H. Fowler]] observed that the relationship between the density, energy, and temperature of white dwarfs could be explained  by viewing them as a gas of nonrelativistic, non-interacting electrons and nuclei that obey [[Fermi–Dirac statistics]].<ref>{{cite journal | last1 = Fowler | first1 = R. H. | year = 1926 | title = On Dense Matter | journal = Monthly Notices of the Royal Astronomical Society | volume = 87 | issue = 2| pages = 114–122 | bibcode=1926MNRAS..87..114F | doi=10.1093/mnras/87.2.114| doi-access = free }}</ref>  This [[Fermi gas]] model was then used by the British physicist [[Edmund Clifton Stoner]] in 1929 to calculate the relationship among the mass, radius, and density of white dwarfs, assuming they were homogeneous spheres.<ref>{{cite journal | last1 = Stoner | first1 = Edmund C. | year = 1929 | title = The Limiting Density of White Dwarf Stars | journal = Philosophical Magazine | volume = 7 | issue = 41| pages = 63–70 | doi=10.1080/14786440108564713}}</ref> [[Wilhelm Anderson]] applied a relativistic correction to this model, giving rise to a maximum possible mass of approximately {{val|1.37e30|u=kg}}.<ref>{{cite journal | doi = 10.1007/BF01340146 | volume=56 | issue=11–12 | title=Uber die Grenzdichte der Materie und der Energie | year=1929 | journal=Zeitschrift für Physik | pages=851–856 | last1 = Anderson | first1 = Wilhelm|bibcode = 1929ZPhy...56..851A | s2cid=122576829 }}</ref> In 1930, Stoner derived the [[internal energy]]–[[density]] [[equation of state]] for a Fermi gas, and was then able to treat the mass–radius relationship in a fully relativistic manner, giving a limiting mass of approximately {{val|2.19e30|u=kg}} (for {{math|''μ''<sub>e</sub> {{=}} 2.5}}).<ref>{{cite journal | last1 = Stoner | first1 = Edmund C. | year = 1930 | title = The Equilibrium of Dense Stars | journal = Philosophical Magazine | volume = 9 | pages = 944–963 }}</ref>  Stoner went on to derive the [[pressure]]–[[density]] equation of state, which he published in 1932.<ref>{{cite journal | last1 = Stoner | first1 = E. C. | year = 1932 | title = The minimum pressure of a degenerate electron gas | journal = Monthly Notices of the Royal Astronomical Society | volume = 92 | issue = 7| pages = 651–661 | bibcode=1932MNRAS..92..651S | doi=10.1093/mnras/92.7.651| doi-access = free }}</ref>  These equations of state were also previously published by the [[Soviet Union|Soviet]] [[physicist]] [[Yakov Frenkel]] in 1928, together with some other remarks on the physics of [[degenerate matter]].<ref>{{cite journal | doi = 10.1007/BF01328867 | volume=50 | issue=3–4 | title=Anwendung der Pauli-Fermischen Elektronengastheorie auf das Problem der Kohäsionskräfte | year=1928 | journal=Zeitschrift für Physik | pages=234–248 | last1 = Frenkel | first1 = J.|bibcode = 1928ZPhy...50..234F | s2cid=120252049 }}.</ref>  Frenkel's work, however, was ignored by the astronomical and astrophysical community.<ref>{{cite journal | last1 = Yakovlev | first1 = D. G. | year = 1994 | title = The article by Ya I Frenkel' on 'binding forces' and the theory of white dwarfs | journal = Physics-Uspekhi | volume = 37 | issue = 6| pages = 609–612 | bibcode=1994PhyU...37..609Y | doi=10.1070/pu1994v037n06abeh000031| s2cid = 122454024 }}</ref>

A series of papers published between 1931 and 1935 had its beginning on a trip from India to England in 1930, where the Indian physicist [[Subrahmanyan Chandrasekhar]] worked on the calculation of the statistics of a degenerate Fermi gas.<ref name="nasbio">[http://www.nap.edu/readingroom/books/biomems/schandrasekhar.html Chandrasekhar's biographical memoir at the National Academy of Sciences] {{Webarchive|url=https://web.archive.org/web/19991008143159/http://www.nap.edu/readingroom/books/biomems/schandrasekhar.html |date=1999-10-08 }}, web page, accessed 12-01-2007.</ref> In these papers, Chandrasekhar solved the [[hydrostatic equation]] together with the nonrelativistic Fermi gas [[equation of state]],<ref name="chandra3"/> and also treated the case of a relativistic Fermi gas, giving rise to the value of the limit shown above.<ref name="chandra4"/><ref name="chandra2"/><ref name="chandra1"/><ref>{{cite journal | last1 = Chandrasekhar | first1 = S. | year = 1934 | title = Stellar Configurations with degenerate Cores | journal = The Observatory | volume = 57 | pages = 373–377 | bibcode = 1934Obs....57..373C}}</ref>  Chandrasekhar reviews this work in his Nobel Prize lecture.<ref name="chandranobel"/>

The existence of a related limit, based on the conceptual breakthrough of  combining relativity with  Fermi degeneracy, was first established in separate  papers published by [[Wilhelm Anderson]] and [[Edmund Clifton Stoner|E. C. Stoner]] for a  uniform density star in 1929.  Eric G. Blackman wrote that the roles of Stoner and Anderson in the discovery of mass limits were overlooked when [[Freeman Dyson]] wrote a biography of Chandrasekhar.<ref>Eric G. Blackman, "Giants of physics found white-dwarf mass limits", [http://adsabs.harvard.edu/abs/2006Natur.440..148B ''Nature'' 440, 148 (2006)]</ref> Michael Nauenberg claims that Stoner established the mass limit first.<ref>Michael Nauenberg, "Edmund C. Stoner and the Discovery of the Maximum Mass of White Dwarfs," [http://adsabs.harvard.edu/abs/2008JHA....39..297N ''Journal for the History of Astronomy'', Vol. 39, p. 297-312, (2008)] {{Webarchive|url=https://web.archive.org/web/20220125032719/https://ui.adsabs.harvard.edu/abs/2008JHA....39..297N/abstract |date=2022-01-25 }}</ref>
The priority dispute has also been discussed at length by [[Virginia Trimble]] who writes that: "Chandrasekhar famously, perhaps even notoriously did his critical calculation on board ship in 1930, and ... was not aware of either Stoner's or Anderson's work at the time. His work was therefore independent, but, more to the point, he adopted Eddington's polytropes for his models which could, therefore, be in hydrostatic equilibrium, which constant density stars cannot, and real ones must be."<ref name=Trimble2011>Virginia Trimble, "Chandrasekhar and the history of astronomy", [https://www.worldscientific.com/doi/10.1142/9789814374774_0005 ''Fluid Flows to Black Holes'', pp. 49-50 (2011)]</ref>  This value was also computed in 1932 by the Soviet physicist [[Lev Landau]],<ref>On the Theory of Stars, in ''Collected Papers of L. D. Landau'', ed. and with an introduction by D. ter Haar, New York: Gordon and Breach, 1965; originally published in ''Phys. Z. Sowjet.'' '''1''' (1932), 285.</ref> who, however, did not apply it to white dwarfs and concluded that quantum laws might be invalid for stars heavier than 1.5 solar mass.

=== Chandrasekhar–Eddington dispute ===
{{Main|Chandrasekhar–Eddington dispute}}
Chandrasekhar's work on the limit aroused controversy, owing to the opposition of the British [[astrophysicist]] [[Arthur Eddington]]. Eddington was aware that the existence of [[black hole]]s was theoretically possible, and also realized that the existence of the limit made their formation possible. However, he was unwilling to accept that this could happen. After a talk by Chandrasekhar on the limit in 1935, he replied:

{{Blockquote|The star has to go on radiating and radiating and contracting and contracting until, I suppose, it gets down to a few km radius, when gravity becomes strong enough to hold in the radiation, and the star can at last find peace. ... I think there should be a law of Nature to prevent a star from behaving in this absurd way!<ref>{{cite journal | year = 1935 | title = Meeting of the Royal Astronomical Society, Friday, 1935 January 11 | journal = The Observatory | volume = 58 | pages = 33–41 | bibcode=1935Obs....58...33.}}</ref>}}

Eddington's proposed solution to the perceived problem was to modify relativistic mechanics so as to make the law {{math|''P'' {{=}} ''K''<sub>1</sub>''ρ''<sup>5/3</sup>}} universally applicable, even for large {{mvar|ρ}}.<ref>{{cite journal | last1 = Eddington | first1 = A. S. | year = 1935 | title = On "Relativistic Degeneracy" | journal = Monthly Notices of the Royal Astronomical Society | volume = 95 | issue = 3| pages = 194–206 | bibcode=1935MNRAS..95..194E | doi=10.1093/mnras/95.3.194a| doi-access = free }}</ref>  Although [[Niels Bohr]], Fowler, [[Wolfgang Pauli]], and other physicists agreed with Chandrasekhar's analysis, at the time, owing to Eddington's status, they were unwilling to publicly support Chandrasekhar.<ref name="eos">''Empire of the Stars: Obsession, Friendship, and Betrayal in the Quest for Black Holes'', Arthur I. Miller, Boston, New York: Houghton Mifflin, 2005, {{ISBN|0-618-34151-X}}; reviewed at ''The Guardian'': [http://books.guardian.co.uk/reviews/scienceandnature/0,,1472561,00.html The battle of black holes] {{Webarchive|url=https://web.archive.org/web/20061011105404/http://books.guardian.co.uk/reviews/scienceandnature/0,,1472561,00.html |date=2006-10-11 }}.</ref>{{rp|pp.=110–111}}  Through the rest of his life, Eddington held to his position in his writings,<ref>{{cite journal | year = 1935 | title = The International Astronomical Union meeting in Paris, 1935 | journal = The Observatory | volume = 58 | pages = 257–265 [259] | bibcode=1935Obs....58..257.}}</ref><ref>{{cite journal | last1 = Eddington | first1 = A. S. | year = 1935 | title = Note on "Relativistic Degeneracy" | journal = Monthly Notices of the Royal Astronomical Society | volume = 96 | pages = 20–21 | bibcode=1935MNRAS..96...20E|doi = 10.1093/mnras/96.1.20 | doi-access = free }}</ref><ref>{{cite journal | last1 = Eddington | first1 = Arthur | year = 1935| title = The Pressure of a Degenerate Electron Gas and Related Problems | journal = Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences | volume = 152 | issue = 876| pages = 253–272 | jstor=96515 | doi=10.1098/rspa.1935.0190|bibcode = 1935RSPSA.152..253E | doi-access = free }}</ref><ref>''Relativity Theory of Protons and Electrons'', Sir Arthur Eddington, Cambridge: Cambridge University Press, 1936, chapter 13.</ref><ref>{{cite journal | last1 = Eddington | first1 = A. S. | year = 1940 | title = The physics of white dwarf matter | journal = Monthly Notices of the Royal Astronomical Society | volume = 100 | issue = 8| pages = 582–594 | bibcode=1940MNRAS.100..582E | doi=10.1093/mnras/100.8.582| doi-access = free }}</ref> including his work on his [[Arthur Stanley Eddington#Fundamental theory and the Eddington number|fundamental theory]].<ref>''Fundamental Theory'', Sir A. S. Eddington, Cambridge: Cambridge University Press, 1946, §43–45.</ref>  The drama associated with this disagreement is one of the main themes of ''Empire of the Stars'', [[Arthur I. Miller]]'s biography of Chandrasekhar.<ref name="eos"/>  In Miller's view:

{{blockquote|Chandra's discovery might well have transformed and accelerated developments in both physics and astrophysics in the 1930s. Instead, Eddington's heavy-handed intervention lent weighty support to the conservative community astrophysicists, who steadfastly refused even to consider the idea that stars might collapse to nothing. As a result, Chandra's work was almost forgotten.<ref name="eos"/>{{rp|p=150}}}}

However, Chandrasekhar chose to move on, leaving the study of stellar structure to focus on stellar dynamics.<ref name=Trimble2011/>{{rp|51}} In 1983 in recognition for his work, Chandrasekhar shared a Nobel prize "for his theoretical studies of the physical processes of importance to the structure and evolution of the stars" with [[William Alfred Fowler]].<ref>{{Cite web |title=The Nobel Prize in Physics 1983 |url=https://www.nobelprize.org/prizes/physics/1983/summary/ |access-date=2023-10-03 |website=NobelPrize.org |language=en-US}}</ref>