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Chandrasekhar limit

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3968: 129: 4040: 3932: 3430: 3420: 4004: 4028: 3942: 3980: 4016: 204:. Compression of the electron gas increases the number of electrons in a given volume and raises the maximum energy level in the occupied band. Therefore, the energy of the electrons increases on compression, so pressure must be exerted on the electron gas to compress it, producing electron degeneracy pressure. With sufficient compression, electrons are forced into nuclei in the process of 3992: 1105:" may have been spinning so fast that a centrifugal tendency allowed it to exceed the limit. Alternatively, the supernova may have resulted from the merger of two white dwarfs, so that the limit was only violated momentarily. Nevertheless, they point out that this observation poses a challenge to the use of type Ia supernovae as 533: 913:
However, Chandrasekhar chose to move on, leaving the study of stellar structure to focus on stellar dynamics. 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
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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
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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
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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
954:), it eventually sheds enough mass to form a white dwarf having mass below the Chandrasekhar limit, which consists of the former core of the star. For more-massive stars, electron degeneracy pressure does not keep the iron core from collapsing to very great density, leading to formation of a 694:
A more accurate value of the limit than that given by this simple model requires adjusting for various factors, including electrostatic interactions between the electrons and nuclei and effects caused by nonzero temperature. Lieb and Yau have given a rigorous derivation of the limit from a
1394:, Guidebook Part 2 page 44, Accessed Oct. 7, 2013, "...Chandrasekhar limit: The maximum mass of a white dwarf star, about 1.4 times the mass of the Sun. Above this mass, the gravitational pull becomes too great, and the star must collapse to a neutron star or black hole..." 160:
Normal stars fuse gravitationally compressed hydrogen into helium, generating vast amounts of heat. As the hydrogen is consumed, the stars' core compresses further allowing the helium and heavier nuclei to fuse ultimately resulting in stable iron nuclei, a process called
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accumulates in the core, since iron nuclei are incapable of generating further energy through fusion. If the core becomes sufficiently dense, electron degeneracy pressure will play a significant part in stabilizing it against gravitational collapse.
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As the mass of a model white dwarf increases, the typical energies to which degeneracy pressure forces the electrons are no longer negligible relative to their rest masses. The velocities of the electrons approach the speed of light, and
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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:
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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
685: 1005:). Most of this energy is carried away by the emitted neutrinos and the kinetic energy of the expanding shell of gas; only about 1% is emitted as optical light. This process is believed responsible for 1136:. One way to potentially explain the problem of the Champagne Supernova was considering it the result of an aspherical explosion of a white dwarf. However, spectropolarimetric observations of 370:. This is the Chandrasekhar limit. The curves of radius against mass for the non-relativistic and relativistic models are shown in the graph. They are colored blue and green, respectively. 2914: 825:
which could, therefore, be in hydrostatic equilibrium, which constant density stars cannot, and real ones must be." This value was also computed in 1932 by the Soviet physicist
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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
120:. The Chandrasekhar limit is the mass above which electron degeneracy pressure in the star's core is insufficient to balance the star's own gravitational self-attraction. 528:{\displaystyle M_{\text{limit}}={\frac {\omega _{3}^{0}{\sqrt {3\pi }}}{2}}\left({\frac {\hbar c}{G}}\right)^{\frac {3}{2}}{\frac {1}{(\mu _{\text{e}}m_{\text{H}})^{2}}}} 805:, and also treated the case of a relativistic Fermi gas, giving rise to the value of the limit shown above. Chandrasekhar reviews this work in his Nobel Prize lecture. 1067:
therefore represents a factor of less than 2 in luminosity. This seems to indicate that all type Ia supernovae convert approximately the same amount of mass to energy.
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wrote a biography of Chandrasekhar. Michael Nauenberg claims that Stoner established the mass limit first. The priority dispute has also been discussed at length by
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Stars sufficiently massive to pass the Chandrasekhar limit provided by electron degeneracy pressure do not become white dwarf stars. Instead they explode as
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Hachisu, Izumi; Kato, M.; et al. (2012). "A single degenerate progenitor model for type Ia supernovae highly exceeding the Chandrasekhar mass limit".
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and elsewhere, the observations of this supernova are best explained by assuming that it arose from a white dwarf that had grown to twice the mass of the
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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
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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
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Koester, D.; Reimers, D. (1996). "White dwarfs in open clusters. VIII. NGC 2516: a test for the mass-radius and initial-final mass relations".
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The Chandrasekhar limit is a consequence of competition between gravity and electron degeneracy pressure. Electron degeneracy pressure is a
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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
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in 1929 to calculate the relationship among the mass, radius, and density of white dwarfs, assuming they were homogeneous spheres.
1132:. The super-Chandrasekhar mass white dwarfs that gave rise to these supernovae are believed to have had masses up to 2.4–2.8  1186: 688: 169:, remaining that way throughout the rest of the history of the universe absent external forces. Stars above the limit can become 3466: 2563: 2545: 276:– and therefore has radius inversely proportional to the cube root of its mass, and volume inversely proportional to its mass. 3080:, sciencebits.com. Discusses how to find mass-radius relations and mass limits for white dwarfs using simple energy arguments. 3905: 3105: 1290: 1249: 1265:
Bethe, Hans A.; Brown, Gerald (2003). "How A Supernova Explodes". In Bethe, Hans A.; Brown, Gerald; Lee, Chang-Hwan (eds.).
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Mazzali, P. A.; Röpke, F. K.; Benetti, S.; Hillebrandt, W. (2007). "A Common Explosion Mechanism for Type Ia Supernovae".
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Heger, A.; Fryer, C. L.; Woosley, S. E.; Langer, N.; Hartmann, D. H. (2003). "How Massive Single Stars End Their Life".
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has been set equal to 2. Radius is measured in standard solar radii or kilometers, and mass in standard solar masses.
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Howell, D. Andrew (2006). "The type Ia supernova SNLS-03D3bb from a super-Chandrasekhar-mass white dwarf star".
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Timmes, F. X.; Woosley, S. E.; Weaver, Thomas A. (1996). "The Neutron Star and Black Hole Initial Mass Function".
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Eddington's proposed solution to the perceived problem was to modify relativistic mechanics so as to make the law
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worked on the calculation of the statistics of a degenerate Fermi gas. In these papers, Chandrasekhar solved the
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Frenkel, J. (1928). "Anwendung der Pauli-Fermischen Elektronengastheorie auf das Problem der KohÀsionskrÀfte".
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equation of state, which he published in 1932. These equations of state were also previously published by the
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Yakovlev, D. G. (1994). "The article by Ya I Frenkel' on 'binding forces' and the theory of white dwarfs".
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applied a relativistic correction to this model, giving rise to a maximum possible mass of approximately
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must be taken into account. In the strongly relativistic limit, the equation of state takes the form
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For a fully relativistic treatment, the equation of state used interpolates between the equations
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Woosley, S. E.; Heger, A.; Weaver, T. A. (2002). "The evolution and explosion of massive stars".
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stars, it is also possible that instabilities destroy the star completely.) During the collapse,
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Chandrasekhar's work on the limit aroused controversy, owing to the opposition of the British
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Michael Nauenberg, "Edmund C. Stoner and the Discovery of the Maximum Mass of White Dwarfs,"
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An Empirical Initial-Final Mass Relation from Hot, Massive White Dwarfs in NGC 2168 (M35)
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Schaffner-Bielich, JĂŒrgen (2005). "Strange quark matter in stars: a general overview]".
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Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
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is a constant. Solving the hydrostatic equation leads to a model white dwarf that is a
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Hillebrandt, Wolfgang; Niemeyer, Jens C. (2000). "Type IA Supernova Explosion Models".
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Empire of the Stars: Obsession, Friendship, and Betrayal in the Quest for Black Holes
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Formation And Evolution of Black Holes in the Galaxy: Selected Papers with Commentary
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composition of the mass. Chandrasekhar gives the following expression, based on the
361:. When this is done, the model radius still decreases with mass, but becomes zero at 212: 181: 162: 2815: 2733: 2619: 2542: 2501: 2095: 2080: 2012: 1639: 1353: 3984: 3707: 3609: 3383: 3029: 2983: 2963: 2852: 2835: 2807: 2803: 2713: 2660: 2607: 2489: 2411: 2350: 2309: 2202: 2008: 1964: 1927: 1861: 1826: 1797: 1747: 1679: 1627: 1556: 1510: 1460: 1420: 1333: 1181: 1106: 983: 935: 901: 847: 821: 809: 728: 575: 205: 166: 26: 3077: 3626: 3616: 3578: 3237: 2756: 2567: 2549: 2249: 2105: 2040: 1710: 1584: 1233: 740: 711: 2380:, Sir Arthur Eddington, Cambridge: Cambridge University Press, 1936, chapter 13. 1575: 1050:
of supernovae of Type Ia are all approximately the same; at maximum luminosity,
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Anderson, Wilhelm (1929). "Uber die Grenzdichte der Materie und der Energie".
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A strong indication of the reliability of Chandrasekhar's formula is that the
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Lattimer, James M.; Prakash, Madappa (2004). "The Physics of Neutron Stars".
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have been observed that are very bright, and thought to have originated from
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might collapse to nothing. As a result, Chandra's work was almost forgotten.
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derive their energy from runaway fusion of the nuclei in the interior of a
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In the nonrelativistic case, electron degeneracy pressure gives rise to an
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Chandrasekhar, S. (1934). "Stellar Configurations with degenerate Cores".
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of the collapsing core releases a large amount of energy on the order of
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The core of a star is kept from collapsing by the heat generated by the
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Chandrasekhar's biographical memoir at the National Academy of Sciences
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Stoner, Edmund C. (1929). "The Limiting Density of White Dwarf Stars".
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Since the observation of the Champagne Supernova in 2003, several more
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If a main-sequence star is not too massive (less than approximately 8
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Eric G. Blackman, "Giants of physics found white-dwarf mass limits",
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per electron, which depends upon the chemical composition of the star
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contributes to the balance against gravity and the result will be a
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heating, its temperature also increases. This eventually ignites
971: 773: 744: 193: 2907:"Champagne supernova challenges ideas about how supernovae work" 2331:"The Pressure of a Degenerate Electron Gas and Related Problems" 2119:
Virginia Trimble, "Chandrasekhar and the history of astronomy",
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smaller than 0.3, making the large asphericity theory unlikely.
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Chandrasekhar, S. (1931). "The Density of White Dwarf Stars".
1305: 300:. This yields a polytrope of index 3, which has a total mass, 62: 1120:
whose masses exceeded the Chandrasekhar limit. These include
997: 680:{\displaystyle {\frac {M_{\text{Pl}}^{3}}{m_{\text{H}}^{2}}}} 32: 1887:
Stoner, Edmund C. (1930). "The Equilibrium of Dense Stars".
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in 1928, together with some other remarks on the physics of
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Sean Carroll, Ph.D., Caltech, 2007, The Teaching Company,
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before exploding. They believe that the star, dubbed the "
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Timeline of white dwarfs, neutron stars, and supernovae
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Timeline of white dwarfs, neutron stars, and supernovae
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Estimating Stellar Parameters from Energy Equipartition
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Dark Matter, Dark Energy: The Dark Side of the Universe
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Kurtis A. Williams, M. Bolte, and Detlev Koester 2004
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Calculated values for the limit vary depending on the
3956: 1216:"Great Indians: Professor Subrahmanyan Chandrasekhar" 642: 400: 59: 38: 29: 1043:, which disrupts the star and causes the supernova. 687:
The limiting mass can be obtained formally from the
44: 41: 2775: 1908:"The minimum pressure of a degenerate electron gas" 1599: 1147: 50: 2635:Journal of Physics G: Nuclear and Particle Physics 2471: 1577:Standards for Astronomical Catalogues, Version 2.0 1027:white dwarfs that accrete matter from a companion 904:'s biography of Chandrasekhar. In Miller's view: 832: 679: 527: 137: Using the general pressure law for an ideal 2632: 2396:Monthly Notices of the Royal Astronomical Society 2294:Monthly Notices of the Royal Astronomical Society 2187:Monthly Notices of the Royal Astronomical Society 1912:Monthly Notices of the Royal Astronomical Society 1782:Monthly Notices of the Royal Astronomical Society 1663:Monthly Notices of the Royal Astronomical Society 1541:Monthly Notices of the Royal Astronomical Society 1093:away. According to a group of astronomers at the 610:is a constant connected with the solution to the 4052: 132:Radius–mass relations for a model white dwarf. 2685: 1697: 1695: 2822: 2514: 2115: 2113: 1587:, section 3.2.2, web page, accessed 12-I-2007. 1085:observed a type Ia supernova, designated 691:by taking the limit of large central density. 3460: 3099: 3067:White dwarf stars and the Chandrasekhar limit 3059:On Stars, Their Evolution and Their Stability 2771: 2769: 2052: 1703:On Stars, Their Evolution and Their Stability 1655: 1534: 1488: 1450: 1232: 723:model was then used by the British physicist 2746:Schneider, Stephen E.; and Arny, Thomas T.; 1692: 1402: 1400: 1273:. River Edge, NJ: World Scientific. p.  850:. Eddington was aware that the existence of 801:together with the nonrelativistic Fermi gas 3001: 2778:Annual Review of Astronomy and Astrophysics 2110: 1651: 1649: 1530: 1528: 1526: 1089:, in a galaxy approximately 4 billion 3467: 3453: 3419: 3106: 3092: 2997: 2995: 2993: 2766: 2378:Relativity Theory of Protons and Electrons 1723:Lieb, Elliott H.; Yau, Horng-Tzer (1987). 1484: 1482: 1446: 1444: 1264: 3015: 2949: 2881:"The weirdest type Ia supernova yet" 2856: 2789: 2699: 2646: 2593: 2415: 2389: 2354: 2328: 2313: 2287: 2206: 2180: 1931: 1801: 1683: 1613: 1595: 1593: 1560: 1514: 1424: 1413:Journal for General Philosophy of Science 1397: 1384: 1319: 16:Maximum mass of a stable white dwarf star 1990: 1843: 1646: 1523: 1491:"The Maximum Mass of Ideal White Dwarfs" 938:into heavier ones. At various stages of 127: 2990: 2749:Readings: Unit 66: End of a star's life 2467: 2465: 2463: 1946: 1722: 1479: 1441: 880:universally applicable, even for large 4053: 2935: 2828: 2679: 2222: 2220: 2218: 2027: 1905: 1886: 1816: 1775: 1590: 1406: 146: Non-relativistic ideal Fermi gas 3448: 3087: 2535: 2508: 116:stars, which resist collapse through 3941: 2460: 2097:Journal for the History of Astronomy 1569: 1187:Chandrasekhar's white dwarf equation 689:Chandrasekhar's white dwarf equation 2829:Branch, David (21 September 2006). 2573: 2392:"The physics of white dwarf matter" 2290:"Note on "Relativistic Degeneracy"" 2215: 1071:Super-Chandrasekhar mass supernovas 1039:reactions, leading to an immediate 13: 3051: 1242:Three Hundred Years of Gravitation 1007:supernovae of types Ib, Ic, and II 14: 4087: 3070:, Masters' thesis, Dave Gentile, 2444:"The Nobel Prize in Physics 1983" 1156:. If the final mass is below the 768:). Stoner went on to derive the 4038: 4026: 4014: 4002: 3990: 3978: 3966: 3940: 3931: 3930: 3682:Tolman–Oppenheimer–Volkoff limit 3474: 3429: 3428: 3418: 2917:from the original on 1 July 2017 2887:from the original on 6 July 2017 2831:"Astronomy: Champagne supernova" 2136:Collected Papers of L. D. Landau 2043:, web page, accessed 12-01-2007. 1197:Tolman–Oppenheimer–Volkoff limit 1158:Tolman–Oppenheimer–Volkoff limit 1148:Tolman–Oppenheimer–Volkoff limit 25: 3865:Fermi Gamma-ray Space Telescope 3401:White dwarf luminosity function 3113: 2929: 2899: 2873: 2740: 2626: 2436: 2424: 2383: 2371: 2322: 2281: 2255: 2174: 2148: 2128: 2088: 2073: 2046: 2013:10.1070/pu1994v037n06abeh000031 1984: 1940: 1899: 1880: 1837: 1810: 1769: 1758:from the original on 2022-01-25 1716: 1059:is approximately −19.3, with a 921: 839:Chandrasekhar–Eddington dispute 833:Chandrasekhar–Eddington dispute 636:, the limit is of the order of 2808:10.1146/annurev.astro.38.1.191 2183:"On "Relativistic Degeneracy"" 1360: 1299: 1258: 1226: 1218:. 26 January 2014 – via 1208: 992:gravitational potential energy 739:. In 1930, Stoner derived the 513: 489: 1: 3891:X-ray pulsar-based navigation 3870:Compton Gamma Ray Observatory 2099:, Vol. 39, p. 297-312, (2008) 1202: 1192:Schönberg–Chandrasekhar limit 986:, leading to the emission of 974:are formed by the capture of 97:). The limit was named after 860:behaving in this absurd way! 110:electron degeneracy pressure 7: 3860:Rossi X-ray Timing Explorer 3703:Gamma-ray burst progenitors 3368:Quasi-periodic oscillations 3144:Hertzsprung–Russell diagram 2134:On the Theory of Stars, in 1175: 1162:neutron degeneracy pressure 695:relativistic many-particle 70:) is the maximum mass of a 10: 4092: 3916:Most massive neutron stars 3657:Quasi-periodic oscillation 3363:Electron-degenerate matter 3034:10.1088/0004-637X/744/1/69 2665:10.1088/0954-3899/31/6/004 2517:Astronomy and Astrophysics 2494:10.1103/revmodphys.74.1015 2329:Eddington, Arthur (1935). 2122:Fluid Flows to Black Holes 1656:Chandrasekhar, S. (1931). 1535:Chandrasekhar, S. (1935). 1489:Chandrasekhar, S. (1931). 1074: 966:. (For very massive, low- 836: 795:Subrahmanyan Chandrasekhar 702: 208:, relieving the pressure. 123: 99:Subrahmanyan Chandrasekhar 3926: 3883: 3875:Chandra X-ray Observatory 3850: 3824: 3695: 3597: 3539: 3503: 3482: 3414: 3376: 3345: 3293:Cataclysmic variable star 3251: 3157: 3121: 3004:The Astrophysical Journal 2474:Reviews of Modern Physics 2390:Eddington, A. S. (1940). 2288:Eddington, A. S. (1935). 2243:The battle of black holes 2181:Eddington, A. S. (1935). 1831:10.1080/14786440108564713 1465:10.1080/14786443109461710 1426:10.1007/s10838-018-9435-y 186:Pauli exclusion principle 3642:Neutron-star oscillation 3531:Rotating radio transient 2761:Birth and Death of Stars 1407:Illari, Phyllis (2019). 1081:In April 2003, the 1063:of no more than 0.3. A 184:effect arising from the 3320:Super soft X-ray source 2800:2000ARA&A..38..191H 2718:10.1126/science.1090720 2529:1996A&A...313..810K 2417:10.1093/mnras/100.8.582 2208:10.1093/mnras/95.3.194a 1338:10.1126/science.1136259 1114:type Ia supernovae 1083:Supernova Legacy Survey 1019:. This fate may befall 962:, or, speculatively, a 544:reduced Planck constant 154:Ultrarelativistic limit 3896:Tempo software program 2883:(Press release). LBL. 2763:, University of Oregon 2561:arXiv astro-ph/0409447 2356:10.1098/rspa.1935.0190 1949:Zeitschrift fĂŒr Physik 1933:10.1093/mnras/92.7.651 1906:Stoner, E. C. (1932). 1889:Philosophical Magazine 1846:Zeitschrift fĂŒr Physik 1819:Philosophical Magazine 1803:10.1093/mnras/87.2.114 1776:Fowler, R. H. (1926). 1685:10.1093/mnras/91.5.456 1562:10.1093/mnras/95.3.207 1453:Philosophical Magazine 911: 862: 717:Fermi–Dirac statistics 681: 562:gravitational constant 529: 157: 106:gravitational collapse 3911:List of neutron stars 3906:The Magnificent Seven 2582:Astrophysical Journal 2554:Astrophysical Journal 2315:10.1093/mnras/96.1.20 1732:Astrophysical Journal 1602:Astrophysical Journal 1495:Astrophysical Journal 1095:University of Toronto 916:William Alfred Fowler 906: 857: 725:Edmund Clifton Stoner 707:In 1926, the British 682: 530: 131: 3811:Thorne–ƻytkow object 799:hydrostatic equation 697:Schrödinger equation 640: 398: 309:, depending only on 104:White dwarfs resist 3762:Neutron star merger 3622:Chandrasekhar limit 3589:Hulse–Taylor pulsar 3516:Soft gamma repeater 3233:Extreme helium star 3129:Chandrasekhar limit 3026:2012ApJ...744...69H 2968:10.1038/nature05103 2960:2006Natur.443..308H 2849:2006Natur.443..283B 2710:2004Sci...304..536L 2657:2005JPhG...31S.651S 2604:2003ApJ...591..288H 2486:2002RvMP...74.1015W 2408:1940MNRAS.100..582E 2347:1935RSPSA.152..253E 2306:1935MNRAS..96...20E 2276:1935Obs....58..257. 2199:1935MNRAS..95..194E 2169:1935Obs....58...33. 2067:1934Obs....57..373C 2005:1994PhyU...37..609Y 1961:1928ZPhy...50..234F 1924:1932MNRAS..92..651S 1858:1929ZPhy...56..851A 1794:1926MNRAS..87..114F 1744:1987ApJ...323..140L 1676:1931MNRAS..91..456C 1624:1996ApJ...457..834T 1553:1935MNRAS..95..207C 1507:1931ApJ....74...81C 1330:2007Sci...315..825M 1283:2003febh.book.....B 1103:Champagne Supernova 1077:Champagne Supernova 1048:absolute magnitudes 898:Empire of the Stars 674: 659: 612:Lane–Emden equation 589:is the mass of the 431: 21:Chandrasekhar limit 3806:Pulsar wind nebula 3784:Stellar black hole 3308:Intermediate polar 3204:Stellar black hole 2755:2020-02-14 at the 2566:2007-08-19 at the 2548:2007-08-19 at the 2431:Fundamental Theory 2270:: 257–265 . 1935. 2248:2006-10-11 at the 2124:, pp. 49-50 (2011) 2104:2022-01-25 at the 2039:1999-10-08 at the 1969:10.1007/BF01328867 1866:10.1007/BF01340146 1852:(11–12): 851–856. 1709:2010-12-15 at the 1583:2017-05-08 at the 1372:www.britannica.com 1321:astro-ph/0702351v1 1061:standard deviation 1013:Type Ia supernovae 990:. The decrease in 982:in the process of 894:fundamental theory 677: 660: 645: 525: 417: 282:special relativity 182:quantum-mechanical 158: 108:primarily through 3954: 3953: 3735:Supernova remnant 3525:Ultra-long period 3442: 3441: 3337:Carbon detonation 3170:Type Ia supernova 3139:Stellar evolution 3072:DePaul University 2944:(7109): 308–311. 2913:(Press release). 2843:(7109): 283–284. 2759:, Astronomy 122: 2694:(5670): 536–542. 1778:"On Dense Matter" 1314:(5813): 825–828. 1292:978-981-238-250-4 1251:978-0-521-37976-2 1041:carbon detonation 940:stellar evolution 803:equation of state 788:degenerate matter 748:equation of state 675: 667: 652: 523: 509: 499: 480: 466: 446: 440: 408: 388:equation of state 213:equation of state 167:white dwarf stars 163:stellar evolution 4083: 4076:Stellar dynamics 4043: 4042: 4031: 4030: 4029: 4019: 4018: 4017: 4007: 4006: 4005: 3995: 3994: 3983: 3982: 3981: 3971: 3970: 3962: 3944: 3943: 3934: 3933: 3708:Asteroseismology 3610:Fast radio burst 3469: 3462: 3455: 3446: 3445: 3432: 3431: 3422: 3421: 3384:Planetary nebula 3108: 3101: 3094: 3085: 3084: 3046: 3045: 3019: 2999: 2988: 2987: 2953: 2951:astro-ph/0609616 2933: 2927: 2926: 2924: 2922: 2903: 2897: 2896: 2894: 2892: 2877: 2871: 2870: 2860: 2826: 2820: 2819: 2793: 2791:astro-ph/0006305 2773: 2764: 2744: 2738: 2737: 2703: 2701:astro-ph/0405262 2683: 2677: 2676: 2650: 2648:astro-ph/0412215 2641:(6): S651–S657. 2630: 2624: 2623: 2597: 2595:astro-ph/0212469 2577: 2571: 2539: 2533: 2532: 2512: 2506: 2505: 2480:(4): 1015–1071. 2469: 2458: 2457: 2455: 2454: 2440: 2434: 2428: 2422: 2421: 2419: 2387: 2381: 2375: 2369: 2368: 2358: 2341:(876): 253–272. 2326: 2320: 2319: 2317: 2285: 2279: 2278: 2259: 2253: 2224: 2213: 2212: 2210: 2178: 2172: 2171: 2152: 2146: 2140:Phys. Z. Sowjet. 2132: 2126: 2117: 2108: 2092: 2086: 2077: 2071: 2070: 2050: 2044: 2031: 2025: 2024: 1988: 1982: 1980: 1955:(3–4): 234–248. 1944: 1938: 1937: 1935: 1903: 1897: 1896: 1884: 1878: 1877: 1841: 1835: 1834: 1814: 1808: 1807: 1805: 1773: 1767: 1766: 1764: 1763: 1729: 1720: 1714: 1699: 1690: 1689: 1687: 1653: 1644: 1643: 1617: 1615:astro-ph/9510136 1597: 1588: 1573: 1567: 1566: 1564: 1532: 1521: 1520: 1518: 1486: 1477: 1476: 1448: 1439: 1438: 1428: 1404: 1395: 1388: 1382: 1381: 1379: 1378: 1364: 1358: 1357: 1323: 1303: 1297: 1296: 1272: 1262: 1256: 1255: 1230: 1224: 1223: 1212: 1182:Bekenstein bound 1140:showed it had a 1107:standard candles 1065:1-sigma interval 1058: 1000: 984:electron capture 902:Arthur I. Miller 883: 879: 848:Arthur Eddington 822:Virginia Trimble 810:Wilhelm Anderson 767: 757: 755: 738: 736: 729:Wilhelm Anderson 686: 684: 683: 678: 676: 673: 668: 665: 658: 653: 650: 644: 631: 630: 629: 609: 607: 606: 588: 576:molecular weight 573: 559: 550: 541: 534: 532: 531: 526: 524: 522: 521: 520: 511: 510: 507: 501: 500: 497: 484: 482: 481: 473: 471: 467: 462: 454: 447: 442: 441: 433: 430: 425: 415: 410: 409: 406: 378: 369: 360: 356: 340: 336: 317: 308: 299: 275: 273: 272: 269: 266: 255: 242: 234: 230: 206:electron capture 151: 145: 136: 118:thermal pressure 96: 94: 69: 68: 65: 64: 61: 58: 55: 52: 49: 46: 43: 40: 37: 34: 31: 4091: 4090: 4086: 4085: 4084: 4082: 4081: 4080: 4051: 4050: 4049: 4037: 4027: 4025: 4015: 4013: 4003: 4001: 3989: 3979: 3977: 3965: 3957: 3955: 3950: 3922: 3879: 3852: 3846: 3820: 3691: 3627:Gamma-ray burst 3617:Bondi accretion 3593: 3535: 3521:Anomalous X-ray 3499: 3478: 3473: 3443: 3438: 3410: 3372: 3341: 3253: 3247: 3238:Subdwarf B star 3153: 3117: 3112: 3054: 3052:Further reading 3049: 3000: 2991: 2934: 2930: 2920: 2918: 2905: 2904: 2900: 2890: 2888: 2879: 2878: 2874: 2858:10.1038/443283a 2827: 2823: 2774: 2767: 2757:Wayback Machine 2745: 2741: 2684: 2680: 2631: 2627: 2578: 2574: 2568:Wayback Machine 2550:Wayback Machine 2540: 2536: 2513: 2509: 2470: 2461: 2452: 2450: 2442: 2441: 2437: 2429: 2425: 2388: 2384: 2376: 2372: 2327: 2323: 2286: 2282: 2264:The Observatory 2261: 2260: 2256: 2250:Wayback Machine 2225: 2216: 2179: 2175: 2163:: 33–41. 1935. 2157:The Observatory 2154: 2153: 2149: 2133: 2129: 2118: 2111: 2106:Wayback Machine 2093: 2089: 2084:440, 148 (2006) 2078: 2074: 2055:The Observatory 2051: 2047: 2041:Wayback Machine 2032: 2028: 1993:Physics-Uspekhi 1989: 1985: 1945: 1941: 1904: 1900: 1885: 1881: 1842: 1838: 1815: 1811: 1774: 1770: 1761: 1759: 1727: 1721: 1717: 1711:Wayback Machine 1700: 1693: 1654: 1647: 1598: 1591: 1585:Wayback Machine 1574: 1570: 1533: 1524: 1487: 1480: 1459:(70): 592–596. 1449: 1442: 1405: 1398: 1389: 1385: 1376: 1374: 1366: 1365: 1361: 1304: 1300: 1293: 1263: 1259: 1252: 1240:, eds. (1989). 1231: 1227: 1214: 1213: 1209: 1205: 1178: 1150: 1079: 1073: 1057: 1051: 995: 924: 881: 875: 865: 841: 835: 765: 759: 753: 751: 741:internal energy 734: 732: 712:Ralph H. Fowler 705: 669: 664: 654: 649: 643: 641: 638: 637: 621: 619: 618: 605: 602: 601: 600: 596: 587: 581: 574:is the average 572: 566: 557: 548: 539: 516: 512: 506: 502: 496: 492: 488: 483: 472: 455: 453: 449: 448: 432: 426: 421: 416: 414: 405: 401: 399: 396: 395: 377: 371: 368: 362: 358: 352: 342: 338: 332: 322: 316: 310: 307: 301: 295: 285: 270: 267: 264: 263: 261: 254: 248: 240: 232: 226: 216: 156: 149: 147: 143: 141: 134: 126: 92: 90: 87: 84: 28: 24: 17: 12: 11: 5: 4089: 4079: 4078: 4073: 4068: 4063: 4048: 4047: 4035: 4023: 4011: 3999: 3987: 3975: 3952: 3951: 3949: 3948: 3938: 3927: 3924: 3923: 3921: 3920: 3919: 3918: 3908: 3903: 3898: 3893: 3887: 3885: 3881: 3880: 3878: 3877: 3872: 3867: 3862: 3856: 3854: 3848: 3847: 3845: 3844: 3839: 3834: 3828: 3826: 3822: 3821: 3819: 3818: 3813: 3808: 3803: 3798: 3793: 3792: 3791: 3781: 3780: 3779: 3769: 3764: 3759: 3754: 3749: 3744: 3743: 3742: 3737: 3727: 3726: 3725: 3720: 3710: 3705: 3699: 3697: 3693: 3692: 3690: 3689: 3684: 3679: 3674: 3669: 3664: 3659: 3654: 3649: 3644: 3639: 3637:Neutron matter 3634: 3629: 3624: 3619: 3614: 3613: 3612: 3601: 3599: 3595: 3594: 3592: 3591: 3586: 3581: 3576: 3571: 3570: 3569: 3564: 3559: 3549: 3543: 3541: 3540:Binary pulsars 3537: 3536: 3534: 3533: 3528: 3527: 3526: 3523: 3518: 3507: 3505: 3504:Single pulsars 3501: 3500: 3498: 3497: 3492: 3486: 3484: 3480: 3479: 3472: 3471: 3464: 3457: 3449: 3440: 3439: 3437: 3436: 3426: 3415: 3412: 3411: 3409: 3408: 3403: 3398: 3393: 3392: 3391: 3380: 3378: 3374: 3373: 3371: 3370: 3365: 3360: 3355: 3349: 3347: 3343: 3342: 3340: 3339: 3334: 3329: 3324: 3323: 3322: 3312: 3311: 3310: 3305: 3300: 3290: 3288:Symbiotic nova 3285: 3280: 3275: 3274: 3273: 3268: 3257: 3255: 3249: 3248: 3246: 3245: 3240: 3235: 3230: 3229: 3228: 3223: 3213: 3212: 3211: 3201: 3200: 3199: 3194: 3189: 3179: 3178: 3177: 3167: 3161: 3159: 3155: 3154: 3152: 3151: 3146: 3141: 3136: 3131: 3125: 3123: 3119: 3118: 3111: 3110: 3103: 3096: 3088: 3082: 3081: 3075: 3063: 3053: 3050: 3048: 3047: 2989: 2928: 2911:spacedaily.com 2898: 2872: 2821: 2765: 2739: 2678: 2625: 2612:10.1086/375341 2588:(1): 288–300. 2572: 2559:, pp. L49–L52 2534: 2507: 2459: 2448:NobelPrize.org 2435: 2423: 2402:(8): 582–594. 2382: 2370: 2321: 2280: 2254: 2237:; reviewed at 2214: 2193:(3): 194–206. 2173: 2147: 2127: 2109: 2087: 2072: 2045: 2026: 1999:(6): 609–612. 1983: 1939: 1918:(7): 651–661. 1898: 1879: 1836: 1809: 1788:(2): 114–122. 1768: 1752:10.1086/165813 1715: 1691: 1670:(5): 456–466. 1645: 1632:10.1086/176778 1589: 1568: 1547:(3): 207–225. 1522: 1516:10.1086/143324 1478: 1440: 1396: 1383: 1359: 1298: 1291: 1257: 1250: 1234:Hawking, S. W. 1225: 1206: 1204: 1201: 1200: 1199: 1194: 1189: 1184: 1177: 1174: 1149: 1146: 1075:Main article: 1072: 1069: 1055: 1037:nuclear fusion 923: 920: 890:Wolfgang Pauli 873: 845:astrophysicist 837:Main article: 834: 831: 763: 704: 701: 672: 663: 657: 648: 615: 614: 603: 594: 585: 579: 570: 564: 555: 553:speed of light 546: 519: 515: 505: 495: 491: 487: 479: 476: 470: 465: 461: 458: 452: 445: 439: 436: 429: 424: 420: 413: 404: 375: 366: 350: 330: 314: 305: 293: 252: 224: 148: 142: 133: 125: 122: 112:, compared to 85: 82: 15: 9: 6: 4: 3: 2: 4088: 4077: 4074: 4072: 4071:Neutron stars 4069: 4067: 4064: 4062: 4059: 4058: 4056: 4046: 4041: 4036: 4034: 4024: 4022: 4012: 4010: 4000: 3998: 3993: 3988: 3986: 3976: 3974: 3969: 3964: 3963: 3960: 3947: 3939: 3937: 3929: 3928: 3925: 3917: 3914: 3913: 3912: 3909: 3907: 3904: 3902: 3899: 3897: 3894: 3892: 3889: 3888: 3886: 3882: 3876: 3873: 3871: 3868: 3866: 3863: 3861: 3858: 3857: 3855: 3853:investigation 3849: 3843: 3840: 3838: 3837:Centaurus X-3 3835: 3833: 3830: 3829: 3827: 3823: 3817: 3814: 3812: 3809: 3807: 3804: 3802: 3801:Pulsar planet 3799: 3797: 3794: 3790: 3789:Related links 3787: 3786: 3785: 3782: 3778: 3777:Related links 3775: 3774: 3773: 3770: 3768: 3765: 3763: 3760: 3758: 3755: 3753: 3750: 3748: 3745: 3741: 3740:Related links 3738: 3736: 3733: 3732: 3731: 3728: 3724: 3721: 3719: 3716: 3715: 3714: 3711: 3709: 3706: 3704: 3701: 3700: 3698: 3694: 3688: 3685: 3683: 3680: 3678: 3675: 3673: 3670: 3668: 3665: 3663: 3660: 3658: 3655: 3653: 3650: 3648: 3645: 3643: 3640: 3638: 3635: 3633: 3630: 3628: 3625: 3623: 3620: 3618: 3615: 3611: 3608: 3607: 3606: 3603: 3602: 3600: 3596: 3590: 3587: 3585: 3582: 3580: 3577: 3575: 3572: 3568: 3565: 3563: 3562:X-ray burster 3560: 3558: 3555: 3554: 3553: 3550: 3548: 3545: 3544: 3542: 3538: 3532: 3529: 3524: 3522: 3519: 3517: 3514: 3513: 3512: 3509: 3508: 3506: 3502: 3496: 3493: 3491: 3488: 3487: 3485: 3481: 3477: 3470: 3465: 3463: 3458: 3456: 3451: 3450: 3447: 3435: 3427: 3425: 3417: 3416: 3413: 3407: 3404: 3402: 3399: 3397: 3394: 3390: 3387: 3386: 3385: 3382: 3381: 3379: 3375: 3369: 3366: 3364: 3361: 3359: 3356: 3354: 3351: 3350: 3348: 3344: 3338: 3335: 3333: 3330: 3328: 3327:Binary pulsar 3325: 3321: 3318: 3317: 3316: 3313: 3309: 3306: 3304: 3301: 3299: 3296: 3295: 3294: 3291: 3289: 3286: 3284: 3281: 3279: 3276: 3272: 3269: 3267: 3264: 3263: 3262: 3259: 3258: 3256: 3250: 3244: 3243:Helium planet 3241: 3239: 3236: 3234: 3231: 3227: 3224: 3222: 3219: 3218: 3217: 3214: 3210: 3209:Related links 3207: 3206: 3205: 3202: 3198: 3197:Related links 3195: 3193: 3190: 3188: 3185: 3184: 3183: 3180: 3176: 3173: 3172: 3171: 3168: 3166: 3163: 3162: 3160: 3156: 3150: 3149:Mira variable 3147: 3145: 3142: 3140: 3137: 3135: 3132: 3130: 3127: 3126: 3124: 3120: 3116: 3109: 3104: 3102: 3097: 3095: 3090: 3089: 3086: 3079: 3076: 3073: 3069: 3068: 3064: 3061: 3060: 3056: 3055: 3044:. Article 69. 3043: 3039: 3035: 3031: 3027: 3023: 3018: 3013: 3009: 3005: 2998: 2996: 2994: 2985: 2981: 2977: 2973: 2969: 2965: 2961: 2957: 2952: 2947: 2943: 2939: 2932: 2916: 2912: 2908: 2902: 2886: 2882: 2876: 2868: 2864: 2859: 2854: 2850: 2846: 2842: 2838: 2837: 2832: 2825: 2817: 2813: 2809: 2805: 2801: 2797: 2792: 2787: 2783: 2779: 2772: 2770: 2762: 2758: 2754: 2751: 2750: 2743: 2735: 2731: 2727: 2723: 2719: 2715: 2711: 2707: 2702: 2697: 2693: 2689: 2682: 2674: 2670: 2666: 2662: 2658: 2654: 2649: 2644: 2640: 2636: 2629: 2621: 2617: 2613: 2609: 2605: 2601: 2596: 2591: 2587: 2583: 2576: 2569: 2565: 2562: 2558: 2555: 2551: 2547: 2544: 2538: 2530: 2526: 2522: 2518: 2511: 2503: 2499: 2495: 2491: 2487: 2483: 2479: 2475: 2468: 2466: 2464: 2449: 2445: 2439: 2432: 2427: 2418: 2413: 2409: 2405: 2401: 2397: 2393: 2386: 2379: 2374: 2366: 2362: 2357: 2352: 2348: 2344: 2340: 2336: 2332: 2325: 2316: 2311: 2307: 2303: 2299: 2295: 2291: 2284: 2277: 2273: 2269: 2265: 2258: 2251: 2247: 2244: 2240: 2236: 2235:0-618-34151-X 2232: 2228: 2223: 2221: 2219: 2209: 2204: 2200: 2196: 2192: 2188: 2184: 2177: 2170: 2166: 2162: 2158: 2151: 2144: 2141: 2137: 2131: 2125: 2123: 2116: 2114: 2107: 2103: 2100: 2098: 2091: 2085: 2083: 2076: 2068: 2064: 2060: 2056: 2049: 2042: 2038: 2035: 2030: 2022: 2018: 2014: 2010: 2006: 2002: 1998: 1994: 1987: 1978: 1974: 1970: 1966: 1962: 1958: 1954: 1950: 1943: 1934: 1929: 1925: 1921: 1917: 1913: 1909: 1902: 1894: 1890: 1883: 1875: 1871: 1867: 1863: 1859: 1855: 1851: 1847: 1840: 1832: 1828: 1825:(41): 63–70. 1824: 1820: 1813: 1804: 1799: 1795: 1791: 1787: 1783: 1779: 1772: 1757: 1753: 1749: 1745: 1741: 1737: 1733: 1726: 1719: 1712: 1708: 1705: 1704: 1698: 1696: 1686: 1681: 1677: 1673: 1669: 1665: 1664: 1659: 1652: 1650: 1641: 1637: 1633: 1629: 1625: 1621: 1616: 1611: 1607: 1603: 1596: 1594: 1586: 1582: 1579: 1578: 1572: 1563: 1558: 1554: 1550: 1546: 1542: 1538: 1531: 1529: 1527: 1517: 1512: 1508: 1504: 1500: 1496: 1492: 1485: 1483: 1474: 1470: 1466: 1462: 1458: 1454: 1447: 1445: 1436: 1432: 1427: 1422: 1418: 1414: 1410: 1403: 1401: 1393: 1387: 1373: 1369: 1363: 1355: 1351: 1347: 1343: 1339: 1335: 1331: 1327: 1322: 1317: 1313: 1309: 1302: 1294: 1288: 1284: 1280: 1276: 1271: 1270: 1261: 1253: 1247: 1243: 1239: 1235: 1229: 1221: 1217: 1211: 1207: 1198: 1195: 1193: 1190: 1188: 1185: 1183: 1180: 1179: 1173: 1171: 1167: 1163: 1159: 1155: 1145: 1143: 1139: 1135: 1131: 1127: 1123: 1119: 1115: 1110: 1108: 1104: 1100: 1096: 1092: 1088: 1084: 1078: 1068: 1066: 1062: 1054: 1049: 1044: 1042: 1038: 1034: 1033:compressional 1030: 1026: 1022: 1018: 1014: 1010: 1008: 1004: 999: 993: 989: 985: 981: 977: 973: 969: 965: 961: 957: 953: 948: 945: 941: 937: 933: 929: 919: 917: 910: 905: 903: 899: 895: 891: 887: 878: 872: 868: 861: 856: 853: 849: 846: 840: 830: 828: 823: 819: 818:Freeman Dyson 815: 811: 806: 804: 800: 796: 791: 789: 785: 784:Yakov Frenkel 782: 779: 775: 771: 762: 749: 746: 742: 730: 726: 722: 718: 713: 710: 700: 698: 692: 690: 670: 661: 655: 646: 635: 628: 624: 613: 599: 595: 592: 584: 580: 577: 569: 565: 563: 556: 554: 547: 545: 538: 537: 536: 517: 503: 493: 485: 477: 474: 468: 463: 459: 456: 450: 443: 437: 434: 427: 422: 418: 411: 402: 393: 390:for an ideal 389: 385: 380: 374: 365: 355: 349: 345: 335: 329: 325: 319: 313: 304: 298: 292: 288: 283: 277: 259: 251: 246: 238: 229: 223: 219: 214: 209: 207: 203: 202:energy levels 199: 195: 191: 187: 183: 178: 176: 172: 171:neutron stars 168: 164: 155: 140: 130: 121: 119: 115: 114:main sequence 111: 107: 102: 100: 88: 79: 76: 73: 67: 22: 4066:White dwarfs 4061:Astrophysics 4033:Solar System 3713:Compact star 3687:Urca process 3677:Timing noise 3662:Relativistic 3621: 3557:X-ray binary 3552:X-ray pulsar 3476:Neutron star 3358:Urca process 3332:Helium flash 3315:X-ray binary 3216:Compact star 3182:Neutron star 3134:PG 1159 star 3128: 3066: 3058: 3010:(1): 76–79. 3007: 3003: 2941: 2937: 2931: 2919:. 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Index

/ˌtʃəndrəˈʃeÉȘkər/
stable
white dwarf
star
M
Subrahmanyan Chandrasekhar
gravitational collapse
electron degeneracy pressure
main sequence
thermal pressure

Fermi gas
Ultrarelativistic limit
stellar evolution
white dwarf stars
neutron stars
black holes
quantum-mechanical
Pauli exclusion principle
electrons
fermions
band
energy levels
electron capture
equation of state
pressure
mass density
polytrope
special relativity
nuclear

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