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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Chandrasekhar limit ： ウィキペディア英語版 Chandrasekhar limit The Chandrasekhar limit () is the maximum mass of a stable white dwarf star. The limit was first indicated in papers published by Wilhelm Anderson and E. C. Stoner, and was named after Subrahmanyan Chandrasekhar, the Indian astrophysicist who independently discovered and improved upon the accuracy of the calculation in 1930, at the age of 19, in India. This limit was initially ignored by the community of scientists because such a limit would logically require the existence of black holes, which were considered a scientific impossibility at the time. White dwarfs resist gravitational collapse primarily through electron degeneracy pressure. (By comparison, main sequence stars resist collapse through thermal pressure.) 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. Consequently, white dwarfs with masses greater than the limit would be subject to further gravitational collapse, evolving into a different type of stellar remnant, such as a neutron star or black hole. (However, white dwarfs generally avoid this fate by exploding before they undergo collapse.) Those with masses under the limit remain stable as white dwarfs.〔Sean Carroll, Ph.D., Cal Tech, 2007, The Teaching Company, ''Dark Matter, Dark Energy: The Dark Side of the Universe'', 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..."〕 The currently accepted value of the limit is about 1.39 $M\_\backslash odot$ (2.765 × 1030 kg).〔p. 55, How A Supernova Explodes, Hans A. Bethe and Gerald Brown, pp. 51–62 in ''Formation And Evolution of Black Holes in the Galaxy: Selected Papers with Commentary'', Hans Albrecht Bethe, Gerald Edward Brown, and Chang-Hwan Lee, River Edge, New Jersey: World Scientific: 2003. ISBN 981-238-250-X.〕 ==Physics== Electron degeneracy pressure is a quantum-mechanical effect arising from the Pauli exclusion principle. Since electrons are fermions, no two electrons can be in the same state, so not all electrons can be in the minimum-energy level. Rather, electrons must occupy a band of energy levels. 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 will increase upon 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 electron capture, relieving the pressure. In the nonrelativistic case, electron degeneracy pressure gives rise to an equation of state of the form $P\; =\; K\_1\; \backslash rho^$, where ''P'' is the pressure, $\backslash rho$ is the mass density, and $K\_1$ is a constant. Solving the hydrostatic equation then leads to a model white dwarf which is a polytrope of index 3/2 and therefore has radius inversely proportional to the cube root of its mass, and volume inversely proportional to its mass.〔The Density of White Dwarf Stars, S. Chandrasekhar, ''Philosophical Magazine'' (7th series) 11 (1931), pp. 592–596.〕 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 special relativity must be taken into account. In the strongly relativistic limit, the equation of state takes the form $P\; =\; K\_2\; \backslash rho^$. This will yield a polytrope of index 3, which will have a total mass, Mlimit say, depending only on K2.〔(The Maximum Mass of Ideal White Dwarfs ), S. Chandrasekhar, ''Astrophysical Journal'' 74 (1931), pp. 81–82.〕 For a fully relativistic treatment, the equation of state used will interpolate between the equations $P\; =\; K\_1\; \backslash rho^$ for small ρ and $P\; =\; K\_2\; \backslash rho^$ for large ρ. When this is done, the model radius still decreases with mass, but becomes zero at Mlimit. 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. μe has been set equal to 2. Radius is measured in standard solar radii〔(''Standards for Astronomical Catalogues, Version 2.0'' ), section 3.2.2, web page, accessed 12-I-2007.〕 or kilometers, and mass in standard solar masses. Calculated values for the limit will vary depending on the nuclear composition of the mass.〔 Chandrasekhar〔(The Highly Collapsed Configurations of a Stellar Mass ), S. Chandrasekhar, ''Monthly Notices of the Royal Astronomical Society'' 91 (1931), 456–466.〕, eq. (36),〔(The Highly Collapsed Configurations of a Stellar Mass (second paper) ), S. Chandrasekhar, ''Monthly Notices of the Royal Astronomical Society'', 95 (1935), pp. 207--225.〕, eq. (58),〔(''On Stars, Their Evolution and Their Stability'' ), Nobel Prize lecture, Subrahmanyan Chandrasekhar, December 8, 1983.〕, eq. (43) gives the following expression, based on the equation of state for an ideal Fermi gas: :$M\_\; =\; \backslash frac\backslash left\; (\; \backslash frac\backslash right\; )^\backslash frac,$ where: *''$\backslash hbar$'' is the reduced Planck constant *''c'' is the speed of light *''G'' is the gravitational constant *''μ''e is the average molecular weight per electron, which depends upon the chemical composition of the star. *''mH'' is the mass of the hydrogen atom. *$\backslash omega\_3^0\; \backslash approx\; 2.018236$ is a constant connected with the solution to the Lane-Emden equation. As $\backslash sqrt$ is the Planck mass, the limit is of the order of :$\backslash frac.$ 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.〔(The Neutron Star and Black Hole Initial Mass Function ), F. X. Timmes, S. E. Woosley, and Thomas A. Weaver, ''Astrophysical Journal'' 457 (February 1, 1996), pp. 834–843.〕 Lieb and Yau〔(A rigorous examination of the Chandrasekhar theory of stellar collapse ), Elliott H. Lieb and Horng-Tzer Yau, ''Astrophysical Journal'' 323 (1987), pp. 140–144.〕 have given a rigorous derivation of the limit from a relativistic many-particle Schrödinger equation. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Chandrasekhar limit」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.