查看“錢德拉塞卡極限”的源代码

'''錢德拉塞卡極限'''（{{lang|en|Chandrasekhar Limit}}），以印度裔美籍天文物理學家[[蘇布拉馬尼揚·錢德拉塞卡]]命名，是無自轉恆星以[[電子簡併壓力]]阻擋[[重力塌縮]]所能承受的最大質量，這個值大約是1.4倍[[太陽質量]] <ref>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, NJ: World Scientific: 2003. ISBN 981238250X.</ref><ref>{{cite journal
  | author=Mazzali, P. A.; K. Röpke, F. K.; Benetti, S.; Hillebrandt, W.
  | title=A Common Explosion Mechanism for Type Ia Supernovae 
  | journal=Science | year=2007 | volume=315
  | issue=5813 | pages=825-828
  | doi=10.1126/science.1136259
  | accessdate=2007-05-24 }}</ref>，計算的結果會依據[[原子核]]的結構和溫度而有些差異<ref name=timmes>[http://adsabs.harvard.edu/abs/1996ApJ...457..834T 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.</ref>。錢德拉塞卡<ref name="chandra1">[http://adsabs.harvard.edu/abs/1931MNRAS..91..456C The Highly Collapsed Configurations of a Stellar Mass], S. Chandrasekhar, ''Monthly Notices of the Royal Astronomical Society'' '''91''' (1931), 456–466.</ref><sup>, eq. (36),</sup><ref name="chandra2">[http://adsabs.harvard.edu/abs/1935MNRAS..95..207C The Highly Collapsed Configurations of a Stellar Mass (second paper)], S. Chandrasekhar, ''Monthly Notices of the Royal Astronomical Society'', '''95''' (1935), pp. 207--225.</ref><sup>, eq. (58),</sup><ref name="chandranobel">[http://nobelprize.org/nobel_prizes/physics/laureates/1983/chandrasekhar-lecture.pdf ''On Stars, Their Evolution and Their Stability''], Nobel Prize lecture, Subrahmanyan Chandrasekhar, December 8, 1983.</ref><sup>, eq. (43)</sup> 给出
:<math>\frac{\omega_3^0 \sqrt{3\pi}}{2}\left ( \frac{\hbar c}{G}\right )^{3/2}\frac{1}{(\mu_e m_H)^2}.</math>
此處， μ<sub>e</sub>是分子的每電子平均質量，<math>m_H</math>是氫原子的質量，而<math>\omega_3^0 \approx 2.018236</math>是與[[萊恩-恩登方程式]]有關的常數，在數值上，這個值大約是 (2/μ<sub>e</sub>)<sup>2</sup> · 2.85 · 10<sup>30</sup> 公斤，或是<math>1.43 (2/\mu_e)^2 M_{\bigodot}</math>，此處的<math>M_{\bigodot}=1.989\cdot 10^{30} \ {\rm kg}</math>是標準的[[太陽質量]] <ref name="stds">[http://vizier.u-strasbg.fr/doc/catstd-3.2.htx ''Standards for Astronomical Catalogues, Version 2.0''], section 3.2.2, web page, accessed 12-I-2007.</ref>，而<math>\sqrt{\hbar c/G}</math>是[[普朗克質量]]， <math>M_{\rm Pl}\approx 2.176\cdot 10^{-8}\  {\rm kg}</math>，是M的數量級極限M<sub>Pl</sub><sup>3</sup>/m<sub>H</sub><sup>2</sup>。

對[[白矮星]]而言，[[電子簡併壓力]]是其抵抗重力的唯一力量，因此這個值也是白矮星的質量上限。[[主序星]]的質量若超過8倍的太陽質量，在演化結束前不能拋掉足夠的質量成為穩定的[[白矮星]]，因此會成為[[中子星]]或是[[黑洞]]  <ref name="ifmr1">[http://adsabs.harvard.edu/abs/1996A%26A...313..810K White dwarfs in open clusters. VIII. NGC 2516: a test for the mass-radius and initial-final mass relations], D. Koester and D. Reimers, ''Astronomy and Astrophysics'' '''313''' (1996), pp. 810–814.</ref><ref name="ifmr2">[http://adsabs.harvard.edu/abs/2004ApJ...615L..49W An Empirical Initial-Final Mass Relation from Hot, Massive White Dwarfs in NGC 2168 (M35)], Kurtis A. Williams, M. Bolte, and Detlev Koester, ''Astrophysical Journal'' '''615''', #1 (2004), pp. L49–L52; also [http://arxiv.org/abs/astro-ph/0409447 arXiv astro-ph/0409447].</ref><ref name="evo">[http://adsabs.harvard.edu/abs/2003ApJ...591..288H How Massive Single Stars End Their Life], A. Heger, C. L. Fryer, S. E. Woosley, N. Langer, and D. H. Hartmann, ''Astrophysical Journal'' '''591''', #1 (2003), pp. 288–300.</ref>。

== 物理學 ==
[[File:ChandrasekharLimitGraph.svg|thumb|200px|right|白矮星模型的半徑相對於質量圖。]]
[[電子簡併壓力]]是依據[[量子力學]]的[[泡利不相容原理|-{zh-cn:泡利不相容原理;zh-hant:包利不相容原理;}-]]所產生的效應。因為電子是[[費米子]]，在一個原子內不能有兩個電子有著相同的量子狀態，所以不可能讓所有的電子都在最低的能量。換言之，電子必然會佔有不同的能階。當原子被壓縮時，由於電子的數量和必須佔有不同的能階，所以必然會佔有一定量的體積。因此電子的能量將因為壓縮而增加，電子也必須施加壓力來抗拒電子雲的進一步壓縮。這就是電子簡併壓力的起源。

在非相對論的情況下，電子簡併壓力可以由[[狀態方程]]求得，形式為P=K<sub>1</sub>ρ<sup>5/3</sup>。解白矮星[[多方模型]]的流體靜力學等效方程式可以導出係數為3/2的半徑反比於質量的立方，和體積反比於質量的關係。<ref name="chandra3">The Density of White Dwarf Stars, S. Chandrasekhar, ''Philosophical Magazine'' (7th series) '''11''' (1931), pp. 592–596.</ref>
當白矮星模型的質量增加時，電子簡併壓力使得特有的電子能量相對於它們的靜止質量不再是微不足道的。電子的速度接近光速，因此必須考慮到[[狹義相對論]]。在強大的相對論效應下，我們發現[[狀態方程]]的形式為P=K<sub>2</sub>ρ<sup>4/3</sup>。這將使多方模型的係數成為3，這會使總質量M<sub>limit</sub>只與K<sub>2</sub>相關聯。</sub>.<ref name="chandra4">[http://adsabs.harvard.edu/abs/1931ApJ....74...81C The Maximum Mass of Ideal White Dwarfs], S. Chandrasekhar, ''Astrophysical Journal'' '''74''' (1931), pp. 81–82.</ref>

== 參考資料 ==
{{reflist|2}}

== 延伸讀物 ==
*[http://nobelprize.org/nobel_prizes/physics/laureates/1983/chandrasekhar-lecture.pdf ''On Stars, Their Evolution and Their Stability''], Nobel Prize lecture, Subrahmanyan Chandrasekhar, [[December 8]], 1983.
*[http://www.davegentile.com/thesis/white_dwarfs.html ''White dwarf stars and the Chandrasekhar limit''], Masters' thesis, Dave Gentile, [[帝博大學]], 1995.  
*[http://www.sciencebits.com/StellarEquipartition Estimating Stellar Parameters from Energy Equipartition], sciencebits.com. Discusses how to find mass-radius relations and mass limits for white dwarfs using simple energy arguments.

== 相關條目 ==
*[[簡併物質]]
*[[托爾曼－奧本海默－沃爾科夫方程]]
* [[馬克士威-玻茲曼統計]]

{{Template:白矮星}}

[[Category:天体物理学|Qian2]]