# 白矮星

## 質量-半徑關係和質量極限

$E_k \approx \frac{N (\Delta p)^2}{2m} \approx \frac{N \hbar^2 n^{2/3}}{2m} \approx \frac{M^{2/3} N^{5/3} \hbar^2}{2m R^2}.$

$|E_g|\approx\frac{GM}{R} = E_k\approx\frac{M^{2/3} N^{5/3} \hbar^2}{2m R^2}.$

$R \approx \frac{N^{5/3} \hbar^2}{2m GM^{1/3}}.$

$R \sim \frac{1}{M^{1/3}}, \,$

$E_{k\ {\rm relativistic}} \approx \frac{M^{1/3} N^{4/3} \hbar c}{R}.$

$M_{\rm limit} \approx N^2 \left(\frac{\hbar c}{G}\right)^{3/2}.$

## 歷史上的發現

1892年，Alvan Graham Clark發現天狼星的伴星。根據對恆星數據的分析，這個伴星的質量約一個太陽質量，表面溫度大約25000K，但是其光度大約是天狼星的萬分之一，所以根據光度和表面積的關係，推斷出其大小與地球相當。這樣的密度是地球上的物質達不到的。1917年，Adriaan Van Maanen發現了目前已知離太陽最近的白矮星Van Maanen星。

1930年，蘇布拉馬尼揚·錢德拉塞卡發現了白矮星的質量上限（錢德拉塞卡極限），並因此獲得1983年的諾貝爾物理學獎

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## 外部鏈結和延伸讀物

### 一般

• White Dwarf Stars, Steven D. Kawaler, in Stellar remnants, S. D. Kawaler, I. Novikov, and G. Srinivasan, edited by Georges Meynet and Daniel Schaerer, Berlin: Springer, 1997. Lecture notes for Saas-Fee advanced course number 25. ISBN 3-540-61520-2.