# 周边昏暗

• 恒星的密度由中心向外逐渐降低
• 恒星的温度因为与中心距离的增加而逐渐降低。

## 周边昏暗的计算

${\displaystyle {\frac {I(\psi )}{I(0)}}=\sum _{k=0}^{N}a_{k}\,{\textrm {cos}}^{k}(\psi )}$

${\displaystyle \sum _{k=0}^{N}a_{k}=1}$

${\displaystyle a_{0}=1-a_{1}-a_{2}\,}$
${\displaystyle a_{1}=0.93\,}$
${\displaystyle a_{2}=-0.23\,}$

（参考Cox, 2000）。注－周边昏暗方程式有时也会写成：

${\displaystyle {\frac {I(\psi )}{I(0)}}=1+\sum _{k=1}^{N}A_{k}\,(1-\cos(\psi ))^{k}}$

${\displaystyle \cos(\psi )={\frac {\sqrt {\cos ^{2}(\theta )-\cos ^{2}(\Omega )}}{\sin(\Omega )}}}$

${\displaystyle I_{m}={\frac {\int I(\psi )d\omega }{\int d\omega }}}$

${\displaystyle {\frac {I_{m}}{I(0)}}=2\sum _{k=0}^{N}{\frac {a_{k}}{k+2}}}$

## 参考资料

• Billings, Donald E. A Guide to the Solar Corona. Academic Press, New York. 1966.
• Cox, Arthur N. (ed). Allen's Astrophysical Quantities 14th ed. Springer-Verlag, NY. 2000. ISBN 0-387-98746-0.
• Milne, E.A. MNRAS. 1921, 81: 361–375. 缺少或|title=为空 (帮助)
• Minnaert, M. Z.f. Ap. 1930, 1: 209. 缺少或|title=为空 (帮助)
• Neckel, H. and Labs, D. Solar Limb Darkening 1986-1990. Solar Physics. 1994, 153: 91–114.
• van de Hulst, H. C. Bull. Astron. Inst. Netherlands. 1950, 11 (410): 135. 缺少或|title=为空 (帮助)