尺度不变恒星结构
Scale invariant stellar structure
摘要：
在尺度不变的流体静力正压流中，径向演化方程与局部重力能和内能成线性关系。从这个一阶方程中，可以直接得到多面体的所有性质和重要的质量-半径关系。求积则导出了规则的莱恩-埃姆登函数及其皮卡德和帕德近似，这在恒星近似或精确多变的情况下很有用。我们说明了这一点，特别是为n=3的规则多面体，并获得解析近似的解决方案的莱恩-埃姆登方程，有效的相对论性退化的大部分恒星（大质量白矮星）和化学均匀的恒星在辐射平衡（ZAMS星）。
英文摘要：
In scale invariant hydrostatic barotropes, the radial evolutionary equation linearly relates the local gravitational and internal energies. From this first-order equation, directly follow all the properties of polytropes and the important mass-radius relation. Quadrature then leads to the regular Lane-Emden functions and their Picard and Pade approximations, which are useful wherever stars are approximately or exactly polytropic. We illustrate this particularly for the n=3 regular polytrope and obtain analytic approximations to the solution of the Lane-Emden equation, valid over the bulk of relativistic degenerate stars (massive white dwarfs) and chemically homogeneous stars in radiative equilibrium (ZAMS stars).
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