On Self-Gravitating Polytropic Cylinders and Slabs

M. N. Anandaram
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Abstract

In this review paper the 2-D Lane-Emden equation (LEEq) model of a self-gravitating gas distribution in the form of an infinitely long cylinder shaped polytrope of finite radius is obtained and its basic radial properties are outlined. Similarly reviewed is the derivation of the 1-D LEEq model of an infinitely wide planar polytrope of finite thickness and its basic properties across thickness are discussed. These two polytropes are solved numerically along with the 3-D models for comparison using the 2 nd order Euler-Richardson method (ERM) and their index based parameters are determined. The Python script used in these computations has been shown to be not only fast but is capable of matching fourth order performance. However, these models are found to have finite radii for all polytropic indices unlike the restricted spherical analogs and have astrophysical applications. Distortion due to rotation in polytropic rings has also been computed using ERM.
关于自重力多向圆柱体和平板
本文建立了具有有限半径的无限长圆柱形多向体形式的自重力气体分布的二维Lane-Emden方程(LEEq)模型,并概述了其基本径向性质。同样回顾了有限厚度的无限宽平面多面体的一维LEEq模型的推导,并讨论了其跨厚度的基本性质。采用二阶欧拉-理查德森法(ERM)对这两种多面体进行数值求解,并结合三维模型进行比较,确定了它们的指标参数。在这些计算中使用的Python脚本已被证明不仅速度快,而且能够匹配四阶性能。然而,与受限制的球形类似物不同,这些模型对于所有多向指数具有有限的半径,并且具有天体物理应用。用ERM计算了多向环旋转引起的畸变。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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