标题： 从维度约化角度研究旋转体的结构 显示英文标题

标题： Approaching the structure of rotating bodies from dimension reduction

摘要： 我们证明了通过假设纯粹的球状分层结构，可以相对精确地获取刚性旋转的自引力物体的二维结构。 在此假设下，二维问题变为一维问题，并且涉及根据赤道面质量密度和等密线的偏心率来求解两个耦合的固定点方程。 我们提出了一种基于自洽场方法的简单算法来解决此问题。 与完整的无约束表面二维问题相比，归一化焓场的精度绝对值优于$10^{-3}$，计算时间也大幅减少。 此外，这种一维方法非常适合快速旋转天体，适用于任意密度分布（包括任意准静态状态方程），并且能够解释系统中的质量密度跃迁，包括存在环境压力的情况。 给出了多个测试实例。 显示英文摘要

摘要： We show that the two-dimensional structure of a rigidly rotating self-gravitating body is accessible with relatively good precision by assuming a purely spheroidal stratification. With this hypothesis, the two-dimensional problem becomes one-dimensional, and consists in solving two coupled fixed-point equations in terms of equatorial mass density and eccentricity of isopycnics. We propose a simple algorithm of resolution based on the self-consistent field method. Compared to the full unconstrained-surface two-dimensional problem, the precision in the normalized enthalpy field is better than $10^{-3}$ in absolute, and the computing time is drastically reduced. In addition, this one-dimensional approach is fully appropriate to fast rotators, works for any density profile (including any barotropic equation of state), and can account for mass density jumps in the system, including the existence of an ambient pressure. Several tests are given.