论文标题
平衡I的嵌套球形图。刚性旋转的近似解决方案
Nested spheroidal figures of equilibrium I. Approximate solutions for rigid rotations
论文作者
论文摘要
我们讨论了由两个均质成分组成的身体的平衡条件，这些组件被块状球体表面和相对运动。尽管不允许确切的溶液进行刚性旋转（除非特定的环境压力），但是对于涉及小共聚焦参数的配置，可以获得近似值。然后，该问题取决于沿公共界面的压力（与圆柱半径的恒定或二次）接收两个溶液家族。在这两种情况下，我们都会给予压力和旋转速率，这是分数半径，椭圆度和质量密度跳跃的函数。允许各种程度的平坦程度，但正如经典理论所知道的那样（例如，共焦和螺旋溶液的不可能，椭圆度向外梯度）。相对旋转状态的约束要小得多，但是这些需要质量密度的跳跃。这种分析方法与从自洽场方法获得的数值解决方案成功进行了比较。实用公式以适合缓慢旋转的恒星/行星内饰的小椭圆率的极限得出。
We discuss the equilibrium conditions for a body made of two homogeneous components separated by oblate spheroidal surfaces and in relative motion. While exact solutions are not permitted for rigid rotation (unless a specific ambient pressure), approximations can be obtained for configurations involving a small confocal parameter. The problem then admits two families of solutions, depending on the pressure along the common interface (constant or quadratic with the cylindrical radius). We give in both cases the pressure and the rotation rates as a function of the fractional radius, ellipticities and mass-density jump. Various degrees of flattening are allowed but there are severe limitations for global rotation, as already known from classical theory (e.g. impossibility of confocal and coelliptical solutions, gradient of ellipticity outward). States of relative rotation are much less constrained, but these require a mass-density jump. This analytical approach compares successfully with the numerical solutions obtained from the Self-Consistent-Field method. Practical formula are derived in the limit of small ellipticities appropriate for slowly-rotating star/planet interiors.
