First Integrals of Adiabatic Stellar Oscillations
First Integrals of Adiabatic Stellar Oscillations
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绝热恒星振荡的一阶积分
DOI：
10.1093/pasj/58.4.759
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发表时间：
2006
影响因子：
2.3
通讯作者：
M. Takata
中科院分区：
文献类型：
--
作者：
M. Takata
本文用解析方法研究了恒星的线性绝热振荡方程。球对称恒星的非径向振动有两个已知的第一积分，它们存在于任何恒星结构中。一个是通过集成的径向振荡的情况下的线性化泊松方程。另一个是偶极振荡情况下的动量守恒。这两个积分都将微分方程的阶数从4降为2，这并不是微不足道的。我们发现，这个属性可以理解的事实，即绝热恒星振荡的问题可以制定为一个哈密顿系统。然后，我们研究的对称性的系统，对应于这些第一积分。我们最后表明，没有其他的第一个积分是有效的任意结构的恒星。
We consider the equations of linear adiabatic oscillations of stars analytically. There are two known first integrals of nonradial oscillations of spherically symmetric stars, which exist for any stellar structure. One is obtained by integrating the linearized Poisson equation in the case of radial oscillations. The other is derived from momentum conservation in the case of dipolar oscillations. Both of these integrals reduce the order of the differential equations from four to two, which is not trivial. We find that this property can be understood from the fact that the problem of adiabatic stellar oscillations can be formulated as a Hamiltonian system. We then examine the symmetry of the system that corresponds to these first integrals. We finally show that there is no other first integral that is valid for arbitrary structures of stars.