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R-mode oscillations of general relarivistic and rapidly rotating stars by the Cowling approximation

通过考林近似计算广义相对论和快速旋转恒星的 R 模式振荡

基本信息

批准号：
14540244
负责人：
ERIGUCHI Yoshiharu
金额：
$ 2.24万
依托单位：
The University of Tokyo
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2002
资助国家：
日本
起止时间：
2002 至 2003
项目状态：
已结题

项目摘要

We have succeeded in developing anew formulation for solving r-mode oscillations of general relativistic and rapidly rotating stars in the framework of the Cowling approximation. By following this formulation we have developed a numerical code and obtained r-mode oscillations of several equilibrium sequences of rapidly rotating general relativistic polytropes. In order to check the numerical code works properly, we have computed r-mode oscillations of rotating stars in the Newtonian limit as well as those of slowly rotating general relativistic stars and compared our results with those obtained by different methods. they agree very well. We have computed r-mode oscillations of uniformly rotating polytropic sequences with the polytropic indices N=0.5 and 1.0 whose strengths of gravity are M/R=0.1 and 0.2. Here M and R are the gravitational mass and the radius of the spherical stars. Oscillation frequencies and eigenfunctions of m=2 r-modes are obtained for the equilibrium sequences from the spherical configurations to the critical configurations of mass shedding limits. The important results are as follows. First, the rations of the eigenfirequencies of the r-modes to the angular velocityies of the unperturbed rotating stars depend scarcely on the polytropic indices. This is the same as that in the Newtonian case. Second, contrary to this, the strength of where T and W are the rotational energy and the gravitational energy, respectively. The values of a and b are a=1.4 and b=1.9 for M/R=0.1 and a=1.5 and b=1.2~1.3 for M/R=0.2. Our present results for barotropic stars imply that there could exist r-mode oscillations for rapidly rotating general relativistic stars.

我们已经成功地发展了在考林近似框架下求解广义相对论和快速旋转恒星的r模振荡的新公式。根据这个公式，我们开发了一个数值代码，并得到了几个快速旋转的广义相对论多向体的平衡序列的r型振荡。为了验证数值代码的正确性，我们计算了牛顿极限下旋转恒星和广义相对论慢速旋转恒星的r模振荡，并与不同方法得到的结果进行了比较。他们意见非常一致。我们计算了重力强度为M/R=0.1和0.2，多向指数N=0.5和1.0的均匀旋转多向序列的R -模振荡。这里M和R是引力质量和球形恒星的半径。得到了从球面构型到质量脱落极限临界构型的平衡序列m=2 r模态的振动频率和本征函数。重要的结果如下。首先，r模的特征频率与未扰动旋转恒星的角速度之比几乎不依赖于多向性指标。这和牛顿的情况是一样的。第二，与此相反，T和W分别为旋转能和引力能的强度。当M/R=0.1时，a和b的值分别为a=1.4和b=1.9，当M/R=0.2时，a=1.5和b=1.2~1.3。我们目前对正压性恒星的研究结果表明，快速旋转的广义相对论恒星可能存在r型振荡。