Asymptotic expressions for the angular dependence of low‐frequency pulsation modes in rotating stars
Asymptotic expressions for the angular dependence of low‐frequency pulsation modes in rotating stars
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旋转恒星低频脉动模式的角度依赖性的渐近表达式
DOI：
10.1046/j.1365-8711.2003.06379.x
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发表时间：
2003
影响因子：
4.8
通讯作者：
R. Townsend
中科院分区：
文献类型：
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作者：
R. Townsend
通过解近似描述赤道俘获波传播的拉普拉斯潮汐方程，得到了均匀旋转恒星中脉动模式的角度依赖性的解析表达式。当旋转频率和脉动频率之比变大时，这些表达式接近低频脉动方程的精确解。
找到了四类渐近解，分别对应于g（重力惯性）、r（Rossby）、Kelvin和柳井模。开尔文模是通过比涡守恒而产生的，很像r模，但传播的方向与旋转相同;它们被认为是扇形模的等价物。如果旋转足够快，则逆柳井模的行为类似于g模;否则，后者表现出r模的特征。
潮汐方程的渐近解和数值解之间的比较表明，前者迅速收敛到后者，g和柳井模式。开尔文和r模式的收敛较慢，因为只有当旋转非常快时，这些模式才会被赤道捕获。有人认为，效用的渐近解不依赖于他们的准确性，但也有价值的物理见解，他们能够提供。
Through the solution of Laplace's tidal equations, approximated to describe equatorially trapped wave propagation, analytical expressions are obtained for the angular dependence of pulsation modes in uniformly rotating stars. As the ratio between rotation and pulsation frequencies becomes large, these expressions approach the exact solutions of the governing low-frequency pulsation equations.
Four classes of asymptotic solution are found, corresponding to g (gravito-inertial), r (Rossby), Kelvin and Yanai modes. The Kelvin modes arise through the conservation of specific vorticity, much like the r modes, but propagate in the same sense as the rotation; they are found to be the equivalents of prograde sectoral modes. The prograde Yanai modes behave like g modes, as do the retrograde ones if the rotation is sufficiently rapid; otherwise, the latter exhibit the character of r modes.
Comparison between asymptotic and numerical solutions to the tidal equations reveals that the former converge rapidly towards the latter, for g and Yanai modes. The convergence is slower for Kelvin and r modes, as these become equatorially trapped only when the rotation is very rapid. It is argued that the utility of the asymptotic solutions does not rest on their accuracy alone, but also on the valuable physical insights that they are capable of providing.