The ratio of small to large separations of acoustic oscillations as a diagnostic of the interior of solar-like stars
The ratio of small to large separations of acoustic oscillations as a diagnostic of the interior of solar-like stars
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DOI：
10.1051/0004-6361:20031318
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发表时间：
2003-11
影响因子：
6.5
通讯作者：
I. Roxburgh;S. Vorontsov
中科院分区：
文献类型：
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作者：
I. Roxburgh;S. Vorontsov
通过考虑具有相同内部结构但不同外层的恒星模型，我们证明了类太阳恒星中声学振荡的小间隔与大间隔的比率基本上与外层结构无关，并且仅由内部结构决定。定义标度欧拉压力扰动τ ε（ω，t）= rp ε/（ρc）1/2，我们通过关系式ω ε/（d ε/dt）= tan（ωt − π ε/ 2 + δ ε）定义内部相移δ ε（ω，t）。δ ε几乎与星核外的声学半径t = Δ dr/c无关，可以从内部的分波解中确定为ω的连续函数，即在星核外足够大的声学半径tf处满足拉普拉斯边界条件的任何ω的振荡方程的解。如果ω是本征频率，则它们满足本征频率方程ωT =（n + ω/ 2）π + α（ω）− δ（ω）w，其中α（ω）是独立表面相移（罗克斯堡& Vorontsov 2000）。利用这一结果，我们表明，小到大的分离的比例是由内部相移δ ′（ω），因此由内部结构单独确定的高精度。对这一结果的误差进行了估计，结果表明，这一结果的误差小于即将进行的MOST、COROT和Eddington空间飞行任务的频率测定误差（± 0.1-0.3 µHz）。
By considering stellar models with the same interior structure but different outer layers we demonstrate that the ratio of the small to large separations of acoustic oscillations in solar-like stars is essentially independent of the structure of the outer layers, and is determined solely by the interior structure. Defining the scaled Eulerian pressure perturbation ψ� (ω,t) = rp � /(ρc) 1/2 we define the internal phase shift δ� (ω,t) through the relation ωψ/(dψ/dt) = tan(ωt − π�/ 2 + δ� ). The δ� are almost independent of acoustic radius t = � dr/c outside the stellar core and can be determined as a continuous functions of ω from partial wave solutions for the interior - that is solutions of the oscillation equations for any ω that satisfy the Laplace boundary condition at a sufficiently large acoustic radius tf outside the stellar core. If the ω are eigenfrequencies then they satisfy the Eigenfrequency Equation ωT = (n + �/ 2)π + α(ω) − δ� (ω )w hereα(ω )i s theindependent surface phase shift (Roxburgh & Vorontsov 2000). Using this result we show that the ratio of small to large separations is determined to high accuracy solely by the internal phase shifts δ� (ω) and hence by the interior structure alone. The error in this result is estimated and shown to be smaller than that associated with the errors in the determination of the frequencies (≈0.1-0.3 µHz) from the upcoming space missions MOST, COROT and Eddington.