Surface layer independent model fitting by phase matching: theory and application to HD 49933 and HD 177153 (aka Perky)
Surface layer independent model fitting by phase matching: theory and application to HD 49933 and HD 177153 (aka Perky)
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DOI：
10.1051/0004-6361/201425289
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发表时间：
2014-06
影响因子：
6.5
通讯作者：
I. Roxburgh
中科院分区：
文献类型：
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作者：
I. Roxburgh
目标。我们的目标是描述表面层独立的相位匹配模型拟合的理论，并将其应用到恒星HD 49933观测的CoRoT，和HD 177153（aka Perky）观测的开普勒。方法.我们使用理论分析、相移和模型拟合。结果定义了模型星星频率集的内、外相移，并证明了外相移（几乎）与度无关，内相移的函数（相函数）在外层坍缩为与频率无关的函数.然后，我们将展示如何使用这个结果的模型拟合技术，找到一个最适合的模型，以观察到的频率集，通过计算内部相移的模型使用观察到的频率，并确定在何种程度上的相函数崩溃到一个单一的功能，在外层的频率。这种技术不依赖于分配给观测频率的径向阶数n。我们给出了两个例子，应用这种技术的频率集的HD 49933观测的CoRoT和HD 177153（又名Perky）观测的开普勒，角直径和热通量的测量是可用的。对于HD 49933，我们发现一个非常广泛的模型与数据一致（所有对流核心过冲）-并得出结论，数据不够精确，无法对这颗星星的结构进行任何有用的限制。对于HD 177153，我们的最佳拟合模型没有对流核心，质量范围为1：15 - 1：17 M，年龄为4：45 - 4：70 - 10 - 9 yr，Z范围为0：021 - 0：024，XH = 0：71 - 0：72，Y = 0：256 - 0：266，混合长度参数= 1：8。我们将我们的结果与以前的研究进行了比较。我们对比的相位匹配技术，使用的比例小到大的分离，表明它避免了相关的问题，在分离比拟合和分配径向阶n的模式的错误。
Aims. Our aim is to describe the theory of surface layer independent model fitting by phase matching and to apply this to the stars HD 49933 observed by CoRoT, and HD 177153 (aka Perky) observed by Kepler. Methods. We use theoretical analysis, phase shifts, and model fitting. Results. We define the inner and outer phase shifts of a frequency set of a model star and show that the outer phase shifts are (almost) independent of degree ‘, and that a function of the inner phase shifts (the phase function) collapses to an ‘ independent function of frequency in the outer layers. We then show how to use this result in a model fitting technique to find a best fit model to an observed frequency set by calculating the inner phase shifts of a model using the observed frequencies and determining the extent to which the phase function collapses to a single function of frequency in the outer layers. This technique does not depend on the radial order n assigned to the observed frequencies. We give two examples applying this technique to the frequency sets of HD 49933 observed by CoRoT and HD 177153 (aka Perky) observed by Kepler, for which measurements of angular diameters and bolometric fluxes are available. For HD 49933 we find a very wide range of models to be consistent with the data (all with convective core overshooting) ‐ and conclude that the data is not precise enough to make any useful restrictions on the structure of this star. For HD 177153 our best fit models have no convective cores, masses in the range 1:15 1:17 M , ages of 4:45 4:70 10 9 yr, Z in the range 0:021 0:024, XH = 0:71 0:72, Y = 0:256 0:266 and mixing length parameter = 1:8. We compare our results to those of previous studies. We contrast the phase matching technique to that using the ratios of small to large separations, showing that it avoids the problem of correlated errors in separation ratio fitting and of assigning radial order n to the modes.