臺灣博碩士論文加值系統

當行星通過其恆星盤面時, 恆星的亮度會下降, 我們稱其現象為 ”凌日”. 最近,凌日法成為一種尋找太陽系外行星的普遍方式. 許多被證實的行星系統顯示, 恆星的 ”臨邊昏暗效應” 是重要且不可被忽略的. 我們希望發展出一種方法, 建立一種囊括了 ”臨邊昏暗效應” 的凌日光度曲線理論模型. 透過我們的方法, OGLE-TR-211行星系統的觀測資料可以決定行星的物理和軌道參數. 此外, 我們計算出最佳的軌道參數,和參數平面在90%的信心區域. 再者, 我們研究了恆星的徑向速度. 我們主要是利用徑向速度來決定行星的質量.

The transit, i.e. the flux-drop of a star due to the passing of a planet, has recently become one of the most popular methods in the search of extra-solar planets,
and those confirmed cases show that the limb-darkening effect is important and cannot be ignored. We here develop a method to do the theoretical modeling of the transit light curves when the limb-darkening is included. Through our method, the observational data of a few planetary systems is used to determine the physical and orbital parameters. In addition to the best fitting parameters of planetary systems, the regions of the parameter space at different confidence levels will be presented. Finally, the effects of additional data of the host star's radial velocities are also investigated.

1 Introduction 1
2 The Model 3
2.1 The Orbits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.2 The Limb Darkening Effect . . . . . . . . . . . . . . . . . . . . . . . 6
2.3 The Method to Calculate Theoretical Fluxes . . . . . . . . . . . . . 10
2.3.1 Un-occulted Case . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.3.2 Partly Occulted Case . . . . . . . . . . . . . . . . . . . . . . . 10
2.3.3 Completely Occulted Case . . . . . . . . . . . . . . . . . . . . 11
2.4 The Effect of Parameters . . . . . . . . . . . . . . . . . . . . . . . . . 13
3 The Chi-Square Fitting and Confidence Level 18
3.1 The Chi-Square Fitting . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.2 Confidence Level . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.3 The Derivatives of Flux . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.3.1 The Derivatives of • . . . . . . . . . . . . . . . . . . . . . . . 21
3.3.2 Un-Occulted Case . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.3.3 Partly Occulted Case . . . . . . . . . . . . . . . . . . . . . . . 22
3.3.4 Completely Occulted Case . . . . . . . . . . . . . . . . . . . . 24
4 The Result 28
4.1 The Observational Data . . . . . . . . . . . . . . . . . . . . . . . . . 28
4.1.1 The Host Star . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
4.1.2 The Photometric Data . . . . . . . . . . . . . . . . . . . . . . 29
4.2 The Z-folding Method . . . . . . . . . . . . . . . . . . . . . . . . . . 31
4.3 The Best Fitting Parameters . . . . . . . . . . . . . . . . . . . . . . . 34
5 Radial Velocities 40
5.1 The Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
5.1.1 The Stellar Radial Velocity . . . . . . . . . . . . . . . . . . . 42
5.1.2 The Effect of Parameters . . . . . . . . . . . . . . . . . . . . . 43
5.2 Radial Velocity Data . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
5.2.1 Chi Square ‾fitting . . . . . . . . . . . . . . . . . . . . . . . . . 43
6 Conclusions and Future Work 47
6.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
6.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

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