系外行星系統的研究在近幾十年來發展迅速。在發現系外行星的方法中， 一種被稱為凌星時間變化的方法，已被證實對了解系外行星的運動狀態和 偵測其他的系外行星是非常有用的。除了用於發現新的系外行星外，其透射 光譜也經常用於了解該系外行星之大氣。在本研究中，我們對兩個選定的目 標:HAT-P-37 b (熱木星) 及HAT-P-26 b (海王星質量之行星) 進行了分析其凌 星時間變化和透射光譜的研究。
我們將展示HAT-P-37 b 的地面光度觀測結果，並利用此結果和過往的光度 曲線及先前發表之數據來計算更為精準的行星參數。從凌星時間變化之分析， 其訊號強度約為1.74 ± 0.17 分鐘，此變化可以由一顆小於地球質量的行星在1:2 的共振軌道上，與HAT-P-37 b 的重力交互作用產生。我們推論此系統有可能有 其他行星。對於此第二顆行星的質量上限分析，我們可以排除軌道週期小於六 天的土星質量行星。另外，HAT-P-37 b 的寬波帶透射光譜，顯示其擁有雲狀大 氣模型。
對於HAT-P-26 b，透過了SPEARNET 望遠鏡所進行的多頻帶地面光度 觀測資料，我們展示了新的凌星光度曲線。這些新的光度曲線，結合來 自HST、TESS 和先前發表的地面數據的光度曲線，我們計算出更精準的HAT- P-26 b 行星參數。凌星時間變化的分析結果顯示訊號強度為1.98 ± 0.05 分鐘， 這可能是由於在1:2 共振軌道上的另一顆約0.02倍木星質量的行星所致。而其大氣組成分析顯示HAT-P-26 b 的大氣含有約2.4+2.9-1.6% 的水，其溫度約為590+60−50 K。

In recent decades, the study of exoplanetary systems has grown rapidly. One successful method used for discovering exoplanets is called Transit Timing Varia- tions (TTVs), which have proven effective for studying exoplanetary dynamics and detecting additional planets. Beyond the detection of new exoplanets, transmis- sion spectroscopy is used to characterize planetary atmospheres. In this study, we performed TTVs analysis and transmission spectroscopy studies for the selected targets: the hot Jupiter HAT-P-37 b and the Neptune-mass planet HAT-P-26 b. We presented our ground-based photometric observations of HAT-P-37 b and refined the planetary parameters using both our light curves and previously pub- lished data. The possibility of an additional planet is inferred by the TTVs ampli- tude signal of 1.74 ± 0.17 minutes, which could be explained by the gravitational interaction of a sub-Earth mass planet at the 1:2 mean-motion resonance. From the analysis of an upper mass limit for the second planet, the Saturn-mass planet with an orbital period less than 6 days is excluded. The broad-band transmission spectra of HAT-P-37 b favor a cloudy atmospheric model with an outlier spectrum in the B-filter.
For HAT-P-26 b, we presented a new set of transit light curves obtained through the multiband photometric ground-based observations conducted by the SPEARNET telescopes network. These new light curves were combined with the light curves from the HST, TESS, and previously published ground-based data. We refined the planetary parameters of HAT-P-26 b. The TTV analysis shows an amplitude signal of 1.98 ± 0.05 minutes, which could result from the presence of an additional ∼ 0.02 MJup planet at the 1:2 mean-motion resonance orbit. The atmospheric composition analysis demonstrated that the atmosphere of HAT-P-26 b contains 2.4+2.9-1.6% of H2O, with a derived temperature of 590+60 K.

Abstract (Chinese).................. I
Abstract............................ II
Contents............................ III
List of Figures..................... VI
List of Tables...................... IX
1 Introduction...................... 1
2 Methodology........................ 6
2.1 TransitExoplanet............................ 6
2.2 StellarLimbDarkening......................... 7
2.3 DynamicExoplanet........................... 9
2.3.1 TransitTimingVariations(TTVs) ..................... 9
2.3.2 Upper-mass Limit for an Additional Planet ..........11
2.4 Detection of Exoplanet Atmosphere by using Transmission Spec-
troscopy................................. 12
2.5 AnOverviewofNumericalTools ................... 14
2.5.1 MarkovChainMonteCarlo(MCMC) ................. 14
2.5.2 NestedSampling ........................ 15
2.6 Implements ............................... 16
3 Investigating Transit Timing of HAT-P-37 b.. 17
3.1 Background ............................... 17
3.2 ObservationalData........................... 18
3.2.1 Photmetric Follow-up Observations and Data Reduction....18
3.2.2 LiteratureData......................... 20
3.3 Light-CurveModeling ......................... 21
3.4 ObservedNoise ............................. 23
3.5 TransitTimingAnalysis ...................... 26
3.5.1 TimingVariationModeling .................. 26
3.5.2 TheFrequencyAnalysisofTTVs ............... 30
3.5.3 UpperMassLimitforanAdditionalPlanet ...... 36
4 Investigating Transit Timing of HAT-P-26 b..... 39
4.1 Background ............................... 39
4.2 ObservationalData........................... 41
4.2.1 SPEARNET Observations and Data Reduction ...41
4.2.2 ExistingGround-basedData................... 44
4.2.3 HSTWFC3GrismData ................... 45
4.2.4 TESSData ........................... 46
4.3 Light-CurveModeling ......................... 46
4.4 ObservedNoise ............................. 58
4.5 TransitTimingAnalysis ........................ 60
4.5.1 ARefinedEphemeris...................... 60
4.5.2 TheFrequencyAnalysisofTTVs ............... 62
5 Transmission Spectroscopy............... 67
5.1 TheTransmissionSpectrumofHAT-P-37b ..............67
5.2 TheAtmosphericModelingofHAT-P-26b ...............72
6 Summaries and Conclusions..................... 80
6.1 ThehotJupiterHAT-P-37b...................... 80
6.2 TheNeptune-massplanetHAT-P-26b ............. 82
6.3 FutureWork............................... 83
Bibliography..................................85

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