The Size and Temperature Distributions of Spots and Faculae on Kepler-17 and Kepler-71

以作者查詢圖書館館藏

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姓名

張慈恆(Tzu-Heng Chang) 查詢紙本館藏

畢業系所

天文研究所

論文名稱

The Size and Temperature Distributions of Spots and Faculae on Kepler-17 and Kepler-71
(Kepler-17 和 Kepler-71 的黑子與光斑溫度與大小分布)

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摘要(中)

自從凌日法的發明後，該方法不只為系外行星的探索開啟了新的時代，也提出了磁場活動活躍的恆星更進一步的細節。一些系外行星繞行著太陽類型的恆星
，具有强烈的磁場活動，其特徵是在其表面形成大的黑子或亮斑(光斑)，如黑子/光斑的溫度和大小。這些非常重要的物理性質可以透過相應的光變曲線來得知，當行星遮擋住黑子時，我們儀器所測得的亮度會增加，因此在光變曲線中會有凸起的結構；反之，當光斑被行星遮掩時，我們儀器所測得的光度會增加，因此在光變曲線中會有凹下的結構。利用這些結構的高度以及寬度可以進而推得黑子以及光斑的溫度與大小。為了方便比較，我們使用兩顆相似類型且磁場活躍的恆星進行比較，Kepler-17以及Kepler-71皆屬於G型恆星，這兩顆的恆星的磁場活動也很活躍，且這兩顆恆星的行星軌道傾角也趨近於母恆星的赤道，因此當凌日發生時，我們所看到的黑子/光斑結構會更加的明顯。在我們的结果中，當黑子或光斑溫度越低时，黑子或光斑的大小就越大。另外，黑子溫度可能會受到半影溫度的影響，導致黑子平均溫度上升。Kepler-17和Kepler-71的光斑與黑子的面積比都大於1。這個结果表示，Kepler-17和Kepler-71都是光斑為主的不活躍恆星。另一方面，由於此方法從行星大小到黑子/光斑大小，以及步調信號皆會受限於觀測因素條件影響。因此，我們也發展出一套數值模擬來探索此方法對黑子與光斑的限制以及影響，而未來我們也將朝此方向進行研究。

摘要(英)

Since the development of the transit method, the approach opened a new era for exoplanet hunting and proposed advanced details of the stellar-magnetic structure. Some exoplanets hosting solar-type stars with intense magnetic activity can be characterized by forming large dark spots or bright spots (faculae) on their surfaces, such as spot temperature and size. These important physical properties are examined by the corresponding light curves during exoplanet transits. In this thesis, we will apply Kepler-17 and Kepler-71 as our targets. Both stars are G-type stars and the edge-on-planet orbit. And the light curve modulations are apparent, which means the active magnetic activity and easy to observe. We utilize Kepler short cadence data and derive the dark (or bright) spot radius and temperature equations from the transit light curve. In the results, as the dark (or bright) spot temperature is lower, the dark (or bright) spot size is larger. And the spot temperature may be affected by the penumbra temperature and make the higher average spot temperature. Both the area ratios of the facula-to-spot of Kepler-17 and Kepler-71 are more significant than 1. The result suggests that Kepler-17 and Kepler-71 are faculae dominant and inactive stars. Among many factors, the precision depends on the observational statistics, the ratio of the exoplanet′s size to that of the dark (or bright) spot, and the cadence used in the light curve measurements. Hence, we also have developed a numerical code to explore the effects and limitations of such a method for spots and faculae. And, this numerical method will be our direction for further research.

關鍵字(中)

★ 恆星黑子
★ 光斑
★ 凌日
★ 系外行星
★ 恆星活動

關鍵字(英)

★ Starspots
★ Faculae
★ Transit
★ Exoplanet
★ Stars activity

論文目次

1 Introduction 1
1.1 Transit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Starspots and faculae . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Target . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.3.1 Kepler-17 system . . . . . . . . . . . . . . . . . . . . . . . . 5
1.3.2 Kepler-71 system . . . . . . . . . . . . . . . . . . . . . . . . 6
2 Simulation 8
2.1 Limb-darkening effect . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2 Limb-darkening coefficients . . . . . . . . . . . . . . . . . . . . . . 8
2.3 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.4 Simulation light curve with different planet/spot size . . . . . . . 12
2.5 Time integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.6 Rspot vs Rp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.7 Spots and faculae simulation . . . . . . . . . . . . . . . . . . . . . 18
2.8 G, K, M type star . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3 TAP analysis 23
3.1 Observation data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.2 Transit Analysis Package . . . . . . . . . . . . . . . . . . . . . . . . 23
3.3 Temperature and radius calculation . . . . . . . . . . . . . . . . . 25
4 Results 32
4.1 Spots/Faculae temperature . . . . . . . . . . . . . . . . . . . . . . 32
4.2 Spots/Faculae size . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
iii
4.3 Relationship between spots/faculae size and temperature . . . . 35
5 Discussions 40
5.1 starspots/faculae size and temperature . . . . . . . . . . . . . . . 40
5.1.1 Radius . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
5.1.2 Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
5.2 Facula and spot ratio . . . . . . . . . . . . . . . . . . . . . . . . . . 43
6 Conclusions and Future works 45
7 Addendum 47
Bibliography 50
A Spots and faculae samples from Kepler-17 and Kepler-71 55
iv

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54

指導教授

葉永烜(Wing-Huen Ip)

審核日期

2022-9-19

推文