關於 Ia 型超新星，人們普遍相信它的形成是來自於密近雙星系統內，碳氧白 矮星在吸積物質的過程中產生了熱核爆炸後的結果。它們有著極亮的光度與可校 準的光度曲線，這些特色使他們活躍於探測宇宙膨脹的研究當中。然而，Ia 型超 新星的前身星系統時至今日都仍是個謎，這使得它們在宇宙學上的使用受到了一 定程度的限制。近期有研究表明，噴發物速度較高(大於每秒一萬兩千公里)的 Ia 型超新星，其宿主星系似乎有著質量較大、金屬豐度較高等特徵 。在理論研究 方面，亦有學者認為噴發物速度很有機會能用於區分不同 Ia 型超新星的前身星系 統。
在本篇論文中，我們將測量可見光光譜中 SiII6355 吸收線的速度。母樣本 當中的 Ia 型超新星皆是由 Pan-STARRS1 Medium Deep Survey(PS1 MDS)所發 現的。鑑於大部分 PS1 MDS 的 Ia 型超新星紅移都偏高(中位數約為 0.3)，它們 光譜的訊噪比通常較一般低紅移的光譜要來得更低。因此我們採用了一種特殊方 法來平滑這些光譜，讓我們能更準確的測量出超新星樣本的噴發物速度。為了研 究 Ia 型超新星之噴發物速度與紅移之間的潛在關係，並以此來增進 Ia 型超新星 在宇宙學應用上的準確度。我們將透過一些數學方法分析高噴發物速度 Ia 型和正 常噴發物速度 Ia 型之間是否有統計學意義上的差異，並進行討論。

Type Ia Supernovae (SNe Ia) are exceptionally bright explosions, and their calibrateable brightness make them powerful tools in probing the cosmic expansion. However, the progenitors of SNe Ia are still unclear. This could introduce uncertainties in their use in cosmology. Recent studies have shown that the ejecta velocity is an important variable in controlling SN Ia luminosities, even after the standard light-curve shape and color corrections have been performed. Theoretical studies also suggested that ejecta velocity could be promising in disentangling different SN Ia progenitor scenarios.
In this work, we will measure the ejecta velocity from Si II 6355 absorptions line in the optical spectra. We will use SNe Ia discovered by Pan-STARRS1 Medium Deep Survey (PS1 MDS) as our parent sample. Given that a large fraction of PS1 MDS SNe Ia are at high redshift (with a median redshift of ~0.3), their spectra are generally noisier than that of local sample. We will adopt a unique method to smooth these spectra and help us better determine the ejecta velocities of these SNe. We aim to investigate the relation between SN Ia ejecta velocities and the redshift. Our high-redshift SN Ia sample will allow us to study the potential evolution with the redshift, which is crucial for a high-precision cosmology.

目錄
摘要·································· I
Abstract·································· II
目錄·································· III
圖目錄·································· V
表目錄·································· VI
第一章、緒論(Introduction) ·································· 1
1.1 超新星的各種類別(Supernovae classification)·································· 2
1.2 Ia 型超新星的光度曲線與光譜(Light curve and spectra of SN Ia) ················ 3
1.3 Ia 型超新星的前身系統(SN Ia progenitor system) ······························· 4
1.4 Ia 型超新星在宇宙學當中的應用(Cosmological use of SN Ia)·························7
1.5 Ia 型超新星之噴發物速度的相關研究(Ejecta velocity of SN Ia) ····················· 8
1.6 論文簡述(Outline of this thesis)············································· 10
第二章、 觀測與資料處理(Observation and data reduction)·····························11
2.1 泛星計畫(Pan-STARRS) ························································ 11
2.2 儀器與觀測(Instruments and observations) ····································· 13
2.3 預處理與目標篩選(Reduction and data selection)································ 16
第三章、資料分析與結果(Data Analysis and Results) ·································· 19
3.1 分析方法與公式································································· 19
3.1.1 逆方差加權高斯濾波器(inverse-variance-weighted Gaussian filter)··············· 19
3.1.2 如何取得方差譜(variance spectrum)以及決定平滑因子(smoothing factor)···· 21
3.2 從光譜數據中求得 Si II λ6355 的噴發速度·········································· 23
第四章、討論(Discussion)··························································· 28
4.1 額外的低紅移數據(Additional Low Redshift SNe Ia Data)······························· 28
4.2 矽譜線速度與紅移的關係(Relation between SNe Ia silicon velocity and their redshift)··· 30
第五章、結論(Conclusion) ······························································· 35
5.1 總結(Summary) ····································································· 35
5.2 未來的研究方向(Future work)·························································· 35
參考資料(Reference)···································································· 36
附錄一:PS1-MDS 之超新星觀測與測量數據表················································ 38
附錄二:PS1-MDS 之超新星光譜與測量數據圖················································ 39

1. Arnett W. D., 1969, AP&SS, 5, 180
2. Blondin S. et al., 2006, AJ, 131, 1648
3. Blondin S., Tonry J. L., 2007, ApJ, 666, 1024
4. Bloom J. S. et al., 2012a, ApJ, 744, L17
5. Branch D., Tammann G. A., 1992, ARA&A, 30, 359
6. Colgate S. A., McKee C., 1969, ApJ, 157, 623
7. Conley A. et al., 2008, ApJ, 681, 482
8. Dettman K. G. et al., 2021, ApJ, 923, 267
9. Filippenko A. V. et al., 1992a, AJ, 104, 1543
10. Filippenko A. V. et al., 1992b, ApJ, 384, L15
11. Filippenko A. V., 1997, ARA&A, 35, 309
12. Henry R. B. C., Worthey G., 1999, PASP, 111, 919
13. Hoeflich P. et al., 1996, ApJ, 472, L81
14. Homeier D. et al., 1998, A&A, 338, 563
15. Hoyle F., Fowler W. A., 1960, ApJ, 132, 565
16. Huterer D., Turner M. S., 1999, Phys. Rev. D, 60, 081301
17. Iben Jr. I., Tutukov A. V., 1984, ApJS, 54, 335
18. Jha S., Riess A. G., Kirshner R. P., 2007, ApJ, 659, 122
19. Kessler R. et al., 2009, ApJS, 185, 32
20. Li W. D. et al., 2000, in AIP Conf. Proc. 522, Cosmic Explosions, ed. S. S. Holt &
W. W. Zhang (New York: AIP)
21. Miknaitis G. et al., 2007, ApJ, 666, 674
22. Minkowski R., 1941, PASP, 53, 224
23. Nugent P. E. et al., 2011, Nature, 480, 344
36
24. Pan Y. C., 2015, MNRAS, 446, 354
25. Pan Y. C., 2020, ApJL, 895, L5
26. Phillips M. M. et al., 1992, AJ, 103, 1632
27. Phillips M. M. et al., 1999, AJ, 118, 1766
28. Phillips M. M., 1993, ApJ, 413, L105
29. Polin A., Nugent P., Kasen D., 2019, ApJ, 873, 84
30. Rest A. et al., 2014, ApJ, 795, 44
31. Riess A. G. et al., 1998, AJ, 116, 1009
32. Riess A. G. et al., 2007, ApJ, 659, 98
33. Riess A. G., Press W. H., Kirshner R. P., 1996, ApJ, 473, 88
34. Scolnic D. et al., 2015, ApJ, 815, 117
35. Scolnic D. M. et al., 2018, ApJ, 859, 101
36. Siebert M. R. et al., 2019, MNRAS, 486, 5785
37. Siess L., Lebreuilly U., 2018, A&A, 614, A99
38. Sullivan M. et al., 2010, MNRAS, 406, 782
39. Sullivan M., et al., 2011b, ApJ, 737, 102
40. Suzuki N., et al., 2012, ApJ, 746, 85
41. Tripp R., 1998, A&A, 331, 815
42. Turatto M., 2003, Supernovae and Gamma-Ray Bursters. Edited by K. Weiler.,
Lecture Notes in Physics, vol. 598, p.21-36
43. Wang X. et al., 2009, ApJ, 699, L139
44. Wang X. et al., 2013, Science, 340, 170
45. Wheeler J. C., Harkness R. P., 1990, Rep. Prog. Phys., 53, 1467
46. Whelan J., Iben Jr. I., 1973, ApJ, 186, 1007
47. Zhang K. D. et al., 2020, MNRAS, 499, 5325