本篇論文包含兩個主題，第一篇已先發表於期刊 (Hsiang and Chang, 2021)。第一 篇主題為探討X射線脈衝星以及周圍X射線脈衝星雲間之關聯。我們總共收集三十 五顆目標星球，他們的輻射能由旋轉動能來供給，並且記錄其自旋、光譜相關參數 進行不同模型與數據擬合分析。我們將不同參數以對數形式組成一次函式，分別組 合不同參數進行數據擬合。結果顯示，關於脈衝星其中之一的自旋相關參數:旋轉 能量遞減率 E_dot與脈衝星亮度有強烈正相關性，與早期相關研究結論一致。此外， 我們發現脈衝星另一個自旋相關參數:光速圓柱域之磁場強度 (Magnetic field in light cylinder, B_lc) 同樣與脈衝星亮度也存在明顯正相關性。另一方面，我們新發現 脈衝星表面溫度與降冪模型之指數、特定自旋相關參數組合:P、 P_dot有著緊密的關 係:log(T^−1 * P^-0.5 * P_dot^0.125 )。這顯示出脈衝星表面溫度可能與其磁層中放射出的電漿粒子 對之能量散佈有強烈關聯，待與理論模型的建立比對進而解釋此結果。
第二篇主題探討小型康普頓偏極性儀 (Compton Polarimeter, Compol) 應用於觀 測伽瑪射線輻射源的偏極性。 於先前探討中， (Yang et al., 2020) 我們使用溴化 鈰 CeBr3 為其閃爍體材料，並根據計算推演及數據模擬，評估此儀器能觀測到天 鵝座X-1 伽瑪射線源 (Cygnus X-1)的偏極性。 因此，在本文中，我們嘗試更換釓 鎵鋁石榴石 (Gadolinium Aluminium Gallium Garnet, Gd3Al2Ga3O12, GAGG) 為閃 爍體材料，以及放大閃爍體矩陣的單位面積大小為 6mm ×6mm，避開溴化鈰易潮 解的特性，進一步探討其對於天鵝座X-1 伽瑪射線源偏極性的量測可行性。結果 顯示GAGG能有相對良好的表現。 此外，我們也以上述GAGG的模型來討論蟹狀 伽馬星雲及脈衝星系統於不同週期之偏極性的量測可行性。結果指出 Compol可量 測出此系統於Off-pulse phase 的偏極性，驗證 INTEGRAL/IBIS 46 % (Forot et al., 2008) 或是 INTEGRAL/SPI 72 % (Dean et al., 2008)發表的觀測結果，幫助我們得 到更準確的結果。此外，Compol也能驗證 Off-pulse phase裡面偏極性的特殊趨勢 (Vadawale et al., 2018)，及Bridge phase的偏極性，開拓以前至今我們對此相位的 理解，並且更了解這些輻射源的機制及形成原因。

This thesis is composed of two parts. In the first part, we report some connections between X-ray detected pulsar wind nebulae and their pulsars. We collected timing properties and spectral information from 35 rotational-powered pulsars. The fitting results agree with the earlier studies, which show there be a strong correlation between E ̇ and the pulsar’s luminosity. Moreover, we discovered the magnetic field in pulsar’s light cylinder (B_lc) also shows similar results to E_dot. On the other hand, the correlation between temperature from pulsar’s surface and the timing properties: P and P_dot fitting with the indices of non-thermal power-law model shows also strong: log(T^−1 * P^-0.5 * P_dot^0.125). This indicates pulsar’s surface temperature is highly related to energy distribution of the radiating pair plasma in pulsar’s magnetospheres. Most of the content has been published (Hsiang and Chang, 2021).
In the second part, we extended a previous study (Yang et al., 2020) of feasibility of measuring gamma ray polarization of Cygnus X-1 with considerations of different crystal size and material. We studied Compton Polarimeter (Compol) models of CeBr3 and Gadolinium Aluminium Gallium Garnet (GAGG) scintillators and of pixel sizesof3mm×3mmand6mm×6mm. Theresultsofdifferentmodelsis similar, except for the GAGG models in 400-2000 keV, which shows a somewhat better performance. We also studied the feasibility of measuring the polarization of the Crab using Compol. We found that with 10-Ms Crab observation, the Compol measurement can be expected to resolve the issue of discrepancy between INTEGRAL/IBIS and INTEGRAL/SPI results, which report 46 % (Forot et al., 2008), and larger than 72 % (Dean et al., 2008) polarization degree, respectively. Moreover, the polarization trend measured during off-pulse of the Crab and the polarization in the bridge phase (Vadawale et al., 2018) can also be examined. It’s possible to achieve 10-Ms observation in a two years space mission for the Crab.

Abstract...................................... i
大綱........................................ ii
Acknowledgments................................ iii
致謝........................................ iv
Contents................................ v
ListofFigures................................... vii
ListofTables................................... ix

I Non-thermal X-ray emissions of pulsar wind nebulae and their pulsars
1 Introduction 1
1.1 Pulsar wind nebulae and the connection with pulsars . . . . . . . . . . 1
1.2 Pulsars’timingproperties ......................... 2
1.3 Motivationandobjectiveofthisproject.................. 7
2 Data Selection 8
2.1 pulsar types included in database ..................... 11
2.1.1 Rotation-PoweredPulsars ..................... 11
2.1.2 Detailsofeachsource........................ 12
2.2 Pulsartypesexcludedfromdatabase ................... 12
2.2.1 AccretionpoweredBinaries .................... 12
2.2.2 PulsarwithMagnetar-likeOutbursts . . . . . . . . . . . . . . . 12
2.2.3 UnresolvedPulsarsorPWNe ................... 13
Non-thermal X-ray emissions of pulsar wind nebulae and their pulsars 13
Analysis 14
3.1 PrincipleofFittingMethods........................ 14
3.2 FittingParameters ............................. 14
4 Results 17
4.1 Correlations of Timing and Spectral Fitting Parameters . . . . . . . . . 17
4.1.1 One-variable Results ........................ 17
4.1.2 Two-variable Results ........................ 22
4.2 Thermal-variable Results.......................... 24
5 Discussion 27
5.1 Known Correlations Using Larger Samples . . . . . . . . . . . . . . . . 27
5.2 New correlated parameter: Blc ...................... 27
5.3 Surface Temperatureof Pulsars ...................... 28
5.4 AnOutlier: Millisecond Pulsar: PSRJ2124-3358. . . . . . . . . . . . . 29
6 Summary 30

II Feasibility of measuring Gamma-ray polarization from Cygnus X-1 and the Crab using small Compton polarimeter 30
7 Introduction 31
7.1 Motivationandobjectiveofthisproject. . . . . . . . . . . . . . . . . . 31
7.2 Instrumentconcept............................. 31 7.2.1 Structure .............................. 31
7.2.2 Scintillator.............................. 34
7.3 Polarization determination with Compton scattering . . . . . . . . . . 36
7.4 Megalib and the orbital background.................... 42
8 Measuring polarization from Cygnus X-1 with different Compol models 44
8.1 BriefintroductiontoCygnus-X1...................... 44
8.2 EffectiveareaandDataratestudy .................... 46
8.2.1 Effectivearea ............................ 46
8.2.2 Datarate .............................. 48
8.3 Maximumdetectablepolarization(MDP). . . . . . . . . . . . . . . . . 52
8.4 Discussion.................................. 56
9 Feasibility of measuring polarization from the Crab with Compol 57
9.1 BriefintroductiontotheCrab....................... 57
9.2 Maximum detectable polarization (MDP) achievable with 10-Ms observation .................................... 62
9.3 Discussion.................................. 67
10 Summary 69
Appendix A:
Supplemental information for individual pulsars studies in Part I 70
Appendix B:
Detailed information used in deriving Minimum detectable polariza- tion (MDP) in Part II 76

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