偏極化量測提供一個判斷天體內部機制與圖像的方法，例如磁場、吸積盤或噴流，但目前在MeV能量段的觀測仍然很少。偏極特性能夠給予不同天體內極端環境的線索，像是波霎、活躍星系核、黑洞和伽瑪射線爆。

康普頓散射被用來觀測伽碼射線能量段內的偏極。本篇論文使用基於Geant4的模擬分析工具MEGAlib進行蒙地卡羅模擬，呈現康普頓成像光譜儀(COSI)及康普頓偏光儀(Compol)兩個康普頓望遠鏡的偏極化性能分析。

康普頓成像光譜儀(COSI)為一密集康普頓望遠鏡，由高純度鍺探測器構成，在0.2至2.0 MeV波段中的偏極量測有高靈敏度。在2016年的太空氣球飛行任務中，COSI觀測到一顆長時間伽瑪射線爆GRB 160530A，並使用方位角散射分佈分析其偏極。為了確認COSI的偏極化儀器響應與系統誤差，我們於飛行前在實驗室進行偏極化性能驗證，量測藉由閃爍器散射放射源產生的一個部分偏極光束，然後將量測結果與模擬的未偏極放射源比較，以此確認系統誤差。在偏極調變與角度上，量測與模擬沒有明顯的系統誤差。在本篇論文中，除前述驗證結果外，也展示了COSI在不同通量伽瑪射線爆的可量測最小偏極值(MDP)。

在天文觀測中，立方衛星搭載的小型儀器也能達成有意義的應用。搭載於3U立方衛星的康普頓偏光儀(Compol)是一個以觀測天鵝座X-1偏極為目標的儀器，其包含使用矽探測器與溴化鈰閃爍器構成的六種模型。我們發現這些模型於低軌道傾角與低海拔的地球軌道上一百萬秒的正軸方向觀測中，可量測最小偏極值(MDP)能在160-250 keV波段中降低到10%、250-400 keV到20%跟400-2000 keV到65%，此結果呈現出一個3U立方衛星可提供天鵝座X-1在伽瑪波段偏極的有用資訊。

Polarization measurements offer a unique method to determine the emission mechanisms and source geometries (e.g. magnetic field, accretion disk, and jet), but there are still only few measurements in the MeV band. Determining the polarization characteristics will provide crucial clues about the extreme environments in different astrophysical sources such as pulsars, AGNs, Galactic black holes, and gamma­-ray bursts (GRBs).
Gamma-­ray polarization can be determined by Compton scattering. In this thesis, we use Monte Carlo simulations with a Geant4­-based MEGAlib package (Zoglauer et al., 2006) to study the polarimetric performance of two Compton telescopes: Compton Spectrometer and Imager (COSI) and Compton Polarimeter (Compol).
The Compton Spectrometer and Imager (COSI) is a compact Compton tele­ scope which is inherently sensitive to gamma­-ray polarization in the energy range of 0.2 – 2.0 MeV. A long duration gamma­-ray burst, GRB 160530A, was detected by COSI during its 2016 COSI's balloon flight. The polarization of GRB 160530A was constrained based on the distribution of azimuthal scattering angles from each incident photon inside COSI's germanium detector array (Lowell et al., 2017a). In order to determine COSI's polarization response and to identify systematic devia­tions from an ideal sinusoidal modulation, the polarization performance of COSI was validated in the laboratory prior to the 2016. A partially polarized beam was created by scattered emission from a radioactive source off a scintillator. In addi­tion, measurements and simulations of unpolarized radioactive sources were com­pared to validate our capability of capturing the instrument systematics in the sim­ulations. No statistically significant differences exist between the measured and simulated modulations and polarization angle, where the upper bound on the systematic error is 3% – 4% (Lowell, 2017). In this thesis, the aforementioned val­idation simulation is reported. The minimum detectable polarization of COSI for GRBs with different fluences is also presented. These results have been published in Yang et al. (2018).
Instruments flown on CubeSats are small. Meaningful applications of Cube­ Sats in astronomical observations rely on the choice of a particular subject that is feasible for CubeSats. Compol is the instrument to observe gamma-­ray polariza­tion from Cygnus X­-1 using a small Compton polarimeter on board a 3U CubeSat. Silicon detectors and cerium bromide scintillators were employed in the instru­ment models that we discuss in this study. We found that, with a 10 Ms on­ axis, zenith-­direction observation in a low­-inclination, low-­altitude, Earth-­orbit radia­tion background environment, the minimum detectable polarization degree can be down to about 10% in 160–250 keV, 20% in 250–400 keV, and 65% in 400–2000 keV. A 3U CubeSat dedicated to observing Cygnus X­-1 can therefore yield useful information on the polarization state of gamma-­ray emissions from the brightest persistent X­-ray black hole binary in the sky. These results have been published in Yang et al. (2020).

1 Introduction ........................... .................. 1
1.1 Gamma­ Ray Bursts......................................... 1
1.1.1 Overview of GRBs....................................... 2
1.1.2 Fireball Model ........................................ 5
1.1.3 Polarization of GRBs .................................. 5
1.2 Black Hole Binaries...................................... 6
1.2.1 V404 Cygni............................................. 7
1.2.2 Cygnus X­-1............................................. 7
2 The Working Principle of Compton Telescopes ............... 9
2.1 Compton Scattering....................................... 10
2.2 Polarization............................................. 11
2.2.1 Minimum Detectable Polarization ....................... 14
2.3 Reconstruction .......................................... 14
2.4 Event Selections......................................... 16
2.4.1 Energy Cut ............................................ 17
2.4.2 Angular Resolution Measure............................. 17
2.4.3 Distance Between Two Interactions ..................... 18
2.4.4 Earth Horizon Cut ..................................... 18
3 Compton Spectrometer and Imager (COSI) .................... 21
3.1 COSI Instruments......................................... 21
3.1.1 Detectors ............................................. 21
3.1.2 Cryostat and Cryocooler ............................... 22
3.1.3 Scintillator Shields .................................. 23
3.1.4 Missions .............................................. 24
3.2 Calibrations............................................. 27
3.3 Polarimetric Validation of COSI ......................... 27
3.3.1 Laboratory Setup....................................... 28
3.3.2 Simulation Runs ....................................... 29
3.3.3 Event Selections ...................................... 29
3.3.4 Polarization Analysis.................................. 31
3.4 Minimum Detectable Polarization (MDP) of Gamma­Ray Bursts by COSI ... 33
3.5 Summary ................................................. 35
4 Compton Polarimeter (Compol) .............................. 37
4.1 Motivation............................................... 37
4.2 Background Model ........................................ 38
4.3 Source Model (Cygnus X­-1) ............................... 39
4.4 Instrument Models ....................................... 40
4.5 Instrument Performance................................... 44
4.5.1 Detector Compton Efficiency ........................... 44
4.5.2 ShieldEffects.......................................... 46
4.5.3 Data Rate in LEO and Source Detection.................. 47
4.6 Minimum Detectable Polarization (MDP) of Cygnus X­1 by Compol ... 52
4.7 Summary ................................................. 54
A Detailed Information for Deriving the MDP in Section 4.6 ... 57
B Study on Some Modifications for Compol Model 1 ............ 63
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