臺灣博碩士論文加值系統

宇宙中的暗物質可能為模糊暗物質所組成。當模糊暗物質的質量小於10^{−22} eV時，它不但能有和冷暗物質一樣的大尺度結構，同時它也能解決冷暗物質所碰到的“小尺度危機”。利用最近兩組Lyman-α觀測的數據(BOSS 和 XQ-100)，一些研究推測模糊暗物質的最低可允許質量應該要被提高到10^{−21} eV。但是這個最低允許質量是由一個冷暗物質的模擬加上模糊暗物質的初始狀態所得出，並沒有考慮模糊暗物質的額外效應:量子壓力。量子壓力可能會在尺度小的地方產生不可忽略的效應。在利用一維模擬確認我們的方法的有效性後，我們有系統地從宇宙尺度模擬探究量子壓力的效應，並且發現在小尺度區間，量子壓力會對物質功率頻譜和暗物質暈質量方程式造成額外的抑制。此外我們計算了相對應於Lyman-α觀測的通量功率頻譜並和 BOSS 和 XQ-100 的數據做比較。我們仔細地探討計算通量功率頻譜時的誤差和氫原子氣體溫度造成的誤差，並推斷一旦適當地考慮量子壓力的效應和中性氫原子氣體溫度所造成的誤差就不能以統計上顯著地排除能解決小尺度危機的質量區間 (質量小於10^{−22} eV的模糊暗物質)。

Fuzzy dark matter is one of the dark matter candidates, which can not only have the same large-scale success of cold dark matter but also alleviates the ”small scale crisis” of it when the fuzzy dark matter mass is smaller than 10^{−22} eV. With recent Lyman-alpha forest data from BOSS and XQ-100, some studies suggested that the lower mass limit on the fuzzy dark matter particles is lifted up to 10^{−21} eV. However, such a limit was obtained by cold dark matter simulations with the fuzzy dark matter initial condition and the quantum pressure of fuzzy dark matter was not taken into account which could have generated non-trivial effects on small scales. After checking the validity of our methodology using one-dimensional simulation, we investigate the effects of quantum pressure in cosmological simulations systematically, and find that quantum pressure leads to further suppression on the matter power spectrum on small scales, as well as the halo mass function in the low mass end. Furthermore, we estimate the one-dimensional flux power spectrum of Lyman-alpha forest, and compare it with the data from BOSS and XQ-100. We carefully estimate the uncertainty in the calculation of one-dimensional flux power spectrum due to the temperature of hydrogen gas. We conclude that if one properly takes into account the effect of quantum pressure and the temperature of the hydrogen gas, one cannot exclude the fuzzy dark matter of mass smaller than 10^{−22} eV, which is the interesting mass range for solving the small scale crisis, at statistically significant levels.

Contents ii
List of Tables iii
List of Figures vii
Chapter 1: Introduction .......................... 1
Chapter 2: Fuzzy Dark Matter Model .......................... 4
2.1 Brief History of FDM .......................... 4
2.2 The Physics of FDM .......................... 5
2.3 Implementation of FDM in Simulations .......................... 6
2.4 Dark Halo Structure of FDM .......................... 7
Chapter 3: Lyman-alpha Forest .......................... 10
3.1 Basic Concept of Lyman-alpha Forest .......................... 10
3.2 BOSS and XQ-100 .......................... 13
Chapter 4: Methodology .......................... 15
4.1 Quantum Pressure as Particle-Particle Interaction .......................... 15
4.2 Verification of the Particle-Particle method .......................... 19
4.3 Simulation Settings and Initial Condition .......................... 22
4.4 1D Flux Power Spectrum .......................... 25
Chapter 5: Numerical Result .......................... 28
5.1 Density Field and Halo Mass Function .......................... 28
5.2 Impacts on Lyman-alpha Forest Fitting .......................... 32
Chapter 6: Systematic Uncertainty Discussion .......................... 38
6.1 Simulation Uncertainty .......................... 38
6.2 Gas Temperature Uncertainty .......................... 40
Chapter 7: Conclusion and Prospect .......................... 44
Appendix .......................... 45
A. From the Quantum Pressure to the Acceleration .......................... 45
B. Generalization to an Expanding Universe .......................... 45
References .......................... 52