臺灣博碩士論文加值系統

我們用固有函數展開分析了純量場暗物質暈的模擬。純量場暗物質符合泊松-薛丁格方程式，在宇宙晚期，當暗物質暈達成均功條件時，我們可以解不隨時間變的薛丁格方程式，並且得到固有函數跟相對應的機率振福，我們發現機率分布函數的形式可以被古典無碰撞且會被自身重力影響的系統的機率分布函數描述，另外，我們發展了一個可以解出自洽的密度與重力位勢符的方法，這些解符合泊松-薛丁格方程式並且是平衡態，他的機率分布函數符合費米金模型。我們也使用模擬測試以自洽重力位勢造出來的暗物質暈的穩定性。

We analyze the simulation result of non-interacting scalar eld dark matter halos using energy eigenfunction expansion. The scalar eld dark matter obeys the Poisson-Schrodinger (SP) equation. At late time, when the dark matter halos are virialized, we can solve time independent Schrodinger equation and obtain amplitude of each eigenmode. We nd that the distribution function (DF) of the dark matter halos can be described by models of classical distribution functions, and we develop a method to solve potential and density of a spherically symmetric Schrodinger-Poisson system whose distribution function obeys fermionic King model. Also, we construct arti cial dark matter halos using di erent potentials, and test their stability. The amplitudes of the arti cial halos are generated by fermionic King model.

Contents
Contents i
List of Figures iii
1 Introduction 1
2 Equations and methods 3
2.1 The Schrodinger-Poisson equation . . . . . . . . . . . . . . . . . . . . 3
2.2 Distribution function . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.3 Procedure of solving eigenfunctions and amplitudes . . . . . . . . . . 7
2.4 Models of distribution function for classical collisionless self-gravitating
system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.4.1 Distribution function depends on energy . . . . . . . . . . . . 11
2.4.2 Distribution function depends on energy and L2 . . . . . . . . 12
2.5 Solving self-consistent solutions of fermionic King model . . . . . . . 13
2.6 Method of constructing arti cial halos . . . . . . . . . . . . . . . . . 16
2.7 Time correlation function . . . . . . . . . . . . . . . . . . . . . . . . 17
3 Results 19
3.1 Probability distribution function . . . . . . . . . . . . . . . . . . . . . 19
3.2 Self-consistent solution of fermionic King model . . . . . . . . . . . . 23
3.3 Arti cial halos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.4 Time correlation function . . . . . . . . . . . . . . . . . . . . . . . . 28
4 Conclusion 45
Bibliography 46

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