Ia型超新星對原始黑洞之限制｜國立清華大學博碩士論文庫

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研究生：	陳品融 Chen, Pin-Jung
論文名稱：	Ia型超新星對原始黑洞之限制 Constraints on Primordial Black Holes by Type Ia Supernovae
指導教授：	曾柏彥 Tseng, Po-Yen
口試委員:	張敬民 Cheung, Kingman 陳傳仁 Chen, Chuan-Ren
學位類別：	碩士 Master
系所名稱：	理學院 - 物理學系 Department of Physics
論文出版年：	2024
畢業學年度：	112
語文別：	英文
論文頁數：	89
中文關鍵詞：	原始黑洞、Ia型超新星、白矮星、暗物質、一階相變、暗域、黑洞
外文關鍵詞：	Primordial Black Hole, Type Ia Supernova, White Dwarf, Dark Matter, First-Order Phase Transition, Dark Sector, Black Hole
相關次數：	點閱：31 下載：5
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通過在暗域模型中的一階相變和Yukawa耦合，可以生成質量為$10^{-14}\,M_\odot - 10^{-11}\,M_\odot$的原始黑洞。當這種質量範圍內的原始黑洞穿過由碳和氧組成的白矮星時，在反應介質中發生的Bondi-Hoyle-Lyttleton吸積會產生衝擊波，從而在單個白矮星核心中引發直接爆震點火，最終導致Ia型超新星的發生。本研究的目的是通過對Ia型超新星發生率的計算和觀測結果，提供對原始黑洞的限制，即暗物質中原始黑洞所占的比例，這些對原始黑洞的限制無法由霍金輻射或重力微透鏡效應獲得。Ia型超新星傾向於由以下質量範圍的原始黑洞產生：在Navarro-Frenk-White暗物質分布下為[$7.59\times10^{-13}\,M_{\odot},6.11\times10^{-12}\,M_{\odot}$]，在等溫暗物質分布下為[$7.59\times10^{-13}\,M_{\odot},2.74\times10^{-12}\,M_{\odot}$]，在Kra暗物質分布下為[$9.98\times10^{-13}\,M_{\odot},1.99\times10^{-12}\,M_{\odot}$]，而在Moore暗物質分布下為[$3.11\times10^{-13}\,M_{\odot},1.51\times10^{-11}\,M_{\odot}$]。此外，重力波功率譜進一步表明，本論文提供之對原始黑洞的限制可以通過2040年代微赫茲重力波探測器$\mu$Ares得到驗證。

A primordial black hole (PBH) formation mechanism realised by first-order phase transition and Yukawa coupling in a dark sector model can generate PBHs of mass $10^{-14}\,M_\odot - 10^{-11}\,M_\odot$, and when a PBH within this mass range passes through a white dwarf (WD) made up of carbon and oxygen, Bondi-Hoyle-Lyttleton (BHL) accretion in a reactive medium creates a shock wave which brings about direct detonation ignition in the single WD core and then leads to Type Ia supernova (SN Ia). The aim of this study was to provide constraints on PBHs, the fraction of dark matter (DM) constituted by PBHs, which cannot be constrained by either Hawking radiation or microlensing, through SN Ia event rate obtained from calculations and observations. The SN Ia event rate prefers PBH masses in [$7.59\times10^{-13}\,M_{\odot},6.11\times10^{-12}\,M_{\odot}$], [$7.59\times10^{-13}\,M_{\odot},2.74\times10^{-12}\,M_{\odot}$], [$9.98\times10^{-13}\,M_{\odot},1.99\times10^{-12}\,M_{\odot}$], and [$3.11\times10^{-13}\,M_{\odot},1.51\times10^{-11}\,M_{\odot}$] in the Navarro-Frenk-White (NFW), isothermal, Kra, and Moore profiles, respectively, and the gravitational wave (GW) power spectra further suggest that the constraints provided in this thesis can be probed by $\mu$-Hz GW detector $\mu$Ares by the 2040s'.

 Abstract (Mandarin) II
Abstract III
Acknowledgements IV
Contents VI
List of Figures X
List of Tables XII
List of Algorithms XIII
Introduction 1
1 Motivation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2 Overview of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . 2
3 Notations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
4 BHs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
4.1 Einstein field equations . . . . . . . . . . . . . . . . . . . . 3
4.2 Friedmann equations . . . . . . . . . . . . . . . . . . . . . . 6
4.3 Classification of BHs . . . . . . . . . . . . . . . . . . . . . . 7
5 Relic abundance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
6 Hypothetical evolution of the early Universe . . . . . . . . . . . . . 9
VI
7 PBHs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
8 DM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
8.1 DM Evidence . . . . . . . . . . . . . . . . . . . . . . . . . . 13
8.2 DM density profiles. . . . . . . . . . . . . . . . . . . . . . . 14
8.3 Facts about DM . . . . . . . . . . . . . . . . . . . . . . . . 14
8.4 DM candidates . . . . . . . . . . . . . . . . . . . . . . . . . 15
9 Phase transitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
9.1 Spontaneous symmetry breaking . . . . . . . . . . . . . . . 16
9.2 Phase transitions in the early Universe . . . . . . . . . . . . 17
10 A first-order phase transition in a dark sector model . . . . . . . . 19
10.1 Tunneling probability at zero and nonzero finite temperatures 20
10.2 True vacuum bubble formation at zero temperature due to
quantum fluctuations. . . . . . . . . . . . . . . . . . . . . . 23
10.3 True vacuum bubble formation at nonzero finite temperature due to thermodynamic fluctuations . . . . . . . . . . . 25
10.4 Tunneling probability . . . . . . . . . . . . . . . . . . . . . 26
11 GWs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
11.1 Prediction of the existence of GWs from the Einstein field equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
11.2 Characterisation of GWs . . . . . . . . . . . . . . . . . . . . 27
12 Prediction of stochastic GW power spectra from a first-order phase transition in a dark sector model: thermodynamic parameters . . . 28
12.1 Nucleation temperature $T^{\rm dark}_n$
n . . . . . . . . . . . . . . . . . 29
12.2 Strength $\alpha_n$ of a first-order phase transition in a dark sector
model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
12.3 Fraction $\frac{\beta}{H(T^{\rm dark}_p)}$
. . . . . . . . . . . . . . . . . . . . . . . . 31
12.4 Bubble wall velocity $v_w$ . . . . . . . . . . . . . . . . . . . . 31
VII
13 Prediction of stochastic GW power spectra from a first-order phase transition in a dark sector model: contributions . . . . . . . . . . . 32
13.1 Bubble wall collisions . . . . . . . . . . . . . . . . . . . . . 32
13.2 Sound waves . . . . . . . . . . . . . . . . . . . . . . . . . . 34
13.3 MHL turbulence in the plasma . . . . . . . . . . . . . . . . 35
14 Combustion: detonation and deflagration. . . . . . . . . . . . . . . 36
15 Type Ia supernovae . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
16 Quadrature or numerical integration . . . . . . . . . . . . . . . . . 37
16.1 The Trapezoidal Rule for periodic functions . . . . . . . . . 39
16.2 Simpson’s Rule . . . . . . . . . . . . . . . . . . . . . . . . . 40
16.3 Gaussian quadrature: Gauss-Legendre quadrature . . . . . . 41
16.4 Monte Carlo methods for multi-dimensional integrals . . . . 42
Methodology 44
1 Galactic SN Ia event rate . . . . . . . . . . . . . . . . . . . . . . . 45
1.1 WD number density distribution near 100\,pc of the solar
system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
1.2 The SN Ia event rate near 100\,pc of the solar system for
WDs within a certain mass range . . . . . . . . . . . . . . . 46
1.3 Galactic SN Ia event rate . . . . . . . . . . . . . . . . . . . 50
2 Constraints on PBHs . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3 PBH formation mechanism. . . . . . . . . . . . . . . . . . . . . . . 51
3.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.2 Simplest realisation. . . . . . . . . . . . . . . . . . . . . . . 52
3.3 Energy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.4 Thermal history . . . . . . . . . . . . . . . . . . . . . . . . 57
4 A mechanism for Type Ia supernovae triggered by PBHs . . . . . . 61
VIII
5 Bounds: The change of effective number of neutrinos, Neff . . . . 64
6 Bounds: Stochastic GW power spectra . . . . . . . . . . . . . . . . 64
Results and Discussion 65
1 Galactic SN Ia event rate . . . . . . . . . . . . . . . . . . . . . . . 65
2 Constraints on PBHs . . . . . . . . . . . . . . . . . . . . . . . . . . 66
3 Stochastic GW power spectra . . . . . . . . . . . . . . . . . . . . . 67
Summary 69
A The fourth-order Runge-Kutta method for solving coupled differential equations 70
B Monte Carlo methods for multi-dimensional integrals 74
Bibliography 81
                                

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