在這個論文中，我會探討一個新的矮星系的形成情況。這種星系獲得質量的主要來源是吸積，不像一般的星系有吸積有合併。'鬼魅'星系的命名啟發於Lynden-Bell與Lynden-Bell的文章\cite{Lynden-Bell:1995vu}，這之後'鬼魅'這個詞也被用來描述由再電離前星系所組成殘骸的恆星暈\cite{Ricotti_2005ApJ_DwarfinLocalGroup,Ricotti_2022_GhostlyStellarHalo}，這些星系在再電離後停止了星體形成且保留了再電離前的資訊(例如:化學組成)。鬼魅星系本體不擁有一個星系而是藉由合併其他星系去得到，有些合併得到的星系也包含了再電離前的星系，因此整個星系全是由再電離前星系的殘骸所組成。研究這些殘骸可以讓我們認知再電離前的環境和星體組成，而且不需要觀察高度紅位移的星系。

當鬼魅星系進入一個比較大質量的暗物質暈可能會在動力摩擦(當進入一個更高職量的暗物質暈裡一個暗物質暈會感覺到的摩擦力)的作用下變得比較擴散。主要分枝缺少中心星系倒置鬼魅星系在合併之後變成一個純恆心暈的星系。鬼魅星系擴散般的結構可能跟一些極低表面亮度的星系有關。因此藉由模擬來理解鬼魅星系的性質(光度函數和密度剖面等等)會很有趣。

章節一會先做基礎的介紹。第一個段落我會講超暗矮星系和近來的研究。這個段落會有二個小節。第一個小節是極低表面亮度星系的發現被稱作超暗矮星系。不像矮橢球星系，這種矮星系有著更低的亮度。這些低表面亮度的星系之前不斷的在斯隆數字巡天和DES/Pan-STARRS發現，更勝於之的還有，超彌散星系有著相似的表面亮度但銀河系的大小會在下個小節。第二個段落是在這個研究中用到的模擬。第三段落是星系形成的基礎條件介紹。最後一個段落是它們是否存在於模擬中。

章節二會細說在暗物質暈裡形成星系的條件。並非所有暗物質暈都能形成星系，除非冷卻氣體的效率夠高。冷卻門檻在再電離前可以近似為7000K，再電離後 $4\times10^{4} \mathrm{K}$。個個段落會介紹更多這二個不同的門檻。

章節三是較完整的模擬說明。第一段介紹一個廣泛用在暗物質暈模擬的合併樹。對於用到的模擬，Extended Press-Schechter碼和Copernicus Complexio模擬用來預期一種經由特別的形成歷史的星系的性質。每個小節會講各自的細節和優點。

章節四是整個預測鬼魅星系的成果。我們先調查了鬼魅星系確實能在N-body模擬中發生，然後用半解析模型EPS去做統計確認，還有光度函數和合併時間與合併質量。在非群集區域他們有著傾向的質量在大約$\sim4\times10^{9}\,\mathrm{M_{\odot}}$ 於紅位移等於0的時候，大約5\% 的同質量暗物質暈是鬼魅星系。對於不同再電離強度和光度函數的性質也有被討論。最後我們會做個結論鬼魅星系是否能被觀測和超暗矮星系與超彌散星系的比較。

章節五是總結

In this thesis, I will discuss a new scenario for the formation of dwarf galaxies. These galaxies obtain their stellar mass mostly by accretion, unlike normal galaxies, obtaining their mass by both smooth accretion and mergers. The term 'Ghostly' Galaxy is inspired from Lynden-Bell \& Lynden-Bell\cite{Lynden-Bell:1995vu}, later this 'Ghostly' term is also used to describe stellar halos that come from relics of pre-ionization galaxies \cite{Ricotti_2005ApJ_DwarfinLocalGroup,Ricotti_2022_GhostlyStellarHalo} which shut off their star formation after the reionization and preserved the information (i.e. chemical abundance) before the reionization. Ghostly galaxies do not host a galaxy itself but accrete one through merger and some of them contain only galaxies form before reionization, it is therefore, the entire galaxy is the relics of pre-reionization galaxies. Studying pre-reionization relics gives us insights of the environment and stellar composition before the reionization, and this does not require us to observe extremely high redshift galaxies.

Ghostly galaxies may looked diffuse because the dynamical friction (a halo will feel a friction force when falling into a bigger halo) acting on the galaxies that fall into a higher mass halo. Lacking a central galaxy in the main branch halo makes ghostly galaxies become a pure stellar halo galaxy after mergers. The diffuse structure of ghostly galaxies perhaps relates to some extremely low surface brightness galaxies (i.e. ultra faint dwarfs or ultra diffuse galaxies). It will be interesting to understand the properties (the luminosity function, density profiles, etc) of those ghostly galaxies by simulation.

Chapter 1 is a general introduction. First section I will talk about the ultra-faint dwarfs and recent researches on these objects, why they are important and why they link to our work. There are two subsections in this section, first is the discovery of extremely low surface brightness dwarf galaxies, so-called Ultra Faint Dwarfs (UFDs). Unlike normal dwarf spheroidal galaxies, this type of dwarf galaxies have much lower brightness. These new low surface brightness objects were continuously discovered by Sloan Digital Sky Survey (SDSS) and DES/Pan-STARRS, and furthermore, Ultra diffuse galaxies with similar surface brightness but size of our Milky Way galaxy will be in the next subsection. Second section is the two simulations used in this research. Third section is the basic idea of galaxy forming criteria. The final section talks about their existence in the simulations.


Chapter 2 will talk about the condition of forming a galaxy in a dark matter halo. Not all dark matter halos are able to form a galaxy inside, unless the gas cooling efficiency is high enough to turn the hot gas into cold gas for galaxy formation. The cooling threshold can be approximated as $\mathrm{T_{200} = 7000 K}$ and $\mathrm{T_{200} = 4\times10^{4} K}$ before reionization and after reionization, respectively. More information on the different cooling thresholds are discussed in each section.

Chapter 3 is the simulations and methods that used in this research. The first section introduced the idea of merger tree which is generally used to describe the formation history of dark matter halos. For the simulations, the Extended Press-Schechter (EPS) code \cite{Parkinson2007} and the Copernicus Complexio (Coco) simulation \cite{Hellwing_2016} are tools used to predict the properties of galaxies with a certain type of assembly history. One section will be given to each simulation to explain details and advantages of the simulation.

Chapter 4 present our results of prediction on the ghostly galaxy scenario. We first inspect the ghostly galaxy scenario indeed happened in the coco N-body simulation and then use the EPS semi-analytic model to do the statistical checks and some follow up study which includes luminosity function and merger time and mass ratio. They have a preferential halo mass of $\sim4\times10^{9}\,\mathrm{M_{\odot}}$ at z=0 for field halos, it has a peak of $\sim5$ per cent of all halos of that mass. Properties of different reionization intensity and luminosity function are also discussed. At the End, we will conclude whether ghostly galaxies are detectable and how they match observed UFDs/UDGs.

Chapter 5 is the summary.

Abstract (Chinese)
Publication Statement (Chinese/English)
Abstract
Acknowledgements
Contents
List of Figures
List of Tables
1 Introduction----1
1.1 Detection of diffuse dwarf galaxies----1
1.1.1 Ultra Faint Dwarfs----2
1.1.2 Ultra diffuse Galaxies----2
1.2 Methods for approaching our targets, the Ghostly Galaxies----3
1.3 Not all dark matter halos host a galaxy----4
1.4 Finally, they might be hidden in the dark sky----4
2 Simulation----6
2.1 The merger tree----7
2.2 The Coco Simulation----9
2.3 The EPS methods----10
3 The Virial Temperature Threshold----11
3.1 Gas Cooling----12
3.1.1 Before The Reionization----13
3.1.2 After The Reionization----14
4 Ghosts Hunting Results----16
4.1 Frequency of Ghostly Galaxies----16
4.2 The Luminosity Function----20
4.3 Merger mass ratio and time----27
4.4 Particle tagging methods----29
5 Conclusion----36
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