橢圓星系的基本平面是一种眾所周知的關係，它建立了尺寸、恒星速度離散和亮度之间的聯系。我們能夠根据其他兩個特性估計一個特性，為我們提供了有力的約束，以驗證星系形成和演化理論。在這篇論文中，我們使用STINGS粒子標記技術得到的星系來研究其基本平面的投影關係，半徑——質量关系和費伯——杰克遜關系。這些星系来自Phoenix項目的九個大質量星系团的N-body模擬。在STINGS中，N-body粒子會被分配不同的恒星質量權重，稱為“標籤”，這些權重是使用半解析模型確定的，然后可以通过過考慮這些帶有標籤的粒子的位置和速度來計算相空間分佈。這种方法允許對各种不同的星系形成模型進行高效且高分辨率的預測，以獲取星系團內部光的性質。然而，它在考慮到重子物質的引力位能方面缺乏自洽性。在之前的研究中，STINGS主要用於重子效應对整体位能影響較小的情況。相比之下，驗證星團内大質量星系的基本平面可以測試STINGS的近似是否還成立。

我們發現，在Phoenix模擬中，與觀測相比的情況下，STINGS傾向於在恒定質量下略微低估大質量橢圓星系的半徑，并明顯低估速度離散的數值。這种差异源於STINGS的關鍵參數 “fmb” 如何塑造新形成恒星的結合能分布。我們發現，STINGS應用於Phoenix的常數fmb可以進行微調，以更好地與觀測結果吻合。然而，將 fmb視為在所有恒星形成事件中均匀分布可能不适用於大質量星系。為了解决速度離散方面更嚴重的差异，我們證明可以通過對STINGS的預測引入適當的修正來恢复費伯-杰克遜關係的觀測斜率和分散。此修正基于應用維里定理於投影的質量分布，以彌補由重子物質產生的引力位能缺失。我們討論了這一結果的潛在用途，并建議未來的研究方向，以探索橢圓星系比例關係的起源。

The Fundamental Plane of elliptical galaxies is a well-known relation that establishes connections between size, stellar velocity dispersion, and luminosity. This allows us to estimate one property based on the other two, providing strong constraints on the theories of galaxy formation and evolution. In this thesis we examine the projection of the fundamental plane, the size-mass relation and the Faber-Jackson relation, for galaxies simulated using the STINGS particle tagging technique in nine N-body simulations of massive galaxy clusters from the Phoenix project. In STINGS, N-body particles are assigned distinct stellar mass weights referred to as "tags", these weights are determined using a semi-analytic model, and from there, the phase space distribution can be computed by considering the positions and velocities of these tagged particles. This approach allows efficient and high-resolution predictions of intracluster light properties across a variety of different galaxy formation models. However, it lacks self-consistency in accounting for the gravitational potential of baryons. In previous studies, STINGS has mainly been used in situations where baryonic effects have a minor impact on the overall potential. In contrast, examining the fundamental plane of massive galaxies within clusters can test STINGS in scenarios where its limitations might be more important.

We find that in the Phoenix simulations, STINGS tends to slightly underestimate the sizes and significantly underestimate the velocity dispersion of massive early-type galaxies at constant mass, in comparison to the observations. This discrepancy arises from how STINGS' key parameter, the `most-bound fraction' (fmb), shapes the distribution of binding energy for newly-formed stars. We find that the constant fmb used in STINGS' application to Phoenix could be fine-tuned for better alignment with observations. However, treating fmb as uniform across all star formation events might not be appropriate for massive galaxies. To address the more serious difference in velocity dispersion, we demonstrate that we can recover the observed slope and scatter of the Faber-Jackson relation by introducing an appropriate correction to STINGS' predictions. This correction is based on applying the virial theorem to the projected stellar mass distribution to make up for the missing gravitational potential from the baryons. We discuss potential uses for this outcome and suggest future work to explore the origins of elliptical galaxy scaling relationships.

Abstract (Chinese) I
Acknowledgements (Chinese) III
Abstract IV
Contents VI
List of Figures VIII
List of Tables XIII
1 Introduction - - - - - - - - - - - - - - - - - - - - 1
2 Numerical Method - - - - - - - - - - - - - - - - - - - - 7
2.1 Simulations - - - - - - - - - - - - - - - - - - - - 7
2.2 Particle tagging Technique - - - - - - - - - - - - - - - - - - - - 9
3 ETG Selections - - - - - - - - - - - - - - - - - - - - 17
3.1 STINGS sample of Phoenix ETGs - - - - - - - - - - - - - - - - - - - - 17
3.2 Observation data - - - - - - - - - - - - - - - - - - - - 18
3.2.1 MaNGA survey - - - - - - - - - - - - - - - - - - - - 18
3.2.2 SAMI survey - - - - - - - - - - - - - - - - - - - - 20
4 Early-Type scaling relations in Phoenix - - - - - - - - - - - - - - - - - - - - 22
4.1 Size-Mass relation - - - - - - - - - - - - - - - - - - - - 22
4.2 Mass-to-light ratio within effective radius - - - - - - - - - - - - - - - - - - - - 26
4.3 Mass Faber-Jackson relation - - - - - - - - - - - - - - - - - - - - 29
4.4 Dynamical Mass - - - - - - - - - - - - - - - - - - - - 33
5 Conclusion - - - - - - - - - - - - - - - - - - - - 36
6 Appendix - - - - - - - - - - - - - - - - - - - - 38
6.1 Velocity Dispersion profile - - - - - - - - - - - - - - - - - - - - 38
Bibliography - - - - - - - - - - - - - - - - - - - - 43

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