原恆星盤在將質量轉移到原恆星時扮演著重要角色，也是未來孕育新生行星之地。觀測結果顯示，仍然深埋在分子雲中並受旋轉支撐的原恆星盤在早期階段便從原恆星的包層中形成，並積極地吸積質量。然而，原恆星盤形成的環境因磁場和紊流的存在複雜化，磁流體力學的數值模擬也顯示磁場和紊流對於原恆星盤的是否能夠形成具有顯著的影響。本論文旨在分析幾個處於Class 0階段的原恆星，以了解原恆星盤如何通過吸積流從包層積累質量、極低質量原恆星的原恆星盤的早期演化，以及雙極擴散作用在其中所扮演的角色。
在Lupus 3-MMS中，我使用簡單的三維旋轉塌縮模型，擬合在C$^{18}$O中找到的多個長條狀的氣體結構，得到質量塌縮速率介於$0.5$到$1.1\times10^{-6}\,M_\odot\,\mathrm{yr^{-1}}$之間。此結果與其他Class 0原恆星的觀測結果以及磁流體力學模擬一致，這表示此簡化的塌縮模型即提供一個良好的近似，可以產生與觀測大致相符的結果。在IRAS 15398-3359中，我將緊實而高速的SO發射譜線觀測結果與克卜勒旋轉曲線擬合進行運動學分析，發現其中心原恆星的質量極低，約為$0.034\,M_\odot$，且氣體原恆星盤半徑約為$\sim20\,\mathrm{au}$。根據原恆星質量的吸積率估計，IRAS 15398-3359的年齡小於13,000年。因此，原恆星盤的形成發生在非常早期的階段。在HOPS-370中，我使用了基於雙極擴散效應推導的原恆星盤半徑公式，估計HOPS-370原恆星盤邊緣的雙極擴散係數約為$\sim1.6\times10^{18}\,\mathrm{cm^{2}\,s^{-1}}$。這個結果對應的無因次Els\"{a}sser數約為$\sim2.4$，顯示雙極擴散效應在原恆星盤形成的過程中具有影響力。此外，我還使用了一個理論上自洽的方法計算雙極擴散係數，得到的數值與從觀測結果推導的一致。因此，在理解早期原恆星盤的演化時，應考慮非理想磁流體力學中磁場的擴散效應。

Protostellar disks are important for transferring mass to the protostar, and are the future sites of planet formation. Observations of rotationally-supported protostellar disks in the deeply embedded stages of low-mass star formation show that they form early and are actively accreting mass from the natal protostellar envelope. However, these environments are complicated by magnetic fields and turbulence, which numerical MHD simulations show have a significant impact on whether these disks can even form. This thesis analyzes several Class 0 protostars to understand the envelope mass accretion via streamers, early disk evolution in an extremely low-mass protostar and the role of ambipolar diffusion in the disk environment.
In Lupus 3-MMS, I model multiple extended gas structures found in C$^{18}$O using a simple, 3D rotating-collapse model. The mass-infall rates are between $0.5-1.1\times10^{-6}\,M_\odot\,\mathrm{yr^{-1}}$, which is consistent with other Class 0 sources and MHD simulations, indicating even a simplified infall model can be a good approximation when comparing to observations. In IRAS 15398-3359, I perform kinematic analysis by fitting the compact, high-velocity SO emission with a Keplerian rotation profile to reveal a gas disk radius of $\sim20\,\mathrm{au}$ around an extremely low-mass $\sim0.034\,M_\odot$ protostar. Using the protostellar mass-accretion rate, the age of IRAS 15398-3359 is estimated to be $<$13,000$\,$yr. Thus, protostellar disk formation happens in the very early stages.
In HOPS-370, I use a previously derived analytical expression of the expected protostellar disk radius due to ambipolar diffusion to estimate the ambipolar diffusion coefficient to be $\sim1.6\times10^{18}\,\mathrm{cm^{2}\,s^{-1}}$ at the edge of the HOPS-370 disk. This yields a dimensionless Els\"{a}sser number for ambipolar diffusion of $\sim2.4$, indicating it is influencing the dynamics in this region. Additionally, when using a self-consistent method to calculate the ambipolar diffusion coefficient, it is consistent with the derived value. The diffusion of the magnetic field by non-ideal MHD effects should be considered when understanding the evolution of embedded protostellar disks.

Contents
Abstract (Chinese) ................................................................................ I
Abstract ................................................................................................ II
Acknowledgments ................................................................................ III
Contents ............................................................................................... V
List of Figures ....................................................................................... IX
List of Tables ........................................................................................ XI

1 Introduction ....................................................................................... 1
1.1 The Formation of a Protostellar Disk ............................................... 1
1.1.1 Gravitational Collapse: A Simple Case .......................................... 1
1.1.2 Magnetized Collapse: a Complex Case ........................................ 2
1.2 Observations of Protostellar Environments .................................... 2
1.3 Thesis Overview ............................................................................. 4
1.3.1 Streamers in Class 0 Protostars................................................... 4
1.3.2 A Very Young Class 0 Protostellar Disk ....................................... 4
1.3.3 Ambipolar Diffusion in Protostellar Disk Environments ............... 5

2 Accretion Flows or Outflow Cavities? Uncovering the Gas Dynamics around
Lupus 3-MMS 6
2.1 Abstract ......................................................................................... 6
2.2 Introduction ................................................................................... 7
2.3 Observations ................................................................................ 10
2.4 Results .......................................................................................... 11
2.5 Analysis......................................................................................... 13
2.5.1 The CMU Model ......................................................................... 13
2.5.2 Disk Properties and System Velocity ......................................... 16
2.5.3 Outflow Velocity Structure ......................................................... 16
2.5.4 Infall Velocity Structure .............................................................. 17
2.6 Discussion ..................................................................................... 23
2.6.1 Outflow Cavities or Accretion Flows? .......................................... 23
2.6.2 The Nature of S4 ........................................................................ 24
2.6.3 Degeneracy of the CMU Model .................................................. 25
2.6.4 Accretion Flow Properties and Comparison ............................... 28
2.6.5 The Origin of Accretion Flows ..................................................... 31
2.7 Conclusion ..................................................................................... 32
A Does the CMU Model Produce Streams? ......................................... 34
B PV Diagrams ..................................................................................... 34
C Column Density Maps ...................................................................... 36

3 A Small Protostellar Disk around the Extremely Low-Mass and Young Class
0 Protostar, IRAS 15398-3359 40
3.1 Abstract ......................................................................................... 41
3.2 Introduction ................................................................................... 42
3.3 Observations & Data Reduction .................................................... 44
3.4 Results .......................................................................................... 48
3.4.1 Dust Continuum .......................................................................... 48
3.4.2 Molecular Lines .......................................................................... 51
3.5 Analysis ......................................................................................... 54
3.5.1 Position-Velocity Diagrams ......................................................... 54
3.5.2 PV Analysis with SLAM: Overview .............................................. 56
3.5.3 PV Analysis with SLAM: Single Power-Law ................................. 57
3.5.4 PV Analysis with SLAM: Modified Single Power-Law .................. 60
3.5.5 PV Analysis with SLAM: Double Power-Law ................................ 61
3.6 Discussion ...................................................................................... 62
3.6.1 A Very Low-Mass Protostar and Disk ........................................... 62
3.6.2 Disk-to-Stellar Mass Ratio ........................................................... 64
3.6.3 Mass-Accretion Rate ................................................................... 65
3.6.4 A Proto-Brown Dwarf Candidate? ................................................ 66
3.6.5 An Extremely Small Protostellar Disk ........................................... 66
3.6.6 Dust vs. Gas Disk Radius ............................................................. 67
3.6.7 Specific Angular Momentum ........................................................ 67
3.6.8 A Dynamical Overview of the IRAS 15398-3359 Protostellar
System .................................................................................................. 68
3.7 Conclusion ...................................................................................... 70
A Gallery of Dust Continuum Images .................................................... 73
B Channel Maps of Molecular Lines ...................................................... 73
C SB-only Images of Molecular Lines ................................................... 73

4 The First Estimation of the Ambipolar Diffusion Coefficient from Multi-
Scale Observations of the Class 0/I Protostar, HOPS-370 ................... 80
4.1 Abstract .......................................................................................... 80
4.2 Introduction .................................................................................... 81
4.3 Methods ......................................................................................... 83
4.3.1 The Relation Between the Disk Radius and the Ambipolar Diffusion
Coefficient ........................................................................................... 83
4.3.2 Previously Derived Disk Properties ............................................ 84
4.3.3 Estimating the Poloidal Magnetic Field Strength at the Edge of
the Disk ............................................................................................... 85
4.4 Results .......................................................................................... 89
4.4.1 The First Estimation of the Ambipolar Diffusion Coefficient
from Observations .............................................................................. 89
4.4.2 The Dimensionless Els¨asser Number for Ambipolar Diffusion . 90
4.4.3 Comparing with the Non-Ideal MHD Coefficient and Ionisation
Library ................................................................................................ 91
4.5 Discussion .................................................................................... 97
4.5.1 Is Ambipolar Diffusion the Dominant Non-Ideal MHD Effect at
the Edge of the HOPS-370 Protostellar Disk?.................................... 97
4.5.2 How Measurement Uncertainties Could Impact the Calculation
of the Ambipolar Diffusion Coefficient? ............................................. 98
4.5.3 Non-Ideal MHD Simulations of Disk Formation and the Validity
of this Method .................................................................................... 99
4.6 Conclusion ................................................................................... 100

5 Summary ......................................................................................... 102
Bibliography ....................................................................................... 104

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