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研究生： 林迺芥
Lin, Nai-Chieh
論文名稱： 星際介質熱力學之數值實驗
Numerical Experiments on the Thermodynamics of the Interstellar Medium
指導教授： 李悅寧
Lee, Yueh-Ning
口試委員： 李悅寧
Lee, Yueh-Ning
薛熙于
Schive, Hsi-Yu
呂聖元
Liu, Sheng-Yuan
口試日期： 2023/05/29
學位類別： 碩士
Master
系所名稱： 地球科學系
Department of Earth Sciences
論文出版年： 2023
畢業學年度： 111
語文別： 英文
論文頁數： 91
中文關鍵詞： 星際介質 、數值模擬 、狀態方程式 、冷卻函數
英文關鍵詞： Interstellar Medium, Numerical Simulation, Equation of State, Radiative Transfer, Cooling Function
研究方法: 實驗設計法
DOI URL： http://doi.org/10.6345/NTNU202300784
論文種類： 學術論文
相關次數： 點閱：108  下載：15 
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    • 在本研究中，我們調查了冷星際介質(ISM)的冷卻和加熱過程對其熱力學和動力學的影響。狀態方程描述了形成恆星的分子雲中冷ISM的溫度和密度之間的關係，當數量密度小於每立方公分 10^4 時，其多變熱指數為 γ ∼ 0.7，當數量密度大於每立方公分 n < 10^4時，其多變指數為γ ∼ 1。然而，觀測結果與理論預測存在些許差異，因為這些理論假設加熱或冷卻時間尺度比動態過程時間尺度短因而不考慮壓縮或膨脹所做的功。為了解決這個問題，我們使用自適應網格(AMR) 數值程式 RAMSES 進行數值模擬，以找出有效的動態指數。我們的模擬採用分子雲中主要的發射線冷卻函數和參數化冷卻函數。當使用分子雲中主要的發射線冷卻函數時，分子雲迅速達到平衡。然而，當把冷卻功率降低以模擬低金屬豐度環境時，分子雲偏離了狀態方程的描述。我們還探討了參數化冷卻函數的使用，並找到了滿足分子雲坍縮的特定參數設置，也就是有效的多變指數需小於 4/3。我們的結果顯示，在研究原始冷 ISM 時，應將動力過程所做的功納入理論模型中，因為在低金屬豐度環境的情況下冷卻效率不高。總結來說，我們的研究強調了對冷 ISM 的動力學和熱力學的更全面的理解的需要，以及考慮冷卻和加熱過程對這些系統的影響的重要性。

    In this study, we investigated the impact of cooling and heating processes on the thermodynamics and dynamics of the cold interstellar medium (ISM). The widely accepted polytropic equation of state describes the relationship between temperature and density of the cold ISM in star-forming molecular clouds, with an effective polytropic index of γ ∼ 0.7 when n < 10^4 and γ ∼ 1 when n > 10^4. However, there are discrepancies between observational results and theoretical predictions. Most theoretical studies assume that the heating or cooling timescales are smaller than the dynamical timescale and do not account for the work done by compression or expansion. To address this issue, we use the adaptive mesh refinement (AMR) code RAMSES to conduct numerical simulations and determine the effective polytropic index. Our simulations adopt the physical cooling function and parametric cooling function. When physical cooling functions are used, the molecular cloud rapidly reaches equilibrium. However, when the cooling power is reduced to mimic low metallicity abundance, the molecular cloud deviates from the equilibrium temperature. We also explore the use of a parametric cooling function and found the corresponding equation of state given the cooling function of the medium. Our results suggest that when studying the primordial hot ISM, where the cooling is less effective, the work done by dynamical processes should be included in the theoretical model since cooling is not efficient in low metallicity scenarios. Overall, our study highlights the need for a more comprehensive. understanding of the dynamics and thermodynamics of the cold ISM and the importance of considering the effects of cooling and heating together with dynamical processes in these systems.

    1 Introduction 1 1.1 Thermal behavior of the molecular cloud 1 1.2 Equation of state 4 1.3 Collapse criteria 6 1.4 Cooling and heating 8 2 Methods 11 2.1 Numerical Code 11 2.1.1 RAMSES Code 11 2.2 Cooling functions 12 2.2.1 Physical cooling function 12 2.2.2 Parametric cooling function 16 2.3 Timescales 18 2.4 Stationary Solution 21 2.4.1 Method 1 – Comparing timescales 21 2.4.2 Method 2 – Navier-Stokes equations 23 2.5 Trajectories of quasi-stationary solutions 26 2.6 Initial conditions 27 2.7 Simulation parameters 28 2.7.1 Numerical parameters 29 2.7.2 Physical parameters 29 3 Results 32 3.1 Physical cooling function 32 3.1.1 Spatial structure of the molecular cloud 32 3.1.2 Temperature-density relation 38 3.2 Reduced cooling functions 39 3.2.1 Spatial structure of the molecular cloud 39 3.2.2 Temperature-density relation 42 3.3 Parametric cooling function 46 3.3.1 Spatial structure of the molecular cloud 46 3.3.2 Temperature-density relation 50 4 Discussion 54 4.1 Physical cooling function 54 4.2 Reduced cooling function 55 4.3 Parametric cooling function 56 5 Conclusions and outlook 58 Bibliography 61 A Simulation results 64 A.1 Physical cooling functions with T_0 = 10K 65 A.2 Physical cooling functions with T_0 = 400K 70 A.3 Reduced cooling function with T_0 = 10K 75 A.4 Reduced cooling function with T_0 = 80K 80 A.5 Reduced cooling function with T_0 = 400K 85 B GAMER code 90

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