紅超巨星的物理起源及其質量散失

Abstract

紅超巨星是演化晚期的大質量恆星，膨脹至約1000倍太陽半徑，具有顯著的質量散失，且為核心坍縮超新星的常見前身星，對於周遭星際介質影響巨大。雖然紅超巨星階段在恆星演化模型中總是能夠再現，其物理起源長期存在爭論，至今仍不清楚。透過恆星模型的建造與分析，本論文全面探討恆星天文物理中長期存在的一個問題：「為何恆星會演化成為紅巨星或紅超巨星？」

首先，本研究使用MESA程式建構約2,000個恆星演化模型，探討不同質量與不同金屬量之大質量恆星演化，並從這組模型中發現了一個臨界金屬量——唯有金屬量Z>~0.001的恆星可演化為紅超巨星，並歷經龐大的質量散失。這些模型亦用來計算恆星回饋，並與宇宙學模擬中常用的經驗式比較。

本文進一步分析MESA模型，探討何種機制決定恆星能否演化為紅超巨星。結果顯示一個修正版的「鏡像原理」：恆星外層的移動方向始終與其內部邊界的移動方向相反。此內部邊界由氫燃燒殼層的外緣所定義。根據此鏡像原理，本文建立出一套通用的判準及演化路線圖，判斷恆星能否演化為紅巨星或紅超巨星。此外，當恆星演化至接近紅巨星或紅超巨星時，可找到一個劇烈的結構轉變階段。

為深入考察紅巨星及紅超巨星的物理，本文以數值方法解出穩態恆星結構方程組。結果證實恆星外層的穩態解符合修正版之鏡像原理，並顯示紅巨星及紅超巨星不但對應於恆星外層膨脹的極限半徑，亦為結構上獨特的階段，與較緻密恆星的結構截然不同。這些穩態解也合理解釋，巨星及超巨星分為紅色及藍色兩個分支。

接著，為進一步探討臨界金屬量的物理起源，本研究利用更大量的模型組，測試多個物理參數的效應。結果顯示，對於給定的恆星質量，在主序終點時存在一個半徑閾值——唯有半徑超過此閾值的恆星可演化為紅超巨星。金屬量之所以影響演化結果，是藉由影響不透明度及核反應，因而改變恆星半徑，於是決定恆星能否在主序終點達到紅超巨星形成的半徑閾值。

本文藉由數值方法解出恆星結構與演化，建立一套完整的物理框架，解釋恆星外層朝向紅巨星及紅超巨星階段的演化。此框架不僅在理論上提供後主序星演化機制的理解，亦能說明觀測上巨星及超巨星在赫羅圖的分布。此外，臨界金屬量的確認及恆星回饋的計算，則對早期宇宙的貧金屬星演化有深遠意義。

Red supergiants (RSGs) are evolved massive stars that expand to ~1,000 solar radii, exhibit substantial mass loss, and are common progenitors of core-collapse supernovae, significantly shaping their surrounding interstellar environments. Although the RSG phase is consistently reproduced in stellar evolution models, its physical origin has been long debated and remains unclear. Through the construction and analysis of stellar models, this thesis provides a comprehensive investigation into a longstanding question in stellar astrophysics: why do stars evolve into red giants (RGs) or RSGs?

As a first step, a grid of approximately 2,000 stellar evolution models is computed using the MESA code to explore the evolution of massive stars across a wide range of masses and metallicities. From this grid, a critical metallicity is identified: only stars with Z>~0.001 evolve into RSGs and undergo substantial mass loss. These models are also used to calculate stellar feedback, which is compared with prescriptions commonly adopted in cosmological simulations.

To explore the mechanism that determines whether a star evolves into the RSG phase, further analysis of MESA models suggests a refined version of the “mirror principle”: the stellar envelope consistently moves in the opposite direction to its inner boundary, defined by the outer edge of the hydrogen-burning shell. This principle leads to general criteria and an evolutionary roadmap for determining whether a star will evolve into an RG or RSG. Moreover, a dramatic structural transition is identified as stars approach the RG/RSG phase.

To further investigate the underlying physics of the RG/RSG phase, steady-state stellar structure equations are solved numerically. The resulting envelope solutions validate the refined mirror principle and show that the RG/RSG phase corresponds to both a limiting radius for envelope expansion and a distinct structural phase, markedly different from that of more compact stars. These solutions also naturally explain the bifurcation between red and blue branches of giants and supergiants.

The physical origin of the critical metallicity is further investigated using extended grids of models designed to test the effects of various physical parameters. The results reveal a threshold radius at the terminal-age main sequence (TAMS) for a given stellar mass; only stars exceeding this radius evolve into RSGs. Metallicity governs the evolution outcome by influencing stellar radius through its effects on opacity and nuclear burning, thereby determining whether the threshold TAMS radius for RSG formation is reached.

By numerically solving stellar structure and evolution, this thesis establishes a comprehensive physical framework for explaining envelope expansion toward the RG/RSG phase. This framework not only offers theoretical insight into the evolutionary mechanisms of post-main-sequence stars, but also accounts for the observed distribution of giant and supergiant stars on the Hertzsprung–Russell diagram. The identification of a critical metallicity and the computation of stellar feedback further provide implications for the evolution of metal-poor stars in the early universe.