论文标题
红色巨人的玩具故事
A Red Giants' Toy Story
论文作者
论文摘要
尽管恒星进化论取得了壮观的进步，但仍然没有解决一些简单的问题。这些问题之一是``为什么恒星变成红色巨人？''。在这里，我们为这个问题提供了一个相对简单的分析答案。我们通过构建红色巨人的定量玩具模型来验证我们的分析，并将其预测与完整的恒星进化模型进行比较。 我们发现，信封迫使$ \ nabla = d \ ln t/d \ ln p $ at及更高的值将燃烧的壳变成非常狭窄的可能值范围。 Together with the fact that the stellar material at the burning shell both provides and transports most of the stellar luminosity, this leads to tight relations between the thermodynamic variables at the burning shell and the mass and radius of the core -- $T_s(M_c,R_s)$, $P_s(M_c,R_s)$ and $ρ_s(M_c,R_s)$.当与氦气内核的典型Mass-Radius关系补充时，这意味着对于所有恒星质量，核心的演变都决定了$ t_s $，$ p_s $和$ρ_s$的值。我们表明，对于所有恒星质量，演变都会导致壳和芯之间的压力和密度对比增加，从而迫使燃烧壳顶部的层巨大膨胀。 除了解释为什么恒星变成红色巨人我们的分析还提供了所谓的壳同源性关系的数学演示，并为低质量红色巨人的某些特性提供了简单的定量答案。
In spite of the spectacular progress accomplished by stellar evolution theory some simple questions remain unanswered. One of these questions is ``Why do stars become Red Giants?''. Here we present a relatively simple analytical answer to this question. We validate our analysis by constructing a quantitative toy-model of a red giant and comparing its predictions to full stellar evolutionar models. We find that the envelope forces the value of $\nabla=d \ln T/d \ln P$ at, and above, the burning shell into a very narrow range of possible values. Together with the fact that the stellar material at the burning shell both provides and transports most of the stellar luminosity, this leads to tight relations between the thermodynamic variables at the burning shell and the mass and radius of the core -- $T_s(M_c,R_s)$, $P_s(M_c,R_s)$ and $ρ_s(M_c,R_s)$. When complemented by typical mass-radius relations of the helium cores, this implies that for all stellar masses the evolution of the core dictates the values of $T_s$, $P_s$ and $ρ_s$. We show that for all stellar masses evolution leads to an increase in the pressure and density contrasts between the shell and the core, forcing a huge expansion of the layers on top of the burning shell. Besides explaining why stars become red giants our analysis also offers a mathematical demonstration of the so-called shell homology relations, and provides simple quantitative answers to some properties of low-mass red giants.
