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WHY STARS BECOME RED GIANTS

机译：为什么星星变成红色军团

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The evolution of stars to red giants is revisited in order to promote a better understanding of the behavior of stars on the H-R diagram by separating the essential nonlinear characteristics of stellar structure from detailed effects of input physics such as chemical compositions, opacity, convection criterion, etc. It is shown that the red giant and dwarf structures are clearly discriminated in terms of the variation through the stellar interior of the ratio, W, between the mass interior to the relevant shell and the mass contained in the pressure scale height at the shell (≡ GM_r~2/4πr~4P). For the simplest structures of dwarfs such as main-sequence stars, W increases monotonically from zero at the center to the greatest value at the surface. In later stages of evolution such as the red giants, W evolves to have a local extre-mum near the hydrogen-burning shell. Such a change in the distribution of W is a consequence of the increase in the ratio, Θ, of thermal and/or Fermi energy (P/ρ) between the core center and the envelope. In fact there exists a lower bound to Θ that is required by a red giant structure. During stellar evolution, the increase in Θ is brought about by the gravitational contraction of the core and by the fact that shell burning prevents the envelope from following the core contraction. Structures with an extremum of W correspond to an envelope of the condensed type, the properties of which are strongly regulated by the polytropic index N and the ratio, V [ = (GM_r/r)/(P/ρ)], between the local gravitational potential to the thermal energy in the lower envelope. A large polytropic index N approx> 3 makes the envelope expanded, particularly when V approx= N + 1 is realized in the lower envelope. On the basis of such an understanding, we are able to analyze the effects of input physics on the excursion of the star to a red giant. A key role is played by the gradients of the opacity and of the mean molecular weight. The stellar radius can be larger if the opacity is increasing outward to make N larger than 3. A moderate gradient in the mean molecular weight also allows the value of N to come into the range of 3-5, which is appropriate for V approx= N + 1 to be realized in the bottom of the envelope, while a steep gradient yields too large a value of N. The so-called peculiar evolution of the SN 1987A progenitor, Sk — 69°202, can be understood in such a context. In particular, a constraint is derived for the mechanism of the extra mixing that is responsible for the final red-to-blue excursion of the star.
机译：为了从HR图上更好地理解恒星的行为，我们重新审视了恒星向红色巨星的演化，方法是将恒星结构的基本非线性特征与输入物理的详细影响（例如化学成分，不透明度，对流准则，结果表明，根据恒星内部的变化，明显区分了红巨星和矮星结构，该比率是通过W到相关壳的内部质量与壳的压力刻度高度中所包含的质量之比W来实现的。 （≡GM_r〜2 /4πr〜4P）。对于最简单的矮星结构（例如主序星），W从中心的零单调增加到表面的最大值。在红色巨星等进化后期，W进化为在燃烧氢的壳附近有一个局部极值。 W分布的这种变化是铁心中心和包壳之间的热能和/或费米能（P /ρ）之比Θ增加的结果。实际上，存在红色巨型结构所需的Θ下限。在恒星演化过程中，Θ的增加是由于岩心的重力收缩以及壳层燃烧阻止包膜跟随岩心收缩而引起的。极值为W的结构对应于压缩类型的包络，其特性受多变指数N和局部之间的比率V [=（GM_r / r）/（P /ρ）]强烈调节。下部外壳中热能的重力势能。大的多变折射率N大约> 3使包络扩展，特别是在下包络中实现V近似= N +1时。基于这种理解，我们能够分析输入物理学对恒星向红色巨星偏移的影响。不透明度和平均分子量的梯度起着关键作用。如果向外增加不透明度以使N大于3，则恒星半径可以更大。平均分子量的适度梯度还可以使N的值进入3-5的范围，这适用于Vrox = N +1将在包络线的底部实现，而陡峭的梯度会产生太大的N值。在这种情况下，可以理解SN 1987A祖先的所谓奇异演化，Sk — 69°202 。特别是，得出了一个额外的混合机制的约束，该约束导致了恒星最终的红蓝偏移。

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