强非绝热径向脉动中的热力学交换与模式稳定性
Thermodynamic exchange and mode stability in strongly nonadiabatic radial pulsations
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中文总结 AI 辅助
本研究通过二次平衡关系分析后AGB模型径向脉动，发现强非绝热下热力学交换功率符号不能单独决定模式稳定性，响应功率起关键作用。
中文摘要 AI 辅助
我们将线性非绝热脉动的二次平衡关系应用于一系列后AGB包层模型（覆盖$3.52\leq\log(T_{\rm eff})\leq4.6$）的径向模式。该关系将热力学交换功率$\mathcal{P}_{\rm ex}$、响应功率$\mathcal{P}_{\rm rsp}$和表面贡献$\Delta B$分离，并通过$\mathcal{P}_{\rm ex}+\Delta B=2\gamma\chi_{\rm eff}\mathcal{E}_{\rm kin}$引入有效范数，其中$\gamma$是模式增长率。对于近绝热模式，$\chi_{\rm eff}$接近1，而在强非绝热脉动中，压缩和水平面积变形贡献可使其改变大小甚至反转符号。在较冷的模型中，一大类泛音模式具有$\chi_{\rm eff}<0$，尽管热力学交换功率为正，这些模式仍被阻尼。对于这些模式，响应功率提供了相反的阻尼。相反，在较热模型中，两个低频模式在一系列有效温度范围内被激发，尽管其热力学交换功率为负。它们的不稳定性由正的响应功率产生。奇异模式通常具有$\chi_{\rm eff}>0$，除了一个狭窄的边界敏感过渡期间，冷奇异模式转变为普通p模。具有$\chi_{\rm eff}<0$的激发低频解在更精细的数值网格下仍然存在，并且在所检验的替代外边界公式下也能找到此类模式，尽管其频率依赖于边界条件。因此，对于强非绝热脉动，热力学交换功率的符号单独并不能决定模式稳定性。
英文摘要
We apply the quadratic balance relation for linear nonadiabatic pulsations to radial modes of a sequence of post-AGB envelope models covering $3.52\leq\log(T_{\rm eff})\leq4.6$. The relation separates the thermodynamic exchange power $\mathcal{P}_{\rm ex}$, response power $\mathcal{P}_{\rm rsp}$, and surface contribution $ΔB$, and introduces an effective norm through $\mathcal{P}_{\rm ex}+ΔB=2γχ_{\rm eff}\mathcal{E}_{\rm kin}$, where $γ$ is the mode growth rate. For nearly adiabatic modes $χ_{\rm eff}$ is close to unity, whereas in strongly nonadiabatic pulsations the compression and horizontal area deformation contributions can make it change magnitude or even reverse its sign. In the cooler models, a broad family of overtone modes has $χ_{\rm eff}<0$ and is damped despite positive thermodynamic exchange power. For these modes the response power supplies the opposing damping. Conversely, two low frequency modes in the hotter models are excited over a range of effective temperatures, even though their thermodynamic exchange power is negative. Their instability is produced by the positive response power. Strange modes generally have $χ_{\rm eff}>0$, apart from a narrow boundary-sensitive transition during which a cold strange mode transforms into an ordinary p-mode. The excited low frequency solution with $χ_{\rm eff}<0$ persists with a finer numerical mesh and such modes are found under the alternative outer boundary formulations examined, although their frequencies are boundary condition dependent. Thus, for strongly nonadiabatic pulsations, the sign of the thermodynamic exchange power alone does not determine mode stability.
