非径向非绝热脉动的广义二次平衡关系
A generalized quadratic balance relation for nonradial nonadiabatic pulsations
AI总结：
该研究推导了线性非绝热非径向恒星脉动的广义二次平衡关系，可用于检验本征频率、估计模式激发率，分析了AGB星包层各类模式的功率项，发现模式驱动大小不全由热力学功项决定。
AI中文摘要：
我们从压力-体积-速率功的半线性振幅类比出发，推导了线性非绝热、非径向恒星脉动的广义二次平衡关系。该推导既不要求弱非绝热性，也不需要对脉动周期取平均。该关系以功、广义范数和边界贡献表示，随后被改写为动能-功率形式：$\boldsymbol{\textit{P}}+\boldsymbol{\textit{\u0394B}}=2\boldsymbol{\u211c}(\boldsymbol{\u03c3})\boldsymbol{\textit{E}}_{\rm kin}$。体积功率被分解为热力学交换项以及与压缩、水平面积变形和引力分层效应相关的响应项。该关系的等价形式可用于诊断，以检验计算得到的本征频率并估计模式激发率。我们研究了渐近巨分支（AGB）星模型包层中各类模式的平衡关系性质，分析了径向和非径向p模式、奇异模式，以及低频外包层重力模式和热模式的功率$\boldsymbol{\textit{P}}$各项。结果表明，模式驱动的大小并非仅由热力学功项决定。
英文摘要：
We derive a generalized quadratic balance relation for linear nonadiabatic, nonradial stellar pulsations, starting from a sesquilinear amplitude analogue of the pressure-volume-rate work. The derivation requires neither weak nonadiabaticity nor averaging over a pulsation cycle. The relation is expressed in terms of work, generalized norm and boundary contributions and is subsequently recast into kinetic-energy-power form $\mathcal{P}+ΔB=2\Re(σ)E_{\rm kin}$. The volume power is decomposed into a thermodynamic exchange term and response terms associated with compression, horizontal-area deformation and gravitational stratification effects. The equivalent forms of the relation provide diagnostics for checking the computed eigenfrequencies and estimating mode excitation rates. The properties of the balance relation for various types of modes in an envelope of a model AGB star are examined. We analyze the terms entering the power $\mathcal{P}$ for radial and nonradial p-modes, strange modes as well as examples of low frequency outer-envelope gravity modes and thermal modes. The results show that the magnitude of mode driving is not determined solely by the thermodynamic work term.
