标题： 演化恒星的EGGMiMoSA I脉动学。从次巨星到红巨星阶段的理论混合模式图案 显示英文标题

标题： Asteroseismology of evolved stars with EGGMiMoSA I. Theoretical mixed-mode patterns from the subgiant to the RGB phase

摘要： 这项研究是系列论文的第一篇，提供了一种技术来分析混合模态频率谱并表征次巨星和红巨星分支上恒星的结构。 我们定义了与恒星结构相关的地震指标，并研究它们在模型网格中的演化。 所提出的方法EGGMiMoSA基于混合模态的渐近描述，定义参数的初始猜测，并使用Levenberg-Marquardt技术高效地调整混合模态模式。 我们跟踪从次巨星阶段到RGB凸起的模型网格中混合模态参数的演化，并扩展了之前的工作。 我们展示了质量和成分对其演化的影响。 周期间距$\Delta\pi_1$、压力偏移$\epsilon_p$、重力偏移$\epsilon_g$和耦合因子$q$随$\Delta\nu$的演化受到化学组成的影响较小，并且根据演化阶段的不同呈现出两种不同的制度。 在次巨星分支上，模型表现出适度的核心-包层密度对比。 $\Delta \pi_1$的演化， $\epsilon_p$、$\epsilon_g$和$q$也因此随着质量显著变化。 此外，我们证明，在固定 Z/X 的情况下，并通过适当测量$\Delta\pi_1$和$\Delta\nu$，我们可以无歧义地约束次巨星的质量、半径和年龄。 相反，在红巨星分支上，核心-包层密度对比变得非常大。 因此，$\epsilon_p$、$\epsilon_g$和$q$随$\Delta\nu$的变化独立于质量。 这对于质量为$\lesssim 1.8M_\odot$的恒星中的$\Delta \pi_1$也是如此，这是由于核心电子简并。 对于更高质量的恒星，这种简并被解除，再次允许精确测量年龄。 总体而言，我们的计算在定性上与以往的观测和理论研究一致。 显示英文摘要

摘要： This study is the first of a series of papers that provide a technique to analyse the mixed-modes frequency spectra and characterise the structure of stars on the subgiant and red-giant branches. We define seismic indicators, relevant of the stellar structure and study their evolution on a grid of models. The proposed method, EGGMiMoSA, relies on the asymptotic description of mixed modes, defines initial guesses for the parameters, and uses a Levenberg-Marquardt technique to adjust the mixed-modes pattern efficiently. We follow the evolution of the mixed-modes parameters along a grid of models from the subgiant phase to the RGB bump and extend past works. We show the impact of the mass and composition on their evolution. The evolution of the period spacing $\Delta\pi_1$, pressure offset $\epsilon_p$, gravity offset $\epsilon_g$, and coupling factor $q$ as a function of $\Delta\nu$ is little affected by the chemical composition and it follows two different regimes depending on the evolutionary stage. On the subgiant branch, the models display a moderate core-envelope density contrast. The evolution of $\Delta \pi_1$, $\epsilon_p$, $\epsilon_g$, and $q$ thus significantly changes with the mass. Also, we demonstrate that, at fixed Z/X and with proper measurements of $\Delta\pi_1$ and $\Delta\nu$, we may unambiguously constrain the mass, radius and age of a subgiant star. Conversely, on the red-giant branch, the core-envelope density contrast becomes very large. Consequently, the evolution of $\epsilon_p$, $\epsilon_g$ and $q$ as a function of $\Delta\nu$ becomes independent of the mass. This is also true for $\Delta \pi_1$ in stars with masses $\lesssim 1.8M_\odot$ because of core electron degeneracy. This degeneracy is lifted for higher masses, again allowing for a precise measurement of the age. Overall, our computations qualitatively agree with past observed and theoretical studies.