再探脉动恒星中的浮力故障
Buoyancy glitches in pulsating stars revisited
AI总结：
本文重新分析重力模与混合模恒星中的阶跃状、高斯状和 Dirac-δ 状浮力故障，提出周期扰动解析表达式并评估高斯故障参数拟合的可靠性。
摘要：
尖锐的结构变化会在恒星脉动上产生特定信号，研究这些信号可推断有关恒星分层的局域信息。该信息对于增进我们对导致结构变化的物理过程以及如何建模这些过程的理解至关重要。本文重新审视并扩展了早期工作中对重力模与混合模脉动体中不同类型浮力故障信号的分析，包括阶跃状、高斯状和 Dirac-δ 状故障。特别地，我们给出了周期扰动的解析表达式，并表明这些表达式能够可靠地替代为周期间距给出的表达式，其优势在于使用新表达式不需要观测到具有连续径向阶次的模式。基于与两种极限情形以及模拟数据的比较，我们进一步检验了高斯状故障信号表达式的准确性；该表达式在早期工作中的推导涉及显著近似。我们发现，由拟合该表达式推断出的最不可靠的故障参数是振幅，其可能比真实振幅大至两倍，并在故障较小时达到这一极限。我们还进一步讨论了将故障置于 g 模空腔内半区和外半区时对故障信号的影响，强调了在混合模脉动体情形中发生的对称性破缺。
英文摘要：
Sharp structural variations induce specific signatures on stellar pulsations that can be studied to infer localised information on the stratification of the star. This information is key to improve our understanding of the physical processes that lead to the structural variations and how to model them. Here we revisit and extend the analysis of the signature of different types of buoyancy glitches in gravity-mode and mixed-mode pulsators presented in earlier works, including glitches with step-like, Gaussian-like, and Dirac-$δ$-like shapes. In particular, we provide analytical expressions for the perturbations to the periods and show that these can be reliably used in place of the expressions provided for the period spacings, with the advantage that the use of the new expressions does not require modes with consecutive radial orders to be observed. Based on a comparison with two limit cases and on simulated data, we further tested the accuracy of the expression for the Gaussian-like glitch signature whose derivation in an earlier work involved a significant approximation. We find that the least reliable glitch parameter inferred from fitting that expression is the amplitude, which can be up to a factor of two larger than the true amplitude, reaching this limit when the glitch is small. We further discuss the impact on the glitch signature of considering a glitch in the inner and outer half of the g-mode cavity, emphasising the break of symmetry that takes place in the case of mixed-mode pulsators.
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