从类太阳星到Mira星：在随机噪声存在下对恒星散射子的统一描述
From Solar-like to Mira stars: a unifying description of stellar pulsators in the presence of stochastic noise
摘要：
我们讨论并证明了一个模型的功率谱密度特性，该模型旨在描述恒星中从主序星到渐近巨星分支的脉动。我们表明，在随机噪声的存在下的脉动模式的功率谱密度的预测极限总是很好地近似的洛伦兹函数。虽然在主要是随机驱动的恒星中，洛伦兹的宽度由模式寿命定义，但在驱动主要是相干的恒星中，宽度由随机扰动的幅度定义。在两种驱动都相当的恒星中，宽度由这两个参数定义，并且小于纯随机驱动的预期。我们通过数值模拟说明了我们的模型，并提出了一个定义明确的恒星分类成主要是随机的（类太阳）和主要是相干的（经典的）embritator。我们将该模型应用到Mira变量U Per和半正则变量L2 Pup的研究中，并根据我们的分类得出结论，它们都是经典的双线性算子。我们的模型提供了一个自然的解释，在几个早期的作品中指出的脉动振幅周期关系的行为的变化。此外，我们对L2 Pup的研究使我们能够测试模式线宽和有效温度之间的标度关系，证实指数标度能够很好地再现从主序列到渐近巨分支的所有数据，直到低于先前研究中测试的温度约1000 K。
英文摘要：
We discuss and characterise the power spectral density properties of a model aimed at describing pulsations in stars from the main-sequence to the asymptotic giant branch. We show that the predicted limit of the power spectral density for a pulsation mode in the presence of stochastic noise is always well approximated by a Lorentzian function. While in stars predominantly stochastically driven the width of the Lorentzian is defined by the mode lifetime, in stars where the driving is predominately coherent the width is defined by the amplitude of the stochastic perturbations. In stars where both drivings are comparable, the width is defined by both these parameters and is smaller than that expected from pure stochastic driving. We illustrate our model through numerical simulations and propose a well defined classification of stars into predominantly stochastic (solar-like) and predominately coherent (classic) pulsators. We apply the model to the study of the Mira variable U Per, and the semiregular variable L2 Pup and, following our classification, conclude that they are both classical pulsators. Our model provides a natural explanation for the change in behaviour of the pulsation amplitude-period relation noted in several earlier works. Moreover, our study of L2 Pup enables us to test the scaling relation between the mode line width and effective temperature, confirming that an exponential scaling reproduces well the data all the way from the main sequence to the asymptotic giant branch, down to temperatures about 1000 K below what has been tested in previous studies.
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