arXiv 2001.045582020-01-13astro-ph.SR

经典脉冲发生器中随机信号的建模

Modelling Stochastic Signatures in Classical Pulsators

P. P. Avelino, M. S. Cunha, W. J. Chaplin

备注：: 7 pages, 5 figures, accepted for publication in Monthly Notices of the Royal Astronomical Society
DOI：: 10.1093/mnras/staa125

摘要：

我们考虑了随机扰动对经典非线性系统相干振荡的影响。由此产生的动态模型由一个驱动阻尼谐振子受到外部或内部强迫和白噪声速度波动。我们使用分析和数值工具来表征相位和相对振幅的变化。当强迫是内部的相位变化显示随机游走行为和红噪声功率谱与参差不齐的不稳定的外观。我们确定的均方根相位和相对振幅变化（$σ_{Δφ}$和$σ_{ΔA/A}$，分别）的随机扰动的振幅，阻尼常数$η$，和总的观察时间$t_{\rm obs}$这种情况下，假设相对振幅变化保持小，表明$σ_{Δφ}$增加$t_{\rm obs}^{1/2}$变得比$σ_{ΔA/A}$为$t_{\rm obs} \gg η^{-1}$。在外部强迫的情况下，相位和相对振幅的变化保持相同的顺序，独立于观测时间。在内部强迫的情况下，我们发现$σ_{Δφ}$不依赖于$η$。因此，阻尼时间不能从拟合信号的功率来推断，就像对类太阳振荡器所做的那样，但是随机扰动的幅度可以从观测中得到约束。我们的结果意味着，如果有足够的时间，与内部驱动的经典扰动相关的相位的变化将变得足够大，可以观测到。

英文摘要：

We consider the impact of stochastic perturbations on otherwise coherent oscillations of classical pulsators. The resulting dynamics are modelled by a driven damped harmonic oscillator subject to either an external or an internal forcing and white noise velocity fluctuations. We characterize the phase and relative amplitude variations using analytical and numerical tools. When the forcing is internal the phase variation displays a random walk behaviour and a red noise power spectrum with a ragged erratic appearance. We determine the dependence of the root mean square phase and relative amplitude variations ($σ_{Δφ}$ and $σ_{ΔA/A}$, respectively) on the amplitude of the stochastic perturbations, the damping constant $η$, and the total observation time $t_{\rm obs}$ for this case, under the assumption that the relative amplitude variations remain small, showing that $σ_{Δφ}$ increases with $t_{\rm obs}^{1/2}$ becoming much larger than $σ_{ΔA/A}$ for $t_{\rm obs} \gg η^{-1}$. In the case of an external forcing the phase and relative amplitude variations remain of the same order, independent of the observing time. In the case of an internal forcing, we find that $σ_{Δφ}$ does not depend on $η$. Hence, the damping time cannot be inferred from fitting the power of the signal, as done for solar-like pulsators, but the amplitude of the stochastic perturbations may be constrained from the observations. Our results imply that, given sufficient time, the variation of the phase associated to the stochastic perturbations in internally driven classical pulsators will become sufficiently large to be probed observationally.

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英文摘要：

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