Modelling stochastic signatures in classical pulsators
Modelling stochastic signatures in classical pulsators
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DOI：
10.1093/mnras/staa125
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发表时间：
2020-01
影响因子：
4.8
通讯作者：
P. Avelino;M. Cunha;W. Chaplin
中科院分区：
文献类型：
--
作者：
P. Avelino;M. Cunha;W. Chaplin
我们考虑随机扰动对经典脉动器其他相干振荡的影响。由此产生的动力学由受外部或内部强迫和白噪声速度波动影响的驱动阻尼谐振子建模。我们使用分析和数值工具来表征相位和相对幅度变化。当强迫是内部的时，相位变化表现出随机游走行为和具有参差不齐的不稳定外观的红噪声功率谱。我们确定均方根相位和相对幅度变化（分别为 $\sigma_{\Delta \varphi}$ 和 $\sigma_{\Delta A/A}$）对随机扰动幅度、阻尼常数 $\eta$ 和总观测时间 $t_{\rm obs}$ 的依赖性，假设相对幅度变化保持较小，表明 $\sigma_{\Delta \varphi}$ 随着对于 $t_{\rm obs} \gg \eta^{-1}$，$t_{\rm obs}^{1/2}$ 远大于 $\sigma_{\Delta A/A}$。在外部强迫的情况下，相位和相对幅度变化保持相同的量级，与观测时间无关。在内部强迫的情况下，我们发现 $\sigma_{\Delta \varphi}$ 不依赖于 $\eta$。因此，不能像类太阳脉动器那样通过拟合信号功率来推断阻尼时间，但随机扰动的幅度可能会受到观测结果的限制。我们的结果意味着，如果有足够的时间，与内部驱动的经典脉动器中的随机扰动相关的相位变化将变得足够大，足以进行观测探测。
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 ($\sigma_{\Delta \varphi}$ and $\sigma_{\Delta A/A}$, respectively) on the amplitude of the stochastic perturbations, the damping constant $\eta$, and the total observation time $t_{\rm obs}$ for this case, under the assumption that the relative amplitude variations remain small, showing that $\sigma_{\Delta \varphi}$ increases with $t_{\rm obs}^{1/2}$ becoming much larger than $\sigma_{\Delta A/A}$ for $t_{\rm obs} \gg \eta^{-1}$. 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 $\sigma_{\Delta \varphi}$ does not depend on $\eta$. 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.