$ν_{\rm max}-ν_{\rm c}$关系的基本物理意义
The underlying physical meaning of the $ν_{\rm max}-ν_{\rm c}$ relation
摘要：
随着CoRoT和开普勒飞行任务获得的大量观测结果，对表现出类似太阳振荡的恒星的星震学越来越感兴趣。在这个框架内，星震量和恒星参数之间的标度律正成为研究各种恒星的重要工具。然而，这些标度律的物理基础机制仍然知之甚少。我们的目标是提供一个理论基础之间的缩放功率谱（$ν_{\rm max}$）和截止频率（$ν_{\rm c}$）的类太阳振荡的最大频率。利用SoHO GOLF观测资料和理论分析，我们首先确认振荡功率谱中的最大高度是由所谓的阻尼率的\emph{plateau}决定的。高原的物理起源可以追溯到最上层的熵的拉格朗日扰动的不稳定效应，这变得重要时，模态周期和局部热松弛时间尺度是可比的。基于这种分析，我们发现$ν_{\rm max}$和$ν_{\rm c}$之间存在线性关系，其系数取决于激励湍流的马赫数与混合长度参数的三次方之比。
英文摘要：
Asteroseismology of stars that exhibit solar-like oscillations are enjoying a growing interest with the wealth of observational results obtained with the CoRoT and Kepler missions. In this framework, scaling laws between asteroseismic quantities and stellar parameters are becoming essential tools to study a rich variety of stars. However, the physical underlying mechanisms of those scaling laws are still poorly known. Our objective is to provide a theoretical basis for the scaling between the frequency of the maximum in the power spectrum ($ν_{\rm max}$) of solar-like oscillations and the cut-off frequency ($ν_{\rm c}$). Using the SoHO GOLF observations together with theoretical considerations, we first confirm that the maximum of the height in oscillation power spectrum is determined by the so-called \emph{plateau} of the damping rates. The physical origin of the plateau can be traced to the destabilizing effect of the Lagrangian perturbation of entropy in the upper-most layers which becomes important when the modal period and the local thermal relaxation time-scale are comparable. Based on this analysis, we then find a linear relation between $ν_{\rm max}$ and $ν_{\rm c}$, with a coefficient that depends on the ratio of the Mach number of the exciting turbulence to the third power to the mixing-length parameter.
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