标题： 太阳模型中截止频率的数值确定 显示英文标题

标题： Numerical determination of the cutoff frequency in solar models

摘要： 在分层大气中，声波只有当其频率高于截止值时才能传播。 不同的理论提供了不同的截止值。 我们开发了一种替代方法，在几种标准的太阳模型中推导出截止频率，包括各种宁静日冕和半影大气。 我们对太阳大气中的波传播进行了数值模拟。 截止频率是通过检查两个大气高度处速度信号之间的相位差谱来确定的。 该过程是通过在光球层和色球层之间的所有层中选择高度对，以推导太阳模型中截止频率的垂直分层。 理论计算预测的截止频率与我们的测量结果有显著差异。 在宁静日冕大气中，截止频率对于绝热波传播的磁场具有强烈的依赖性。 当考虑辐射损失时，截止频率大大降低，且截止频率随磁场强度变化的幅度也较低。 了解辐射损失对截止频率的影响对于理解最近的宁静日冕和太阳黑子观测是必要的。 在存在倾斜磁场的情况下，我们的数值计算证实了由于沿磁场方向传播的波所经历的重力减小而导致的截止频率降低。 在温度有显著变化的区域，还发现了额外的降低，这是由于沿磁场引导波路径的温度梯度较低。 我们的结果表明，理论估计未能正确捕捉到截止值。 此外，大多数广泛使用的解析截止公式忽略了磁场和辐射损失的影响，而这些因素在确定波的衰减或传播性质方面起着关键作用。 显示英文摘要

摘要： In stratified atmospheres, acoustic waves can only propagate if their frequency is above the cutoff value. Different theories provide different cutoff values. We developed an alternative method to derive the cutoff frequency in several standard solar models, including various quiet-Sun and umbral atmospheres. We performed numerical simulations of wave propagation in the solar atmosphere. The cutoff frequency is determined from the inspection of phase difference spectra computed between the velocity signal at two atmospheric heights. The process is performed by choosing pairs of heights across all the layers between the photosphere and the chromosphere, to derive the vertical stratification of the cutoff in the solar models. The cutoff frequency predicted by the theoretical calculations departs significantly from our measurements. In quiet-Sun atmospheres, the cutoff shows a strong dependence on the magnetic field for adiabatic wave propagation. When radiative losses are taken into account, the cutoff frequency is greatly reduced and the variation of the cutoff with the strength of the magnetic field is lower. The effect of the radiative losses in the cutoff is necessary to understand recent quiet-Sun and sunspot observations. In the presence of inclined magnetic fields, our numerical calculations confirm the reduction of the cutoff frequency due to the reduced gravity experienced by waves propagating along field lines. An additional reduction is also found in regions with significant changes in the temperature, due to the lower temperature gradient along the path of field-guided waves. Our results show that the cutoff values are not correctly captured by theoretical estimates. In addition, most of the widely-used analytical cutoff formulae neglect the impact of magnetic fields and radiative losses, whose role is critical to determine the evanescent or propagating nature of the waves.