We report and discuss the phase shift and phase travel time of low-frequency (ν < 5.0 mHz) acoustic waves estimated within the photosphere and photosphere–chromosphere interface regions, utilizing multiheight velocities in the quiet Sun. The bisector method has been employed to estimate seven height velocities in the photosphere within the Fe i 6173 Å line scan, while nine height velocities are estimated from the chromospheric Ca ii 8542 Å line scan observations obtained from the narrowband imager instrument installed on the Multi-Application Solar Telescope operational at the Udaipur Solar Observatory, India. Utilizing a fast Fourier transform at each pixel over the full field of view, phase shift and coherence have been estimated. The frequency and height-dependent phase shift integrated over the regions having an absolute line-of-sight magnetic field of less than 10 G indicates the nonevanescent nature of low-frequency acoustic waves within the photosphere and photosphere–chromosphere interface regions. Phase travel time estimated within the photosphere shows nonzero values, aligning with previous simulations and observations. Further, we report that the nonevanescent nature persists beyond the photosphere, encompassing the photospheric–chromospheric height range. We discuss possible factors contributing to the nonevanescent nature of low-frequency acoustic waves. Additionally, our observations reveal a downward propagation of high-frequency acoustic waves indicating refraction from higher layers in the solar atmosphere. This study contributes valuable insights into the understanding of the complex dynamics of acoustic waves within different lower solar atmospheric layers, shedding light on the nonevanescent nature and downward propagation of the acoustic waves.

中文翻译：

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使用多高度速度研究太阳低层大气中声波的相移和传播时间


我们报告并讨论了利用安静太阳中的多高度速度在光球层和光球层-色球层界面区域内估计的低频（ν < 5.0 mHz）声波的相移和相传播时间。平分线法已用于估计 Fe i 6173 Å 线扫描内光球层中的七个高度速度，而九个高度速度是根据安装在 Multi- 上的窄带成像仪获得的色球 Ca ii 8542 Å 线扫描观测值估计的。印度乌代布尔太阳天文台运行的应用太阳望远镜。在整个视场的每个像素处利用快速傅里叶变换，估计了相移和相干性。在绝对视线磁场小于 10 G 的区域上积分的频率和高度相关的相移表明光球层和光球层-色球层界面区域内低频声波的非消失性质。光球内估计的相位传播时间显示非零值，与之前的模拟和观测结果一致。此外，我们报告说，非消失性质持续存在于光球层之外，涵盖光球层-色球层的高度范围。我们讨论了导致低频声波非消失性质的可能因素。此外，我们的观测揭示了高频声波的向下传播，表明来自太阳大气中高层的折射。这项研究为理解不同较低太阳大气层内声波的复杂动力学提供了宝贵的见解，揭示了声波的非消失性质和向下传播。