标题： 太阳黑子本影大气中3分钟慢磁声波的非线性 显示英文标题

标题： Nonlinearity of 3 minute Slow Magnetoacoustic Waves in the Sunspot Umbral Atmosphere

摘要： 具有3分钟周期的慢磁声波是向上传播的波，通过密度分层的本影大气。 密度的降低导致它们的振幅增加，通过倾斜发展成非线性波，最终形成激波。 为了研究这种波非线性的垂直演化，我们利用了太阳动力学天文台（SDO）上的大气成像仪（AIA）多波长数据，覆盖从光球到低日冕的20个活动区。 波形的倾斜导致高次谐波的产生。 我们使用小波分析得到的二阶谐波振幅与基频振幅的比值来量化这一点，称为非线性指数（NI）。 我们发现一种特征模式：非线性从光球层经过低色球层逐渐增加，在AIA 1700 Å形成高度附近达到峰值，并在更高高度处减少，特别是在AIA 304 Å通道中。 这一趋势表明波的逐渐倾斜和随后的能量耗散，在到达AIA 304 Å形成之前，与低层大气中的激波形成一致。 在AIA 131 Å通道中观察到NI的额外上升，随后在AIA 171 Å中下降，表明低日冕中波非线性演化的第二阶段。 基于NI分布和这些通道的形成高度，我们推测非线性波过程最显著地出现在AIA 1700 Å和AIA 304 Å形成层之间，以及AIA 131 Å和AIA 171 Å之间。 显示英文摘要

摘要： Slow magnetoacoustic waves with a 3 minute period are upward-propagating waves traveling through the density-stratified umbral atmosphere. The decreasing density causes their amplitude to increase, developing into nonlinear waves through steepening and eventually forming shocks. To investigate the vertical evolution of this wave nonlinearity, we utilized multi-wavelength data from the Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamics Observatory (SDO), covering from the photosphere to the lower corona across 20 active regions. The steepening of the wave profile leads to the generation of higher harmonics. We quantify this using a nonlinearity index (NI), defined as the ratio of the amplitude of 2nd harmonic to the fundamental obtained using wavelet analysis. We find a characteristic pattern: nonlinearity increases from the photosphere through the lower chromosphere, peaking near the AIA 1700 \r{A} formation height, and decreases at higher altitudes, notably in the AIA 304 \r{A} channel. This trend indicates progressive wave steepening and subsequent energy dissipation before reaching the formation of AIA 304 \r{A}, consistent with shock formation in the lower atmosphere. An additional rise in NI is observed at the AIA 131 \r{A} channel, followed by a decline in AIA 171 \r{A}, suggesting a 2nd phase of wave nonlinearity evolution in the lower corona. Based on the NI profile and the formation heights of these channels, we conjecture that nonlinear wave processes are most prominent between the AIA 1700 \r{A} and AIA 304 \r{A} formation layers and again between AIA 131 \r{A} and AIA 171 \r{A}.