白矮星和B型热亚矮星是中小质量恒星演化晚期形态，其穿越不稳定带时会发生振动。而振动模式的频率和振幅调制是恒星非线性振动理论的一个重要预言。由于该现象的观测研究对数据质量要求极高，直到近年来Kepler卫星提供了超高精度观测数据，才使得该领域研究成为可能。本项目将基于Kepler和TESS卫星的超高精度测光数据，系统地开展脉动白矮星和B型热亚矮星振动模式调制性质及其规律的研究。利用空间观测一年以上的连续数据，可分析这两类演化晚期恒星振动模式的振幅和频率在时域上的调制性质，确定调制形式，构建精确星震学模型，从而在观测上限制非线性振动的关键物理量，得出振动模式的线性增长率。预期研究结果将增进对恒星振动模式调制的认识，推动恒星振动理论的进一步发展。

White dwarfs and hot B subdwarfs are at the evloved phase of low mass stars. When they evolve across the instability stripes, their luminosity reveals variations as they begin to oscillate. Amplitude and frequency modulations of oscillation modes in those types of pulsating stars is well predicted by nonlinear stellar oscillation theory. Due to nonlinear weak interactions between involved modes, the discovery of these phenomena is particular difficult. Thanks for the successful launch of Kepler, now it is possible to have systematic investigation on this field. Our project is exactly on that path based on the ultra-high precise photometry collected by Kepler and TESS mission. Due to the faintness of those stars, only about twenty targets will be suitable for our projects where they are in the Kepler original field and TESS continous viewing zone. We will characterize the precise patterns of amplitude and frequency modulations of resonant modes aiming at investigate their stability and variability over a large number of modes. With the precise resolved eigen frequencies, the precise seismic models will be performed on the most interesting targets. Our works will, observationally, give solid contraints on the nonlinear coefficients within the amplitude equation formalism, as well as the linear growth rates of the resonant modes. The successful results will basically change our view on the knowledge of variability and stability of oscillation modes in compact pulsators, paving an avenue to move the nonlinear theory of stellar oscillation further.