We construct a star with uniform density in frame of tracking Rastall gravity, in which the density of effective dark matter tracks the density of dark energy. To demonstrate stability of the star we analyse the axial gravitational perturbations of the star. We find that echo wavelets naturally appear in the axial gravitational waves when the dark matter plays a significant role in construction of the star. We show that the physical origin of this echo roots in the potential valley near the surface of star. This effect leads to a clue to detect Rastall dark energy from the ringdown phase of gravitational wave from binary stars enriched by dark matter.

中文翻译：

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追踪拉斯托尔引力的恒星回声

我们在跟踪拉斯托尔引力的框架下构建了一颗密度均匀的恒星，其中有效暗物质的密度跟踪暗能量的密度。为了证明恒星的稳定性，我们分析了恒星的轴向引力摄动。我们发现当暗物质在恒星的构造中起重要作用时，回波小波自然出现在轴向引力波中。我们表明，这种回波的物理起源源于恒星表面附近的势能谷。这种效应导致了一条线索，可以从富含暗物质的双星引力波的振铃阶段检测拉斯托尔暗能量。