Gravitational waves from a source moving relative to us can suffer from special-relativistic effects such as aberration. The required velocities for these to be significant are on the order of $1000\mathrm{km}{\mathrm{s}}^{-1}$. This value corresponds to the velocity dispersion that one finds in clusters of galaxies. Hence, we expect a large number of gravitational-wave sources to have such effects imprinted in their signals. In particular, the signal from a moving source will have its higher modes excited, i.e., (3,3) and beyond. We derive expressions describing this effect and study its measurability for the specific case of a circular, nonspinning extreme-mass-ratio inspiral. We find that the excitation of higher modes by a peculiar velocity of $1000\mathrm{km}{\mathrm{s}}^{-1}$ is detectable for such inspirals with signal-to-noise ratios of $\gtrsim 20$. Using a Fisher matrix analysis, we show that the velocity of the source can be measured to a precision of just a few percent for a signal-to-noise ratio of 100. If the motion of the source is ignored, parameter estimates could be biased, e.g., the estimated masses of the components through a Doppler shift. Conversely, by including this effect in waveform models, we could measure the velocity dispersion of clusters of galaxies at distances inaccessible to light.

中文翻译：

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引力波像差引起的激发模式：极端质量比螺旋的可测量性

来自相对于我们运动的源的引力波可能会受到特殊相对论效应的影响，例如像差。使这些显着所需的速度约为$1000\mathrm{公里}{\mathrm{秒}}^{-1}$. 该值对应于人们在星系团中发现的速度色散。因此，我们预计大量引力波源会在它们的信号中留下这种影响。特别是，来自移动源的信号将激发其更高的模式，即 (3,3) 及更高模式。我们推导出描述这种效应的表达式，并研究其在圆形、非旋转极端质量比螺旋的特定情况下的可测量性。我们发现通过特殊的速度激发更高的模式$1000\mathrm{公里}{\mathrm{秒}}^{-1}$ 可检测到信噪比为 $\gtrsim 20$. 使用 Fisher 矩阵分析，我们表明，对于 100 的信噪比，源的速度可以测量到只有几个百分点的精度。如果源的运动被忽略，参数估计可能会有偏差，例如，通过多普勒频移估计的分量质量。相反，通过在波形模型中包含这种效应，我们可以在光无法到达的距离测量星系团的速度色散。