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Gravitational waves from a source moving relative to us can suffer fromspecial-relativistic effects such as aberration. The required velocities forthese to be significant are on the order of $1000\,\textrm{km s}^{-1}$. Thisvalue corresponds to the velocity dispersion that one finds in clusters ofgalaxies. Hence, we expect a large number of gravitational-wave sources to havesuch effects imprinted in their signals. In particular, the signal from amoving source will have its higher modes excited, i.e., $(3,3)$ and beyond. Wederive expressions describing this effect, and study its measurability for thespecific case of a circular, non-spinning extreme-mass-ratio inspiral. We findthat the excitation of higher modes by a peculiar velocity of$1000\,\textrm{km\,s}^{-1}$ is detectable for such inspirals withsignal-to-noise ratios of $\gtrsim20$. Using a Fisher matrix analysis, we showthat the velocity of the source can be measured to a precision of just a fewpercent for a signal-to-noise ratio of 100. If the motion of the source isignored parameter estimates could be biased, e.g., the estimated masses of thecomponents through a Doppler shift. Conversely, by including this effect inwaveform models, we could measure the velocity dispersion of clusters ofgalaxies at distances inaccessible to light.

Exciting modes due to the aberration of gravitational waves: Measurability for extreme-mass-ratio inspirals