Most gravitational waves (GWs) sources are moving relative to us. This motion is often closely related to the environment of the source and can thus provide crucial information about the formation of the source and its host. Recently, LIGO and Virgo
detected for the first time the subdominant modes of GWs. We show that a motion of the center-of-mass of the source can affect these modes, where the effect is proportional to the velocity of the source. The effect on the GWs modes in turn affects the overall frequency of the GW, thus leading to a phase shift. We study the impact of this effect on LIGO/Virgo detections and show that it is detectable for sources with high mass ratios and inclinations. This effect breaks the degeneracy between mass and Doppler shift in GWs observations, and opens a new possibility of detecting the motion of a GWs source even for constant velocities.
The velocity of a gravitational wave (GW) source provides crucial information about its formation and evolution processes. Previous studies considered the Doppler effect on the phase of GWs as a potential signature of a time-dependent velocity of the
source. However, the Doppler shift only accounts for the time component of the wave vector, and in principle motion also affects the spatial components. The latter effect, known as ``aberration for light, is analyzed in this paper for GWs and applied to the waveform modeling of an accelerating source. We show that the additional aberrational phase shift could be detectable in two astrophysical scenarios, namely, a recoiling binary black hole (BBH) due to GW radiation and a BBH in a triple system. Our results suggest that adding the aberrational phase shift in the waveform templates could significantly enhance the detectability of moving sources.
