Excitation of gravitational wave modes by a center-of-mass velocity of the source

Most gravitational wave (GW) 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 GW 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 the mass and Doppler shift in GW observations and opens a new possibility of detecting the motion of a GW source even for constant velocities.