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

Abstract

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 $1000{\text{km s}}^{-1}$. 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, non-spinning extreme-mass-ratio inspiral. We find that the excitation of higher modes by a peculiar velocity of $1000{\text{kms}}^{-1}$ 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.

arXiv commentAccepted PRL

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• Gravitational Wave Astronomy With TianQin
• Detection of astrophysical gravitational wave sources by TianQin and LISA
• Excitation of gravitational wave modes by a center-of-mass velocity of the source
• Identification of Gravitational-waves from Extreme Mass Ratio Inspirals
• Moving gravitational wave sources at cosmological distances: Impact on the measurement of the Hubble constant
• Improving the Cosmological Constraints by Inferring the Formation Channel of Extreme-mass-ratio Inspirals
• Calculating the Gravitational Waves Emitted from High-speed Sources
• Aberration of gravitational waveforms by peculiar velocity
• Astrophysics with the Laser Interferometer Space Antenna
• Gravitational Wave Signatures of Quasi-Periodic Eruptions: LISA Detection Prospects for RX J1301.9+2747