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

TL;DR

This paper investigates how relativistic aberration affects gravitational wave signals from extreme-mass-ratio inspirals, demonstrating that higher modes can be excited and measured, enabling velocity and cluster dispersion estimates at large distances.

Contribution

It derives expressions for aberration effects on gravitational waves and shows their measurability, allowing for velocity measurements and bias reduction in parameter estimation.

Findings

Higher modes are excited by velocities around 1000 km/s.

Velocity can be measured to a few percent accuracy at SNR 100.

Aberration effects can bias mass estimates if ignored.

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 $1000\,\textrm{km s}^{-1}$. 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 $1000\,\textrm{km\,s}^{-1}$ is detectable for such inspirals with signal-to-noise ratios of $\gtrsim20$. 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.