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arXiv · 2010.15842

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

Alejandro Torres-Orjuela·Pau Amaro Seoane·Zeyuan Xuan·Alvin J. K. Chua·María J. B. Rosell·Xian Chen
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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.

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Alejandro Torres-Orjuela, Pau Amaro Seoane, Zeyuan Xuan, Alvin J. K. Chua, María J. B. Rosell, Xian Chen. 2020-10-29. Exciting modes due to the aberration of gravitational waves: Measurability for extreme-mass-ratio inspirals. https://doi.org/10.1103/physrevlett.127.041102

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