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#### Adiabatic waveforms for extreme mass-ratio inspirals via multivoice decomposition in time and frequency

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##### Citation

Hughes, S. A., Warburton, N., Khanna, G., Chua, A. J. K., & Katz, M. L. (2021).
Adiabatic waveforms for extreme mass-ratio inspirals via multivoice decomposition in time and frequency.*
Physical Review D,* *103*(10): 104014. doi:10.1103/PhysRevD.103.104014.

Cite as: https://hdl.handle.net/21.11116/0000-0008-A111-E

##### Abstract

We compute adiabatic waveforms for extreme mass-ratio inspirals (EMRIs) by

"stitching" together a long inspiral waveform from a sequence of waveform

snapshots, each of which corresponds to a particular geodesic orbit. We show

that the complicated total waveform can be regarded as a sum of "voices." Each

voice evolves in a simple way on long timescales, a property which can be

exploited to efficiently produce waveform models that faithfully encode the

properties of EMRI systems. We look at examples for a range of different

orbital geometries: spherical orbits, equatorial eccentric orbits, and one

example of generic (inclined and eccentric) orbits. To our knowledge, this is

the first calculation of a generic EMRI waveform that uses strong-field

radiation reaction. We examine waveforms in both the time and frequency

domains. Although EMRIs evolve slowly enough that the stationary phase

approximation (SPA) to the Fourier transform is valid, the SPA calculation must

be done to higher order for some voices, since their instantaneous frequency

can change from chirping forward ($\dot f > 0$) to chirping backward ($\dot f <

0$). The approach we develop can eventually be extended to more complete EMRI

waveform models, for example to include effects neglected by the adiabatic

approximation such as the conservative self force and spin-curvature coupling.

"stitching" together a long inspiral waveform from a sequence of waveform

snapshots, each of which corresponds to a particular geodesic orbit. We show

that the complicated total waveform can be regarded as a sum of "voices." Each

voice evolves in a simple way on long timescales, a property which can be

exploited to efficiently produce waveform models that faithfully encode the

properties of EMRI systems. We look at examples for a range of different

orbital geometries: spherical orbits, equatorial eccentric orbits, and one

example of generic (inclined and eccentric) orbits. To our knowledge, this is

the first calculation of a generic EMRI waveform that uses strong-field

radiation reaction. We examine waveforms in both the time and frequency

domains. Although EMRIs evolve slowly enough that the stationary phase

approximation (SPA) to the Fourier transform is valid, the SPA calculation must

be done to higher order for some voices, since their instantaneous frequency

can change from chirping forward ($\dot f > 0$) to chirping backward ($\dot f <

0$). The approach we develop can eventually be extended to more complete EMRI

waveform models, for example to include effects neglected by the adiabatic

approximation such as the conservative self force and spin-curvature coupling.