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#### Fast and Fourier: Extreme Mass Ratio Inspiral Waveforms in the Frequency Domain

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2307.12585.pdf

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fams-09-1266739.pdf

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##### Citation

Speri, L., Katz, M., Chua, A. J. K., Hughes, S. A., Warburton, N., Thompson, J. E., et al. (2024).
Fast and Fourier: Extreme Mass Ratio Inspiral Waveforms in the Frequency Domain.* Frontiers in Applied
Mathematics and Statistics,* *9*: 1266739. doi:10.3389/fams.2023.1266739.

Cite as: https://hdl.handle.net/21.11116/0000-000D-82DC-8

##### Abstract

Extreme Mass Ratio Inspirals (EMRIs) are one of the key sources for future

space-based gravitational wave interferometers. Measurements of EMRI

gravitational waves are expected to determine the characteristics of their

sources with sub-percent precision. However, their waveform generation is

challenging due to the long duration of the signal and the high harmonic

content. Here, we present the first ready-to-use Schwarzschild eccentric EMRI

waveform implementation in the frequency domain for use with either graphics

processing units (GPUs) or central processing units (CPUs). We present the

overall waveform implementation and test the accuracy and performance of the

frequency domain waveforms against the time domain implementation. On GPUs, the

frequency domain waveform takes in median $0.044$ seconds to generate and is

twice as fast to compute as its time domain counterpart when considering

massive black hole masses $\geq 2 \times 10^6 \,{\rm M_\odot}$ and initial

eccentricities $e_0 > 0.2$. On CPUs, the median waveform evaluation time is $5$

seconds, and it is five times faster in the frequency domain than in the time

domain. Using a sparser frequency array can further speed up the waveform

generation, reaching up to $ 0.3$ seconds. This enables us to perform, for the

first time, EMRI parameter inference with fully relativistic waveforms on CPUs.

Future EMRI models which encompass wider source characteristics (particularly

black hole spin and generic orbit geometries) will require significantly more

harmonics. Frequency-domain models will be essential analysis tools for these

astrophysically realistic and important signals.

space-based gravitational wave interferometers. Measurements of EMRI

gravitational waves are expected to determine the characteristics of their

sources with sub-percent precision. However, their waveform generation is

challenging due to the long duration of the signal and the high harmonic

content. Here, we present the first ready-to-use Schwarzschild eccentric EMRI

waveform implementation in the frequency domain for use with either graphics

processing units (GPUs) or central processing units (CPUs). We present the

overall waveform implementation and test the accuracy and performance of the

frequency domain waveforms against the time domain implementation. On GPUs, the

frequency domain waveform takes in median $0.044$ seconds to generate and is

twice as fast to compute as its time domain counterpart when considering

massive black hole masses $\geq 2 \times 10^6 \,{\rm M_\odot}$ and initial

eccentricities $e_0 > 0.2$. On CPUs, the median waveform evaluation time is $5$

seconds, and it is five times faster in the frequency domain than in the time

domain. Using a sparser frequency array can further speed up the waveform

generation, reaching up to $ 0.3$ seconds. This enables us to perform, for the

first time, EMRI parameter inference with fully relativistic waveforms on CPUs.

Future EMRI models which encompass wider source characteristics (particularly

black hole spin and generic orbit geometries) will require significantly more

harmonics. Frequency-domain models will be essential analysis tools for these

astrophysically realistic and important signals.