The fast and the frame-dragging: efficient waveforms for asymmetric-mass eccentric equatorial inspirals into rapidly-spinning black holes

Abstract

Observations of gravitational-wave signals emitted by compact binary inspirals provide unique insights into their properties, but their analysis requires accurate and efficient waveform models. Intermediate- and extreme-mass-ratio inspirals (I/EMRIs), with mass ratios q≳102, are promising sources for future detectors such as the Laser Interferometer Space Antenna (LISA). Modelling waveforms for these asymmetric-mass binaries is challenging, entailing the tracking of many harmonic modes over thousands to millions of cycles. The FastEMRIWaveforms (FEW) modelling framework addresses this need, leveraging precomputation of mode data and interpolation to rapidly compute adiabatic waveforms for eccentric inspirals into zero-spin black holes. In this work, we extend FEW to model eccentric equatorial inspirals into black holes with spin magnitudes |a|≤0.999. Our model supports eccentricities e<0.9 and semi-latus recta p<200, enabling the generation of long-duration IMRI waveforms, and produces waveforms in ∼100 ms with hardware acceleration. Characterising systematic errors, we estimate that our model attains mismatches of ∼10−5 (for LISA sensitivity) with respect to error-free adiabatic waveforms over most of parameter space. We find that kludge models introduce errors in signal-to-noise ratios (SNRs) as great as +60%−40% and induce marginal biases of up to ∼1σ in parameter estimation. We show LISA's horizon redshift for I/EMRI signals varies significantly with a, reaching a redshift of 3 (15) for EMRIs (IMRIs) with only minor (∼10%) dependence on e for an SNR threshold of 20. For signals with SNR ∼50, spin and eccentricity-at-plunge are measured with uncertainties of δa∼10−7 and δef∼10−5. This work advances the state-of-the-art in waveform generation for asymmetric-mass binaries.

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Identifiers

ORCID for Zach Nasipak: orcid.org/0000-0002-5109-9704

ORCID for Jonathan E. Thompson: orcid.org/0000-0002-0419-5517

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