Fourier domain gravitational waveforms for precessing eccentric binaries

TL;DR

This paper introduces two families of Fourier domain waveforms for precessing, eccentric binary systems, improving gravitational wave modeling and parameter estimation accuracy.

Contribution

It develops novel Fourier domain waveforms for precessing eccentric binaries using small eccentricity expansion and shifted uniform asymptotics, enhancing waveform accuracy.

Findings

Waveforms achieve median faithfulness above 0.993.

Circular waveforms may bias parameter recovery for large spins.

Residual eccentricity affects parameter estimation even in circularized systems.

Abstract

We build two families of inspiral waveforms for precessing binaries on eccentric orbits in the Fourier domain. To achieve this, we use a small eccentricity expansion of the waveform amplitudes in order to separate the periastron precession timescale from the orbital timescale, and use a shifted uniform asymptotics transformation to compute the Fourier transform in the presence of spin-induced precession. We show that the resulting waveforms can yield a median faithfulness above 0.993 when compared to an equivalent time domain waveform with an initial eccentricity of $e_0 \approx 0.3$. We also show that when the spins are large, using a circular waveform can potentially lead to significant biases in the recovery of the parameters, even when the system has fully circularized, particularly when the accumulated number of cycles is large. This is an effect of the residual eccentricity present when the objects forming the binary have nonvanishing spin components in the orbital plane.