EFPE: Efficient fully precessing eccentric gravitational waveforms for binaries with long inspirals

TL;DR

This paper introduces an efficient method for generating accurate gravitational waveforms from eccentric, precessing binary systems, significantly reducing computation time while maintaining high fidelity for long inspiral signals.

Contribution

It develops a new set of equations of motion for eccentric, precessing binaries that are computationally efficient and accurate, enabling detailed Bayesian analysis of long gravitational wave signals.

Findings

Waveform evaluation time reduced by a factor of 10-50

Maintains mismatch of 10^{-4} - 10^{-6} over long signals

Applicable to Bayesian parameter estimation for LISA sources

Abstract

In this paper, we derive a set of equations of motions for binaries on eccentric orbits undergoing spin-induced precession that can efficiently be integrated on the radiation-reaction timescale. We find a family of solutions with a computation cost improved by a factor $10$ - $50$ down to $\sim 10$ ms per waveform evaluation compared to waveforms obtained by directly integrating the precession equations, that maintain a mismatch of the order $10^{-4}$ - $10^{-6}$ for waveforms lasting a million orbital cycles and a thousand spin-induced precession cycles. We express it in terms of parameters that make the solution regular in the equal-mass limit, thus bypassing a problem of previous similar solutions. We point to ways in which the solution presented in this paper can be perturbed to take into account effects such as general quadrupole momenta and post-Newtonian corrections to the precession equations. This new waveform, with its improved efficiency and its accuracy, makes possible Bayesian parameter estimation using the full spin and eccentricity parameter volume for long lasting inspiralling signals such as stellar-origin black hole binaries observed by LISA.