Rush the inspiral: efficient Effective One Body time-domain gravitational waveforms

TL;DR

This paper introduces a high-order post-adiabatic approximation to the effective-one-body model, enabling fast and accurate generation of gravitational waveforms for binary mergers without solving complex differential equations.

Contribution

The authors develop a high-order post-adiabatic approximation that significantly speeds up waveform computation while maintaining accuracy, reducing reliance on traditional numerical ODE solutions.

Findings

PA approximation achieves less than 10^{-3} rad phase difference up to 3 orbits before merger.

Waveform generation is over 100 times faster than standard ODE-based methods.

Approach reduces systematic errors and computational costs in gravitational wave data analysis.

Abstract

Computationally efficient waveforms are of central importance for gravitational wave data analysis of inspiralling and coalescing compact binaries. We show that the post-adiabatic (PA) approximation to the effective-one-body (EOB) description of the binary dynamics, when pushed to high-order, allows one to accurately and efficiently compute the waveform of coalescing binary neutron stars (BNSs) or black holes (BBHs) up to a few orbits before merger. This is accomplished bypassing the usual need of numerically solving the relative EOB dynamics described by a set of ordinary differential equations (ODEs). Under the assumption that radiation reaction is small, the Hamilton's equations for the momenta can be solved {\it analytically} for given values of the relative separation. Time and orbital phase are then recovered by simple numerical quadratures. For the least-adiabatic BBH case, equal-mass, quasi-extremal spins anti-aligned with the orbital angular momentum, 6PA/8PA orders are able to generate waveforms that accumulate less than $10^{-3}$ rad of phase difference with respect to the complete EOB ones up to $\sim 3$ orbits before merger. Analogous results hold for BNSs. The PA waveform generation is extremely efficient: for a standard BNS system from 10Hz, a nonoptimized Matlab implementation of the TEOBResumS EOB model in the PA approximation is more than 100 times faster ($\sim 0.09$ sec) than the corresponding $C^{++}$ code based on a standard ODE solver. Once optimized further, our approach will allow to: (i) avoid the use of the fast, but often inaccurate, post-Newtonian inspiral waveforms, drastically reducing the impact of systematics due to inspiral waveform modelling; (ii) alleviate the need of constructing EOB waveform surrogates to be used in parameter estimation codes.