Performance of different correction maps in the extended phase-space method for spinning compact binaries

TL;DR

This paper evaluates correction maps in the extended phase-space method for spinning compact binaries, aiming to improve numerical accuracy and stability in gravitational wave signal analysis, especially in chaotic orbits.

Contribution

It introduces new correction maps that reduce energy bias in Hamiltonian subterms, enhancing the method's accuracy for chaotic orbital simulations.

Findings

New correction maps decrease energy bias in Hamiltonian subterms.

Enhanced accuracy and stability in numerical solutions for chaotic orbits.

Provides a novel approach for applying manifold correction in similar algorithms.

Abstract

Since the first detection of gravitational waves by the LIGO/VIRGO team, the related research field has attracted more attention. The spinning compact binaries system, as one of the gravitational-wave sources for broadband laser interferometers, has been widely studied by related researchers. In order to analyze the gravitational wave signals using matched filtering techniques, reliable numerical algorithms are needed. Spinning compact binaries systems in Post-Newtonian (PN) celestial mechanics have an inseparable Hamiltonian. The extended phase-space algorithm is an effective solution for the problem of this system. We have developed correction maps for the extended phase-space method in our previous work, which significantly improves the accuracy and stability of the method with only a momentum scale factor. In this paper, we will add more scale factors to modify the numerical solution in order to minimize the errors in the constants of motion. However, we find that these correction maps will result in a large energy bias in the subterms of the Hamiltonian in chaotic orbits, whose potential and kinetic energy, etc. are calculated inaccurately. We develop new correction maps to reduce the energy bias of the subterms of the Hamiltonian, which can instead improve the accuracy of the numerical solution and also provides a new idea for the application of the manifold correction in other algorithms.