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

Junjie Luo, Jie Feng, Hong-Hao Zhang, Weipeng Lin

Submitted on 3 November 2022


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.


Subjects: General Relativity and Quantum Cosmology; Astrophysics - Instrumentation and Methods for Astrophysics


Energy error of $H_{1}$ and $H_{2}$ calculated by extended phase-space method without any map. In this situation it is a pure explicit symmetric method for the whole Hamiltonian $\widetilde{H}$. Here the absolute energy error $\Delta \mathcal{H}=H_{i}(t)-H(0), (i=1,2)$ , and $H_{i}(t)$ correspond to the value of the Hamiltonian $H_{1}$ or $H_{2}$ at time t, and $H(0)$ is the initial value of origin Hamiltonian $H$. It is obvious that there exist symmetry between $\Delta\mathcal{H}_1$(red) and $\Delta\mathcal{H}_2$(blue).