Compact binary evolutions with the Z4c formulation

TL;DR

This paper demonstrates that the Z4c formulation of the Einstein equations offers significant improvements over BSSNOK in numerical relativity simulations of compact binaries, reducing constraint violations and enhancing gravitational waveform accuracy.

Contribution

The study provides a comprehensive comparison showing Z4c's advantages in accuracy and constraint preservation over BSSNOK in various compact binary simulations.

Findings

Z4c reduces constraint violations by 1-3 orders of magnitude.

Waveform phase and amplitude errors are up to four times smaller with Z4c.

Boundary conditions with Z4c prevent spurious effects in simulations.

Abstract

Numerical relativity simulations of compact binaries with the Z4c and BSSNOK formulations are compared. The Z4c formulation is advantageous in every case considered. In simulations of non-vacuum spacetimes the constraint violations due to truncation errors are between one and three orders of magnitude lower in the Z4c evolutions. Improvements are also found in the accuracy of the computed gravitational radiation. For equal-mass irrotational binary neutron star evolutions we find that the absolute errors in phase and amplitude of the waveforms can be up to a factor of four smaller. The quality of the Z4c numerical data is also demonstrated by a remarkably accurate computation of the ADM mass from surface integrals. For equal-mass non-spinning binary puncture black hole evolutions we find that the absolute errors in phase and amplitude of the waveforms can be up to a factor of two smaller. In the same evolutions we find that away from the punctures the Hamiltonian constraint violation is reduced by between one and two orders of magnitude. Furthermore, the utility of gravitational radiation controlling, constraint preserving boundary conditions for the Z4c formulation is demonstrated. The evolution of spacetimes containing a single compact object confirm earlier results in spherical symmetry. The boundary conditions avoid spurious and non-convergent effects present in high resolution runs with either formulation with a more naive boundary treatment. We conclude that Z4c is preferable to BSSNOK for the numerical solution of the 3+1 Einstein equations with the puncture gauge.