Compact binary evolutions with the Z4c formulation

Numerical relativity simulations of compact binaries with the Z4c and Baumgarte-Shapiro-ShibataNakamura- Oohara-Kojima (BSSNOK) formulations are compared. The Z4c formulation is advantageous in every case considered. In simulations of nonvacuum spacetimes, the constraint violations due to truncation errors are between 1 and 3 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 4 smaller. The quality of the Z4c numerical data is also demonstrated by a remarkably accurate computation of the Arnowitt-Deser-Misner mass from surface integrals. For equal-mass nonspinning 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 2 smaller. In the same evolutions, we find that away from the punctures the Hamiltonian constraint violation is reduced by between 1 and 2 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 confirms earlier results in spherical symmetry. The boundary conditions avoid spurious and nonconvergent 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.