Constraint damping of the conformal and covariant formulation of the Z4 system in simulations of binary neutron stars

Daniela Alic, Wolfgang Kastaun, and Luciano Rezzolla
Phys. Rev. D 88, 064049 – Published 24 September 2013

Abstract

Following previous work in vacuum spacetimes, we investigate the constraint-damping properties in the presence of matter of the recently developed traceless, conformal and covariant Z4 (CCZ4) formulation of the Einstein equations. First, we evolve an isolated neutron star with an ideal gas equation of state and subject to a constraint-violating perturbation. We compare the evolution of the constraints using the CCZ4 and Baumgarte-Shibata-Shapiro-Nakamura-Oohara-Kojima (BSSNOK) systems. Second, we study the collapse of an unstable spherical star to a black hole. Finally, we evolve binary neutron star systems over several orbits until the merger, the formation of a black hole, and up to the ringdown. We show that the CCZ4 formulation is stable in the presence of matter and that the constraint violations are 1 or more orders of magnitude smaller than for the BSSNOK formulation. Furthermore, by comparing the CCZ4 and the BSSNOK formulations also for neutron star binaries with large initial constraint violations, we investigate their influence on the errors on physical quantities. We also give a new, simple and robust prescription for the damping parameter that removes the instabilities found when using the fully covariant version of CCZ4 in the evolution of black holes. Overall, we find that at essentially the same computational costs, the CCZ4 formulation provides solutions that are stable and with a considerably smaller violation of the Hamiltonian constraint than the BSSNOK formulation. We also find that the performance of the CCZ4 formulation is very similar to another conformal and traceless, but noncovariant formulation of the Z4 system, i.e., the Z4c formulation.

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  • Received 28 July 2013

DOI:https://doi.org/10.1103/PhysRevD.88.064049

© 2013 American Physical Society

Authors & Affiliations

Daniela Alic1, Wolfgang Kastaun1, and Luciano Rezzolla1,2

  • 1Max-Planck-Institut für Gravitationsphysik, Albert-Einstein-Institut, Potsdam 14476, Germany
  • 2Institute for Theoretical Physics, Max von Laue Straße 1, 60438 Frankfurt am Main, Germany

See Also

Conformal and covariant formulation of the Z4 system with constraint-violation damping

Daniela Alic, Carles Bona-Casas, Carles Bona, Luciano Rezzolla, and Carlos Palenzuela
Phys. Rev. D 85, 064040 (2012)

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Vol. 88, Iss. 6 — 15 September 2013

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