Volume 439, Number 3, September I 2005
|Page(s)||1033 - 1055|
|Section||Stellar structure and evolution|
|Published online||12 August 2005|
CFC+: improved dynamics and gravitational waveforms from relativistic core collapse simulations
Departamento de Astronomía y Astrofísica, Universidad de Valencia, Dr. Moliner, 50, 46100 Burjassot, Valencia, Spain e-mail: firstname.lastname@example.org
2 Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universität Jena, Max-Wien-Platz 1, 07743 Jena, Germany
3 Institut d'Astrophysique de Paris, 98 boulevard Arago, 75014 Paris, France
4 Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, 85741 Garching, Germany
Accepted: 24 January 2005
Core collapse supernovae are a promising source of detectable gravitational waves. Most of the existing (multidimensional) numerical simulations of core collapse in general relativity were done using approximations of the Einstein field equations. As recently shown by Dimmelmeier et al. (2002a, A&A, 388, 917), Dimmelmeier et al. (2002b, A&A, 393, 523), one of the most interesting such approximations is the so-called conformal flatness condition (CFC) of Isenberg, Wilson; and Mathews. Building on this previous work we present new results from numerical simulations of relativistic rotational core collapse in axisymmetry, with the aim of improving the dynamics and gravitational waveforms. The computer code used for these simulations models the evolution of the coupled system of metric and fluid equations using the formalism, specialized to a new framework for the gravitational field equations we call CFC+. In this approach we add new degrees of freedom to the original CFC equations, which extend them by terms of second post-Newtonian order. The resulting metric equations are still of elliptic type, but the number of equations is significantly augmented in comparison to the original CFC approach. The hydrodynamic evolution and the CFC spacetime metric are calculated with the code developed by Dimmelmeier et al.(2002a, A&A, 388, 917), which has been conveniently extended to account for the additional CFC+ equations. The corrections included in CFC+ are computed by solving a system of elliptic linear equations. The new formalism is assessed with time evolutions of both rotating neutron stars in equilibrium and gravitational core collapse of rotating polytropes. Gravitational wave signals for a comprehensive sample of collapse models are extracted using either the quadrupole formula or directly from the metric. We discuss our results on the dynamics and the gravitational wave emission through a detailed comparison between CFC and CFC+ simulations. The main conclusion is that, for the neutron star spacetimes analyzed in the present work, no significant differences are found among CFC, CFC+, and full general relativity, which highlights the suitability of the former.
Key words: gravitation / gravitational waves / hydrodynamics / methods: numerical / relativity / stars: supernovae: general
© ESO, 2005
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