Issue |
A&A
Volume 439, Number 3, September I 2005
|
|
---|---|---|
Page(s) | 1033 - 1055 | |
Section | Stellar structure and evolution | |
DOI | https://doi.org/10.1051/0004-6361:20042602 | |
Published online | 12 August 2005 |
CFC+: improved dynamics and gravitational waveforms from relativistic core collapse simulations
1
Departamento de Astronomía y Astrofísica, Universidad de Valencia, Dr. Moliner, 50, 46100 Burjassot, Valencia, Spain e-mail: pablo.cerda@uv.es
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
Received:
23
December
2004
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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