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Gravitational Waveform Catalog


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-Core Collapse with a Simple Equation of State

linkPfeilExtern.gifRelativistic Hydrodynamics



H. Dimmelmeier (linkPfeilExtern.gifSection of Astrophysics, Astronomy & Mechanics, linkPfeilExtern.gifAristotle University of Thessaloniki, Greece)
J.A. Font (linkPfeilExtern.gifDepartamento de Astronomía y Astrofísica, linkPfeilExtern.gifUniversidad de Valencia, Spain)
H.-T. Janka
A. Marek
E. Müller
C.D. Ott (linkPfeilExtern.gifDepartment of Astronomy and Steward Observatory, linkPfeilExtern.gifUniversity of Arizona, U.S.A.)


As a service to the scientific community, on this page we provide a waveform catalog of recent general relativistic numerical simulations of rotational core collapse.

For details about the assumptions and approximations of the models, please go to the according simulation pages.

As more sophisticated simulations become available, we will add their results to this page for download.


top linkPfeil.gif General Relativistic Simulations of Rotational Supernova Core Collapse with a Microphysical Equation of State and Deleptonization (Extended Model Set with Variation of the Equation of State and Progenitor Mass):

We have simulated a set of 136 rotational supernova core collapse models in axisymmetry. To simulate these models, we numerically solve the fully general relativistic hydrodynamic equations in a flux-conservative formulation [Banyuls, et al., 1997] on a grid using spherical coordinates. For an accurate resolution of shocks, we have implemented a modern high-resolution shock-capturing scheme, which uses characteristic information of relativistic hydrodynamics [Font, 2000]. The exact metric in the ADM spacetime foliation is approximated by assuming conformal flatness for the three-metric, which significantly reduces the complexity of the hydrodynamic and metric equations.

As initial configuration we choose the presupernova stellar models e15a, e15b, e20a, e20b, s11.2, s15, s20, or s40 [Woosley, et al., 2002]. The progenitor models e15a, e15b, e20a, and e20b have an angular momentum distribution from stellar evolution calculations, while on the s11.2, s15, s20, and s40 models we impose rotation [Komatsu, et al., 1989a, Komatsu, et al., 1989b] with different rates and profiles.

During core collapse, we utilize a microphysical equations of state specifically designed for supernova core collapse, either the one by Shen et al. (Shen EoS) [Shen, et al., 1998] or the one by Lattimer and Swesty (LS EoS) [Lattimer and Swesty, 1998]. To approximate the effects of neutrinos in the infall phase, a very efficient parametric deleptonization scheme is used [Liebendörfer, 2005].

A detailed description of the models and other interesting information can be found in a published article [Dimmelmeier, et al., 2008].

Figures of the waveforms for each model in EPS and JPG format:

   linkPfeil.gifFigures of the waveforms in EPS format

   linkPfeil.gifFigures of the waveforms in JPG format


Raw data of the gravitational wave signal and the maximum density evolution for each model:

   Gravitational wave signal data
       (gzipped tar archive, 9.8 MByte, including a README file).

   Density evolution data
       (gzipped tar archive, 6.3 MByte, including a README file).


top linkPfeil.gif General Relativistic Simulations of Rotational Supernova Core Collapse with a Microphysical Equation of State and Deleptonization:

We have simulated a set of 54 rotational supernova core collapse models in axisymmetry. To simulate these models, we numerically solve the fully general relativistic hydrodynamic equations in a flux-conservative formulation [Banyuls, et al., 1997] on a grid using spherical coordinates. For an accurate resolution of shocks, we have implemented a modern high-resolution shock-capturing scheme, which uses characteristic information of relativistic hydrodynamics [Font, 2000]. The exact metric in the ADM spacetime foliation is approximated by assuming conformal flatness for the three-metric, which significantly reduces the complexity of the hydrodynamic and metric equations.

As initial configuration we choose the presupernova stellar model s20 [Woosley, et al., 2002], on which we impose rotation [Komatsu, et al., 1989a, Komatsu, et al., 1989b] with different rates and profiles.

During core collapse, we utilize a microphysical equation of state [Shen, et al., 1998] specifically designed for supernova core collapse. To approximate the effects of neutrinos in the infall phase, a very efficient parametric deleptonization scheme is used [Liebendörfer, 2005].

A detailed description of the models and other interesting information can be found in a published article [Dimmelmeier, et al., 2007].

Figures of the waveforms for each model in EPS and JPG format:

   linkPfeil.gifFigures of the waveforms in EPS format

   linkPfeil.gifFigures of the waveforms in JPG format


Raw data of the gravitational wave signal and the maximum density evolution for each model:

   Gravitational wave signal data
       (gzipped tar archive, 4.2 MByte, including a README file).

   Density evolution data
       (gzipped tar archive, 1.6 MByte, including a README file).


top linkPfeil.gif General Relativistic Simulations of Rotational Supernova Core Collapse with a Simple Equation of State:

We have simulated a set of 26 rotational supernova core collapse models in axisymmetry. To simulate these models, we numerically solve the fully general relativistic hydrodynamic equations in a flux-conservative formulation [Banyuls, et al., 1997] on a grid using spherical coordinates. For an accurate resolution of shocks, we have implemented a modern high-resolution shock-capturing scheme, which uses characteristic information of relativistic hydrodynamics [Font, 2000]. The exact metric in the ADM spacetime foliation is approximated by assuming conformal flatness for the three-metric, which significantly reduces the complexity of the hydrodynamic and metric equations.

The initial configurations are rotating 4/3-polytropes in equilibrium with a central density of rhoc ini = 1010 g/cm3 constructed by numerically solving the hydrodynamic equilibrium equations in a general relativistic spacetime [Komatsu, et al., 1989a, Komatsu, et al., 1989b]. The initial state is completely determined by the central density, the rotation rate betarot ini = Erot ini / Epot ini, and the rotation parameter A, which specifies the degree of differential rotation.

The equation of state during core collapse consists of a polytropic and a thermal contribution. The collapse is initiated by reducing the adiabatic exponent gamma1. For densities rho > 2.0 . 1014 g/cm3, the adiabatic exponent is set to gamma1 = 2.5 mimicking the stiffening of the equation of state above nuclear matter density. We have also simulated one model with a soft supranuclear equation of state with gamma1 = 2.0.

A detailed description of the models and other interesting information can be found in a series of published articles [Dimmelmeier, et al., 2001, Dimmelmeier, et al., 2002a, Dimmelmeier, et al., 2002b].


Figures of the waveforms for each model in EPS and JPG format:

   linkPfeil.gifFigures of the waveforms in EPS format

   linkPfeil.gifFigures of the waveforms in JPG format


Raw data of the gravitational wave signal, the maximum density evolution, and the radiated gravitational wave energy for each model:

   Gravitational wave signal data
       (gzipped tar archive, 21 MByte, including a README file).

   Density evolution data
       (gzipped tar archive, 15 MByte, including a README file).

   Gravitational wave energy data
       (gzipped tar archive, 20 MByte, including a README file).


top References:

  • Banyuls, F., Font, J.A., Ibanez, J.M., Marti, J.M., Miralles, J.A.,
    "Numerical {3+1} general relativistic hydrodynamics",
    Astrophys. J., 476, 221-231, (1997),
    [linkPfeilExtern.gifArticle in PDF format via Astrophys. J.].

  • Dimmelmeier, H., Font, J.A., and Müller, E.,
    "Gravitational waves from relativistic rotational core collapse",
    Astrophys. J. Lett., 560, L163-L166, (2001),
    [linkPfeilExtern.gifArticle in astro-ph].

  • Dimmelmeier, H., Font, J.A., and Müller, E.,
    "Relativistic simulations of rotational core collapse. I. Methods, initial models, and code tests",
    Astron. Astrophys., 388, 917-935, (2002),
    [linkPfeilExtern.gifArticle in astro-ph].

  • Dimmelmeier, H., Font, J.A., and Müller, E.,
    "Relativistic simulations of rotational core collapse. II. Collapse dynamics and gravitational radiation",
    Astron. Astrophys., 393, 523-542, (2002),
    [linkPfeilExtern.gifArticle in astro-ph].

  • Dimmelmeier, H., Ott, C.D., Janka, H.-T., Marek, A., and Müller, E.,
    "Generic gravitational wave signals from the collapse of rotating stellar cores",
    Phys. Rev. Lett., 98, 251101, (2007),
    [linkPfeilExtern.gifArticle in astro-ph].

  • Dimmelmeier, H., Ott, C.D., Marek, A., and Janka, H.-T.,
    "The gravitational wave burst signal from core collapse of rotating stars",
    Phys. Rev. D, 78, 064056, (2008),
    [linkPfeilExtern.gifArticle in astro-ph].

  • Font, J.A.,
    "Numerical hydrodynamics in general relativity",
    Living Rev. Relativ., 3, (2000),
    [linkPfeilExtern.gifArticle in Living Rev. Relativ.].

  • Komatsu, H., Eriguchi, Y., and Hachisu, I.,
    "Rapidly rotating general relativistic stars - I. Numerical method and its application to uniformly rotating polytropes",
    Mon. Not. R. Astron. Soc., 237, 355-379, (1989),
    [linkPfeilExtern.gifArticle in PDF format via ADS].

  • Komatsu, H., Eriguchi, Y., and Hachisu, I.,
    "Rapidly rotating general relativistic stars - II. Differentially rotating polytropes",
    Mon. Not. R. Astron. Soc., 239, 153-171, (1989)
    [linkPfeilExtern.gifArticle in PDF format via ADS].

  • Lattimer, J.M. and Swesty, F.D.,
    "A generalized equation of state for hot, dense matter",
    Nucl. Phys. A, 535, 331-376, (1991)
    [linkPfeilExtern.gifArticle via journal webpage].

  • Liebendörfer, M.,
    "A simple parameterization of the consequences of deleptonization for simulations of stellar core collapse",
    Astrophys. J., 633, 1042-1051, (2005)
    [linkPfeilExtern.gifArticle in astro-ph].

  • Shen, H., Toki, H., Oyamatsu, K., and Sumiyoshi, K.,
    "Relativistic Equation of State of Nuclear Matter for Supernova Explosion",
    Prog. Theor. Phys., 100, 1013-1031, (1998)
    [linkPfeilExtern.gifArticle in PDF format via Prog. Theor. Phys.].

  • Woosley, S.A, Heger, A., and Weaver, T.A.,
    "The evolution and explosion of massive stars",
    Rev. Mod. Phys., 74, 1015-1071, (2002)
    [linkPfeilExtern.gifArticle in PDF format via Rev. Mod. Phys.].




topComments to: Ewald Müller emailewald@mpa-garching.mpg.de