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-Core Collapse with Microphysics (Extended Model Set)
-Core Collapse with Microphysics
-Core Collapse with a Simple Equation of State

Relativistic Hydrodynamics

Section of Astrophysics, Astronomy & Mechanics

Aristotle University of Thessaloniki

Departamento de Astronomía y Astrofísica

Universidad de Valencia

Department of Astronomy and Steward Observatory

University of Arizona

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.

 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:

   Figures of the waveforms in EPS format

   Figures 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).

 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:

   Figures of the waveforms in EPS format

   Figures 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).

 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 rho_{c 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 beta_{rot ini} = E_{rot ini} / E_{pot 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:

   Figures of the waveforms in EPS format

   Figures 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).

• 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),
  [Article 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),
  [Article 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),
  [Article 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),
  [Article 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),
  [Article 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),
  [Article in astro-ph].


• Font, J.A.,
  "Numerical hydrodynamics in general relativity",
  Living Rev. Relativ., 3, (2000),
  [Article 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),
  [Article 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)
  [Article 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)
  [Article 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)
  [Article 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)
  [Article 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)
  [Article in PDF format via Rev. Mod. Phys.].