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-Model A3B2G4
-Model A3B2G5
-Model A1B3G5
-Model A2B4G1
-Model A4B5G5

Axisymmetric Core Collapse
Relativistic Hydrodynamics
Waveform Catalog

Departamento de Astronomía y Astrofísica

Universidad de Valencia

These movies show the collapse dynamics together with the evolution of the maximum density and the gravitational wave signal of four representative core collapse models in relativstic gravity.

In the left box, the logarithm of the density in a quadrant of the core is color coded. The density is scaled to nuclear matter density, i.e. nuclear matter density corresponts to 0. On top of this, velocity vectors of the meridional velocity v_r + v_theta are shown, scaled to the maximum per frame. Note that the vertical axis corresponds to the rotation axis, and that the radial scale changes during the movie.

In the upper right box, the evolution of the gravitational wave amplitude A^E2₂₀ is plotted, and the lower right box shows the evolution of the maximum density rho_max. Note that for non-toroidal models, the maximum density is identical to the central density.

• Model A3B2G4:

  This is a regular collapse model. Its initial model has moderate differential rotation and a low rotation rate beta_rot ini = 0.5%.

  With a subnuclear adiabatic index gamma₁ = 1.30, the core collapses moderately fast within roughly 40 ms, and subsequently forms a stable remnant. This is clearly visible in the evolution of the maximum density. After the bounce, ringdown oscillations can be identified in this plot.

  The gravitational wave signal is typical for a Type I waveform, with a pronounced negative peak immediately after core bounce, and subsequent ringdown oscillations.

  The rotation plays only a minor role in the collapse dynamics. Both the density distribution, the meridional velocity vectors, and the shock front exhibit only small deviations from spherical symmetry.

  After the formation of the shock front, its outward propagation can be followed in the left box.

  
  Movie in MPG format (8 MB).

  

  
  Movie in AVI format (5 MB).

  

• Model A3B2G5:

  This is a rapid collapse model. Its initial model has moderate differential rotation and a low rotation rate beta_rot ini = 0.5%.

  With a low subnuclear adiabatic index gamma₁ = 1.28, the core collapses rapidly within roughly 30 ms, and subsequently forms a stable remnant. This is clearly visible in the evolution of the maximum density. After the bounce, the ringdown oscillations are strongly suppressed.

  The gravitational wave signal is typical for a Type III waveform, with no strong negative peak immediately after core bounce, and only small amplitude ringdown oscillations. Due to the missing large negative peak, the maximum signal amplitude of such models is comparably small.

  The rotation plays only a minor role in the collapse dynamics. Both the density distribution, the meridional velocity vectors, and the shock front exhibit only small deviations from spherical symmetry.

  After the formation of the shock front, its outward propagation can be followed in the left box. Later, an inward zoom shows the stable core remnant, which is particularly dense in this type of collapse.

  
  Movie in MPG format (11 MB).

  

  
  Movie in AVI format (9 MB).

  

• Model A1B3G5:

  This is a rapid collapse model. Its initial model has almost uniform rotation and a moderate rotation rate beta_rot ini = 0.9%.

  With a low subnuclear adiabatic index gamma₁ = 1.28, the core collapses rapidly within roughly 30 ms, and subsequently forms a stable remnant. This is clearly visible in the evolution of the maximum density. After the bounce, the ringdown oscillations are strongly suppressed.

  The gravitational wave signal is typical for a Type III waveform, with no strong negative peak immediately after core bounce, and only small amplitude ringdown oscillations. Due to the missing large negative peak, the maximum signal amplitude of such models is comparably small.

  The rotation plays only a minor role in the collapse dynamics. Both the density distribution, the meridional velocity vectors, and the shock front exhibit only small deviations from spherical symmetry.

  After the formation of the shock front, its outward propagation can be followed in the left box. Later, an inward zoom shows the stable core remnant, which is particularly dense in this type of collapse.

  
  Movie in MPG format (9 MB).

  

  
  Movie in AVI format (7 MB).

  

• Model A2B4G1:

  This is a multiple bounce collapse model. Its initial model has moderate differential rotation and a medium rotation rate beta_rot ini = 1.8%.

  With a subnuclear adiabatic index gamma₁ = 1.325 close to the initial value gamma_ini = 4 / 3, the core collapses slowly within roughly 100 ms, and subsequently undergoes several phases of re-expansion and contraction. This is clearly visible in the evolution of the maximum density. Eventually, a stable remnant will form, but on a timescale much longer than the collapse time.

  The gravitational wave signal is typical for a Type II waveform, with distinct strong negative peaks synchronous with each of the separate bounces.

  In this collapse type, rotation plays a crucial role in the collapse dynamics. Due to angular momentum conservation, the core collapse is stopped at subnuclear densities by the strong centrifugal forces.

  In each subsequent bounce, the zoom in the left box follows the outward re-expansion and the following contraction to the next bounce. The formation of a new shock front after each bounce is clearly visible.

  
  Movie in MPG format (8 MB).

  

  
  Movie in AVI format (5 MB).

  

• Model A4B5G5:

  This is an extremely rapidly and differentially rotating collapse model. Its initial model has strong differential rotation and a high rotation rate beta_rot ini = 4.0%. As a consequence, the initial density distribution is already toroidal.

  To overcome the additional stabilization by the strong rotation, the model has a small subnuclear adiabatic index gamma₁ = 1.28. The core collapses rapidly within roughly 30 ms, and spins up considerably, displaying an increasingly pronounced toroidal density distribution. It bounces at supernuclear densities, but then re-expands again to form a stable remnant at a much lower subnuclear density. This is clearly visible in the evolution of the maximum density.

  The gravitational wave signal exhibits a single peak, which can be attributed to the core bounce. As such extremely rapidly and differentially rotating cores have a toroidal shape and thus a large quadrupole moment, their maximum signal amplitudes are exceptionally high.

  In this collapse type, rotation has a strong influence on the collapse dynamics. While at the pole the contraction proceeds almost unaffected by centrifugal forces, it is slowed down considerably along the equator. After bounce, a strongly anisotropic shock front and large scale velocity vortices are created, leading to the formation of a short-lived accretion disk. The anisotropy of the shock front is amplified by the toroidal density distribution of the pre-shock matter.

  After core bounce, a strong jtabetlike outflow can be observed along the rotation axis, while the region around the stable torus is still surrounded by the velocity vortices which have formed in the post-shock region after the bounce.

  After the formation of the shock front, its outward propagation can be followed in the left box. Later, an inward zoom shows the stable toroidal core remnant, which exhibits and off-centered and not very dense maximum in this type of collapse.

  
  Movie in MPG format (10 MB).

  

  
  Movie in AVI format (8 MB).