Astron. Astrophys. 320, 209-227 (1997)

Dynamics and gravitational wave signature of axisymmetric rotational core collapse

T. Zwerger and E. Müller ^*

Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, Postfach 1523, D-85740 Garching, Germany

Received 8 August 1996 / Accepted 27 September 1996

Abstract

We have carried out a comprehensive parameter study of the dynamics of rotational core collapse in massive stars. The iron cores have been approximated by axisymmetric rotating polytropes in rotational equilibrium. Any transport effects by neutrinos have been neglected. We have computed 18 initial models which differ by their amount of rotational energy and their distribution of angular momentum. The initial models range from slowly to rapidly rotating and from rigidly to extremely differentially rotating configurations. The collapse was induced by suddenly reducing the adiabatic index to a value with . The stiffening of the equation of state at nuclear matter density and the thermal pressure in the matter heated by the prompt shock was simulated by means of a simplified analytic equation of state consisting of a polytropic and a thermal part. The evolution of a total of 78 models was followed well beyond core bounce using a two dimensional Newtonian hydrodynamic finite difference code.

A subset of models suffers a bounce caused by centrifugal forces at sub-nuclear densities. For a given rotation rate the bounce density decreases with increasing and with increasing degree of differential rotation. Models suffering a bounce due to (or mainly due to) centrifugal forces show large amplitude oscillations of the inner core the central density varying by more than a factor of ten. In several models the rotation rate exceeds the critical value, where MacLaurin spheroids become secularly unstable against tri-axial perturbations. Two of the most differentially and rapidly rotating models reach () and even exceed () the critical value for axisymmetric dynamical stability.

We have also computed the gravitational (quadrupole) wave signal emitted by our core collapse models. We find both type I (spike + ring-down) and type II (several distinct spikes) gravitational wave signals. Which type occurs is solely determined by the adiabatic index. Signals of type I are produced by models with a "soft" equation of state (), while signals of type II require a "stiff" equation of state (). Decreasing the adiabatic index from 1.325 to 1.28 and keeping the other model parameters fixed, we observe a smooth transformation of the signal type. For a third signal type is observed, which shows a large positive and a smaller negative wave amplitude just before and after bounce. Signals of type III are not found for extremely differentially rotating initial models. The energy spectra cover a frequency range of kHz, but most of the power is emitted between 500 Hz and 1 kHz. Models bouncing at sub-nuclear densities have spectra, which drop extremely rapidly above 1 kHz, and models with a type II wave signal have spectra, which show characteristic oscillations. These oscillations vanish when the signal type changes to type I. The spectra are neither very sensitive to the rotation rate nor to the degree of differential rotation. The total amount of energy radiated in form of gravitational waves lies in the range . The corresponding dimensionless wave amplitudes are in the range for a source at a distance of 10 Mpc. The largest signals are either produced by models which are initially slowly rotating and have an adiabatic index , or which are initially rapidly and strongly differentially rotating and have a relatively small adiabatic index ().

Key words: gravitational waves hydrodynamics stars: neutron stars: rotation supernovae: general

* e-mail: emueller@MPA-Garching.MPG.de

Send offprint requests to: E. Müller

Contents

• 1. Introduction
• 2. General considerations
• 3. Numerical model
  • 3.1. Equation of state
  • 3.2. Initial models
  • 3.3. Hydrodynamics
  • 3.4. Gravitational wave signal
• 4. Results: dynamics of rotational core collapse
  • 4.1. Initial models in rotational equilibrium
  • 4.2. Time of bounce
  • 4.3. Bounce
  • 4.4. The inner core
  • 4.5. Evolution of the central density
  • 4.6. Evolution of the rotation rate
  • 4.7. Comparison with other investigations
• 5. Results: the gravitational wave signal
  • 5.1. Quadrupole wave amplitudes
  • 5.2. Energy spectra
• 6. Summary and discussion
• Acknowledgements
• References

© European Southern Observatory (ESO) 1997

Online publication: July 3, 1998
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