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GR Hydro Code Testing

The testing of the GR Hydro Code in the Cactus Framework has involved a number of different physical configurations:
  1. Numerical evolutions of nonrotating spherical relativistic star in stable equilibrium have been performed and small radial pulsations excited by the first-order truncation errors that occur at the center and at the surface of the star have been detected. These pulsations modulate the evolution of the central rest-mass density. This figure hows the evolution of the central rest-mass density for different grid resolutions of a polytropic star. The evolutions shown in this figure extend to 7 ms.

  2. Small-amplitude radial pulsations of an initially static relativistic star> have also been studied. These pulsations are in the linear regime and are produced by the truncation errors of the hydrodynamical schemes while evolving a nonrotating relativistic star in a fixed spacetime.

    The evolution of the central rest-mass density is a superposition of several normal modes of pulsation. Modes with higher frequencies are damped faster by the numerical viscosity of the code so that after a certain time the evolution continues in the fundamental mode of pulsation. This evolution is shown here.

    The frequencies of these small radial pulsations have been compared with that computed by linear perturbation theory and with 2D hydrodynamical simulations obtaining an agreement of 1% for the fundamental normal mode and the next four higher frequency modes.

  3. Highly non-linear oscillations about an stable configuration are produced after the migration of a nonrotating relativistic unstable star to the stable branch. Numerical truncation errors can perturb the unstable equilibrium of a relativistic star which will expand and evolve to a smaller central rest-mass density until a equilibrium configuration within the stable branch is reached.

    Though this migration cannot take place in an astrophysical scenario, it can be used as initial data for large amplitude simulations of relativistic stars. This figure shows the evolution of the central rest-mass density of an unstable relativistic star during the migration to the stable branch. The dotted line represents the evolution of a star with an adiabatic equation of state and the solid line represents the evolution of a star with an ideal fluid equation of state.

  4. Simulations of collapse to Black Hole of nonrotating unstable spherical relativistic star have also been performed with GR Hydro Code by introducing a small radial perturbation in the central rest-mass density of an unstable configuration.

    This figure shows the profiles along the x-axis of the lapse function, the gxx metric component and the normalized rest-mass density, where different times of the evolution are represented by different lines. The solid line indicates the initial profile and the thick dashed line the final timeslice at t=0.29ms.

  5. Long-term evolutions of rapidly rotating relativistic star in stable equilibrium have also been performed. In the case of rapidly rotating stars, the truncation errors produce quasi-radial oscillations causing a shift of the central rest-mass density towards higher values during the evolution. We show here the profiles of the gxx metric component along the x-axis and z-axis at two coordinate times. The solid line refers to t=0 and the dashed line to t=3.78 ms, corresponding to 3 rotational periods, while might appear a short time scale, they represent a considerable achievement in numerical relativity.

    A long-standing problem in relativistic astrophysics, the mode-frequencies of rotating relativistic stars in full general relativity and rapid rotation have been calculated during the long term evolution of the rapidly rotating neutron stars. This figure shows the quasi-radial pulsation frequencies for a sequence of relativistic stars and different rotation rates; the frequencies of the fundamental mode are represented by squares and the first higher frequency mode by circles.

  6. Gravitational waves emitted by a nonrotating relativistic star pulsating mainly in the fundamental quadrupolar mode of oscillation have been extracted by means a perturbative technique.

    This figure shows the waveforms as extracted at 17.7 km and at 23.6 km (top figure), and the figure below shows the amplitude of the l=2, m=0 component of the Zerilli function extracted at 23.6 km for two different resolutions.

This work has been supported by the EU Programme 'Improving the Human Research Potential and the Socio-Economic Knowledge Base' (Research Training Network Contract HPRN-CT-2000-00137).