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Relativistic Hydrodynamics
Gravitational Waveform Catalog

Section of Astrophysics, Astronomy & Mechanics

Aristotle University of Thessaloniki

Copernicus Astronomical Center

Copernicus Astronomical Center

Copernicus Astronomical Center

Neutron stars, which are very compact stars of about one solar mass that are born in a supernova explosions caused by the collapse of a stellar core, have interesting stability properties. If one assumes that they are rapidly rotating and that the matter they are made of obeys a particular type of equation of state, then they become unstable at some point in their life. This instability follows from a softening of the equation of state (i.e. a comparably small pressure rise with density) above a certain threshold density, which could be the result of a conversion of regular hadronic matter to quark matter or a condensate of kaon particles.

Initially, the rotating neutron star is in a stable equilibrium, as its central density lies above the threshold density. However, the neutron star slowly but continuously loses angular momentum and consequently slows down. Finally its core crosses the density threshold, and the instability sets in within a very short, dynamic time scale of only about 1 millisecond. It then undergoes a rapid collapse to higher central densities and contracts as a whole. This collapse is then followed by ring-down pulsations, as the neutron star, which now has a core of quark or kaon matter, acquires a new stable equilibrium state.

When plotting the diagram of total angular momentum against rotation frequency, the migration sets in when the neutron star reaches a local minimum and its previous evolution curve (red line) bends back. The migration path is approximately shown by the horizontal arrow, which finally hits the new equilibrium state on the stable branch (blue line). The hypothetical curve between the last stable state before migration (circle) and the new equilibrium, which can actually be interrupted by physically not permitted states (between the cross and the plus), is thus bypassed by the neutron star. After the migration, the neutron star continues its evolution on the new stable branch (blue line) towards smaller rotation rates.

This dynamic and violent migration process is accompanied by emission of a sizeable amount of gravitational waves, which could be detectable by current and (in particular) future detectors and reveal so far unknown physical properties of the interior of neutron stars. The according waveform of gravitational radiation is most probably very complicated and reflects the complex interactions of various pulsation modes. The analysis of such neutron star pulsations and the extraction of useful information from the resulting gravitational wave signal is known as asteroseismology [Andersson and Kokkotas, 1998].

Recently, Zdunik and collaborators have discovered the back bending phenomenon in a numerical study of rotating neutron stars with a quark matter or kaon condensate core [Zdunik, et al., 2006]. This work was restricted to equilibrium sequences and excluded an investigation of the dynamics migration process itself.

In order to shed light on this important phase in the evolution of such neutron stars, we have performed fully nonlinear numerical simulations of the migration process [Dimmelmeier, et al., 2009]. We find that both during the initial collapse and the subsequent ring-down pulsations, the rotation of the neutron star remains approximately rigid. This proves that the simple picture of horizontal migration in the back bending diagram is rather accurate.

In addition, we have analyzed the frequency structure of the emitted gravitational waves and the nonlinear interactions between the main pulsation modes which are excited by the collapse. We have also come up with a straightforward explanation for the strong damping of the post-bounce pulsations observed in one class of our models, which is due to an efficient dissipation mechanism caused by the equation of state that models a kaon condensate at high densities.

As regular neutron stars typically do not rotate sufficiently rapidly in the first stages of their life, we propose that mostly a special class of highly magnetized neutron stars, known as magnetars, are prospective candidates for this migration scenario. They are expected to rotate with periods close to 1 millisecond already during their birth, and could therefore be subject to this dynamic migration instability within the first 1000 years of their life.

• Andersson, N. and Kokkotas, K.D.,
  "Towards gravitational wave asteroseismology",
  Mon. Not. R. Astron. Soc., 299, 1059-1068, (1998),
  [Article in astro-ph].


• Dimmelmeier, H., Bejger, M., Haensel, P., and Zdunik, J.L.,
  "Dynamic migration of rotating neutron stars due to a phase transition instability",
  Mon. Not. R. Astron. Soc., 396, 2269, (2009),
  [Article in astro-ph].


• Zdunik, J.L., Bejger, M., Haensel, P., and Gourgoulhon, E.,
  "Phase transitions in rotating neutron stars cores: back bending, stability, corequakes and pulsar timing",
  Astron. Astrophys., 450, 747-758, (2006),
  [Article in astro-ph].