Saturation amplitude of the f-mode instability

Wolfgang Kastaun, Beatrix Willburger, and Kostas D. Kokkotas
Phys. Rev. D 82, 104036 – Published 17 November 2010

Abstract

We investigate strong nonlinear damping effects which occur during high amplitude oscillations of neutron stars, and the gravitational waves they produce. For this, we use a general relativistic nonlinear hydrodynamics code in conjunction with a fixed spacetime (Cowling approximation) and a polytropic equation of state (EOS). Gravitational waves are estimated using the quadrupole formula. Our main interest are l=m=2 f modes subject to the CFS (Chandrasekhar, Friedman, Schutz) instability, but we also investigate axisymmetric and quasiradial modes. We study various models to determine the influence of rotation rate and EOS. We find that axisymmetric oscillations at high amplitudes are predominantly damped by shock formation, while the nonaxisymmetric f modes are mainly damped by wave breaking and, for rapidly rotating models, coupling to nonaxisymmetric inertial modes. From the observed nonlinear damping, we derive upper limits for the saturation amplitude of CFS-unstable f modes. Finally, we estimate that the corresponding gravitational waves for an oscillation amplitude at the upper limit should be detectable with the advanced LIGO (Laser Interferometer Gravitational Wave Observatory) and VIRGO interferometers at distances above 10 Mpc. This strongly depends on the stellar model, in particular, on the mode frequency.

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  • Received 28 June 2010

DOI:https://doi.org/10.1103/PhysRevD.82.104036

© 2010 The American Physical Society

Authors & Affiliations

Wolfgang Kastaun

  • International School for Advanced Studies (SISSA) and National Institute of Nuclear Physics (INFN), via Bonomea 265, Trieste 34136, Italy and Theoretical Astrophysics, Eberhard -Karls University of Tübingen, Tübingen 72076, Germany

Beatrix Willburger

  • Theoretical Astrophysics, Eberhard-Karls University of Tübingen, Tübingen 72076, Germany

Kostas D. Kokkotas

  • Theoretical Astrophysics, Eberhard-Karls University of Tübingen, Tübingen 72076, Germany and Department of Physics, Aristotle University of Thessaloniki, Thessaloniki 54124, Greece

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Issue

Vol. 82, Iss. 10 — 15 November 2010

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