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Authors: Ruxandra Bondarescu, Saul A. Teukolsky, Ira Wasserman (Cornell University)

Date: 19 Sep 2008

Abstract: We model the nonlinear saturation of the r-mode instability via three-mode couplings and the effects of the instability on the spin evolution of young neutron stars. We include one mode triplet consisting of the r-mode and two near resonant inertial modes that couple to it. The inertial modes are excited when the r-mode amplitude grows above the parametric instability threshold. We start our evolutions with a star of temperature ~ 10ˆ{10} K and a spin frequency close to the Kepler break-up frequency. The evolution of the star is dynamic and initially dominated by fast neutrino cooling. The outcome of the evolution is determined by when the cooling can be stopped by viscous heating. At first, the r-mode is unstable and its amplitude grows exponentially until it either reaches a large enough amplitude to generate a viscous dissipation that balances the cooling or until it reaches the parametric instability threshold amplitude. If thermal equilibrium is reached first, the star starts spinning down and the evolution can be adequately described by a one-mode model. If parametric instability is reached first, two near-resonant inertial modes that couple to the r-mode are excited. The viscous heating due to the three modes balances the neutrino cooling and the mode amplitudes oscillate around quasi-stationary states that can be determined algebraically. In both cases we find that when the r-mode is unstable the evolution of the temperature and the spin of the star can be approximated by trajectories along sequences of quasi-stationary states. Some of these evolutions lead to gravitational radiation that may be detectable by advanced LIGO if fast spinning young neutron stars exist in our galaxy. Such a detection could yield information on internal dissipation in neutron stars.

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