Institute for Astronomy and Astrophysics

Saturation of the f-mode instability

July 2016

Pantelis Pnigouras, Kostas D. Kokkotas, Marco Surace

Fast-rotating neutron stars are likely to be unstable against certain oscillation modes, due to the emission of gravitational waves. The gravitational-wave signal generated by such an instability (known as the Chandrasekhar-Friedman-Schutz, or CFS, instability) could be used for asteroseismological studies, i.e., for extracting information about the (otherwise inaccessible) neutron star interior. After its initial growth phase, the instability is expected to saturate, due to nonlinear effects. The saturation amplitude of the unstable mode determines the detectability of the generated gravitational-wave signal, but also affects the evolution of the neutron star through the instability window, namely the region where the instability is active. We studied the saturation of CFS-unstable f-modes --which are the fundamental oscillation modes of the star and very good gravitational wave emitters-- due to low-order nonlinear mode coupling. We showed that the unstable (parent) mode resonantly couples to pairs of stable (daughter) modes, which drain the parent’s energy and make it saturate, via a mechanism called parametric resonance instability. We found that the saturation amplitude changes significantly throughout the instability window and, hence, during the neutron star evolution. Using the highest values obtained for the saturation amplitude, a signal from an unstable f-mode may even lie above the sensitivity of current, second-generation, gravitational-wave detectors. In addition, for some optimistic cases, CFS-unstable f-modes throughout the Universe could even produce a detectable stochastic gravitational-wave background.

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