The evolution of the f-mode instability and gravitational wave detection prospectives

We study the dynamical evolution of the gravitational-wave driven instability of the f-mode in rapidly rotating relativistic stars with a polytropic equation of state. We use linear perturbation theory to describe the evolution of the mode amplitude and follow the trajectory of a newborn neutron star through its instability window. An unstable f-mode with a saturation energy of about 10−6M⊙c2 may generate a gravitational-wave signal which can be detected by the Einstein Telescope detector from the Virgo cluster. The effects of the magnetic field on the evolution and the detectability of the gravitational radiation are relevant when its strength is higher than 1012 G, while an unstable r-mode becomes dominant it reaches the maximum saturation value allowed by non-linear mode couplings. From the thermal evolution we find also that the heat generated by shear viscosity during the saturation phase completely balances the neutrinos' cooling and prevents the star from entering the regime of mutual friction. The evolution time of the instability is therefore longer and the star loses significantly larger amounts of angular momentum via gravitational waves.