Gravitational waves from hot young rapidly rotating neutron stars

Gravitational radiation drives an instability in the $r$-modes of young rapidly rotating neutron stars. This instability is expected to carry away most of the angular momentum of the star by gravitational radiation emission, leaving a star rotating at about 100 Hz. In this paper we model in a simple way the development of the instability and evolution of the neutron star during the year-long spindown phase. This allows us to predict the general features of the resulting gravitational waveform. We show that a neutron star formed in the Virgo cluster could be detected by the LIGO and VIRGO gravitational wave detectors when they reach their ``enhanced'' level of sensitivity, with an amplitude signal-to-noise ratio that could be as large as about 8 if near-optimal data analysis techniques are developed. We also analyze the stochastic background of gravitational waves produced by the $r$-mode radiation from neutron-star formation throughout the universe. Assuming a substantial fraction of neutron stars are born with spin frequencies near their maximum values, this stochastic background is shown to have an energy density of about ${10}^{\ensuremath{-}9}$ of the cosmological closure density, in the range 20 Hz to 1 kHz. This radiation should be detectable by ``advanced'' LIGO as well.