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 Ϫ9 of the cosmological closure density, in the range 20 Hz to 1 kHz. This radiation should be detectable by ''advanced'' LIGO as well. ͓S0556-2821͑98͒03616-9͔

We show that gravitational radiation drives an instability in hot young rapidly rotating neutron stars. This instability occurs primarily in the l = 2 r-mode and will carry away most of the angular momentum of a rapidly rotating star by gravitational radiation. On the timescale needed to cool a young neutron star to about T = 10 9 K (about one year) this instability can reduce the rotation rate of a rapidly rotating star to about 0.076ΩK , where ΩK is the Keplerian angular velocity where mass shedding occurs. In older colder neutron stars this instability is suppressed by viscous effects, allowing older stars to be spun up by accretion to larger angular velocities. (and Friedman and Morsink [2] confirmed more generally) that gravitational radiation tends to drive the r-modes of all rotating stars unstable. In this paper we examine the timescales associated with this instability in some detail. We show that gravitational radiation couples to these modes primarily through the current multipoles, rather than the usual mass multipoles. We also evaluate the effects of internal fluid dissipation which tends to suppress this instability. We find that gravitational radiation is stronger than viscosity in these modes and so this instability severely limits the rotation rates of hot young neutron stars. We show that such stars can spin down by the emission of gravitational radiation to about 7.6% of their maximum rotation rates on the timescale (about one year) needed to cool these stars to 10 9 K.The r-modes of rotating barotropic Newtonian stars are solutions of the perturbed fluid equations having (Eulerian) velocity perturbationswhere R and Ω are the radius and angular velocity of the unperturbed star, α is an arbitrary constant, and Y B l m is the magnetic type vector spherical harmonic defined byPapaloizou and Pringle [3] first showed that the Euler equation for r−modes determines the frequencies asFurther use of the Euler equation (as first noted by Provost, Berthomieu and Rocca [4]) in the barotropic case (a good approximation for neutron stars) determines that only the l = m r-modes exist, and that δ v must have the radial dependence given in Eq. (1). These expressions for the velocity perturbation and frequency are only the lowest order terms in expansions for these quantities in powers of Ω. The exact expressions contain additional terms of order Ω 3 . The lowest order expressions for the (Eulerian) density perturbation δρ can also be deduced from the perturbed fluid equations (Ipser and Lindblom [5]): δρ ρ = αR 2 Ω 2 dρ dp (4) where δΨ(r) is proportional to the gravitational potential δΦ and satisfies d 2 δΨ dr 2 + 2 r dδΨ dr + 4πGρ dρ dp − (l + 1)(l + 2) r 2 δΨ = − 8πGl 2l + 1 l l + 1 ρ dρ dp r R l+1 .Eq. (4) is the complete expression for δρ to order Ω 2 . The next order terms are proportional to Ω 4 . Our interest here is to study the evolution of these modes due to the dissipative influences of viscosity and gravitational radiation. For this purpose it is useful to consider the effects of radiation on t...

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