Gravitational Radiation Instability in Hot Young Neutron Stars

We show that gravitational radiation drives an instability in hot young rapidly rotating neutron stars. This instability occurs primarily in the $l\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2$ $r$-mode and will carry away most of the angular momentum of a rapidly rotating star by gravitational radiation. On the time scale needed to cool a young neutron star to about ${T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}10}^{9}\mathrm{K}$ (about one year) this instability can reduce the rotation rate of a rapidly rotating star to about $0.076{\ensuremath{\Omega}}_{K}$, where ${\ensuremath{\Omega}}_{K}$ 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.