Gravitational radiation and the stability of rotating stars

It has been noted that all rotating stars are unstable to the radiation of gravitational waves by non-radial stellar modes. However small the rate of stellar rotation, for each set of modes (for example the p-modes) there is always a critical azimuthal wavenumber msub(crit), such that modes with m>msub(crit) are unstable. Using a scalar theory of gravitation the growth rate of the instability explicitly in the slow-motion regime is calculated. It is found that the instability grows on astronomically interesting timescales only for neutron stars with rotational periods <or approximately a few milliseconds. An indication is given why general relativity is likely to yield the same conclusion. Brief consideration is given to a situation in which an accreting neutron star can radiate a large fraction of the accretion luminosity as gravitational waves. (author)