Dynamical instability of new-born neutron stars as sources of gravitational radiation

The dynamical instability of new-born neutron stars is studied by evolving the linearized hydrodynamical equations. The neutron stars considered in this paper are those produced by the accretion induced collapse of rigidly rotating white dwarfs. A dynamical bar-mode $\mathrm{}(m=2\mathrm{})\mathrm{}$ instability is observed when the ratio of rotational kinetic energy to gravitational potential energy $\beta$ of the neutron star is greater than the critical value ${\beta }_d\approx \mathrm{0.25.}$ This bar-mode instability leads to the emission of gravitational radiation that could be detected by gravitational wave detectors. However, these sources are unlikely to be detected by LIGO II interferometers if the event rate is less than ${10}^{-6}$ per year per galaxy. Nevertheless, if a significant fraction of the pre-supernova cores are rapidly rotating, there would be a substantial number of neutron stars produced by the core collapse undergoing bar-mode instability. This would greatly increase the chance of detecting the gravitational radiation.