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

Abstract

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 (m = 2) instability is observed when the ratio of rotational kinetic energy to gravitational potential energy β of the neutron star is greater than the critical value β d ≈ 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.PACS: 04.30. Db, 95.30.Sf, 97.60.Jd

Gravitational Waves from Gravitational Collapse

“…Liu and Lindblom [184, 183] have applied this equilibrium approach to AIC. Their investigation began with a study of equilibrium models built to represent neutron stars formed from AIC [184].…”

Gravitational Waves from Gravitational Collapse

“…LIGO-I may be able to detect GWs from secular bar-mode instabilities in core collapse SNe [146] and magnetized tori surrounding black hole collapse remnants [251]. LIGO-II could observe GWs from dynamical bar-mode instabilities in AIC [155] and core collapse SNe [86]. LISA should be able to detect the collapse (and any bar-mode instabilities that develop during the collapse) of SMSs [16] and the ringdown of black hole remnants of collapsed Population III stars [86] and SMSs [208].…”

“…Liu and Lindblom [156, 155] have applied this equilibrium approach to AIC. Their investigation began with a study of equilibrium models built to represent neutron stars formed from AIC [156].…”

“…In a continuation of the work of Liu and Lindblom, Liu [155] used linearized hydrodynamics to perform a stability analysis of the cold neutron star AIC remnants of Liu and Lindblom [156]. He found that only the remnant of the O-Ne-Mg white dwarf (Liu and Lindblom’s Model III) developed the dynamical bar-mode ( m =2) instability.…”

“…Such a signal may be marginally detectable with LIGO-II (see Figure 2). Details of the approximations on which these estimates are based can be found in [155]. …”