This thesis presents a study of the dynamical stability of nascent neutron stars resulting from theaccretion induced collapse of rapidly rotating white dwarfs.
Chapter 2 and part of Chapter 3 study the equilibrium models for these neutron stars. They areconstructed by assuming that the neutron stars have the same masses, angular momenta, and specificangular momentum distributions as the pre-collapse white dwarfs. If the pre-collapse white dwarf israpidly rotating, the collapsed object will contain a high density central core of size about 20 km,surrounded by a massive accretion torus extending to hundreds of kilometers from the rotation axis.The ratio of the rotational kinetic energy to gravitational binding energy, β, of these neutron starsis all found to be less than 0.27.
Chapter 3 studies the dynamical stability of these neutron stars by numerically evolving thelinearized hydrodynamical equations. A dynamical bar-mode instability is observed when the β ofthe star is greater than the critical value βd ≈ 0.25. It is expected that the unstable mode willpersist until a substantial amount of angular momentum is carried away by gravitational radiation.The detectability of these sources is studied and it is estimated that LIGO II is unlikely to detectthem unless the event rate is greater than 10-6/year/galaxy.
All the calculations on the structure and stability of the neutron stars in Chapters 2 and 3are carried out using Newtonian hydrodynamics and gravity. Chapter 4 studies the relativisticeffects on the structure of these neutron stars. New techniques are developed and used to constructneutron star models to the first post-Newtonian (1PN) order. The structures of the 1PN modelsare qualitatively similar to the corresponding Newtonian models, but the values of β are somewhatsmaller. The maximum β for these 1PN neutron stars is found to be 0.24, which is 8% smaller thanthe Newtonian result (0.26). However, relativistic effects will also change the critical value βd. Adetailed post-Newtonian stability analysis has yet to be carried out to study the relativistic effectson the dynamical stability of these neutron stars.
