The Gravitational Wave Signature of Stellar Collapse and Dynamics of Compact Stars

This thesis is devoted to the study of the gravitational wave (GW) signature of stellar collapse and the dynamical behavior compact stars. The thesis consists of two parts. In the first one, we study the dynamics of the phase-transition-induced collapse of neutron stars (NSs) and the accretion-induced collapse of white dwarfs (WDs) as well as the associated GW emission. The second part is concerned with the study of the effects of general relativity on the magnetosphere of oscillating NSs. An increase in the central density of a NS may trigger a phase transition from hadronic matter to deconfined quark matter in the core, causing it to collapse to a more compact hybrid-star configuration. We present a study of this, using general relativistic hydrodynamics simulations with a simplified equation of state and considering the case of supersonic phase transition. We confirm that the emitted GW spectrum is dominated by the fundamental quasi-radial and quadrupolar pulsation modes. We observe a nonlinear mode resonance which substantially enhances the emission in some cases. We explain the damping mechanisms operating and estimate the detectability of the GWs. In massive accreting oxygen-neon WDs, their core material may in several circumstances experience rapid electron captures leading to collapse of the WD to a protoneutron star and collapse-driven supernova (SN) explosion. This process is called accretion-induced collapse (AIC) and represents a path alternative to thermonuclear disruption of accreting WDs in Type Ia SNe. An AIC-driven SN explosion is expected to be weak and of short duration, making it hard to detect by electromagnetic means alone. Neutrino and GW observations may provide crucial information necessary to reveal a potential AIC event. Motivated by the need for systematic predictions of the GW signature of AIC, we present results from an extensive set of general-relativistic simulations of AIC using a microphysical finite-temperature equation of state and an approximate treatment of deleptonization during collapse. Investigating a set of 114 progenitor models with wide range of rotational configurations, temperatures and central densities, we extend previous Newtonian studies and confirm that the GW signal of core bounce is of generic morphology known as Type III in the literature. We show that the emitted GWs contain enough information that can be used to constrain the progenitor and postbounce rotation. We discuss the detectability of the emitted GW signal. Rapidly rotating models form massive quasi-Keplerian accretion disks in the early postbounce phase. The disk mass is sensitive to the precollapse rotation and it can be as massive as ∼ 0.8M⊙ in rapidly differentially rotating models, while slowly and/or uniformly rotating models have much smaller disks. We find strong evidence that a subset of rapidly rotating models reaches sufficiently rapid rotation to develop a high- and low-T /|W | dynamical instabilities. Just as a rotating magnetised NS has material pulled away from its surface to populate a magnetosphere, a similar process can occur as a result of NS pulsations rather than rotation. This is of interest in connection with the overall study of NS oscillation modes but with a particular focus on the situation for magnetars. Following a previous Newtonian analysis of the production of a force-free magnetosphere in this way Timokhin et al. [418], we present here a corresponding general-relativistic analysis. We give a derivation of the general relativistic Maxwell equations for small-amplitude arbitrary oscillations of a non-rotating NS with a generic magnetic field and show that these can be solved analytically under the assumption of low current density in the magnetosphere. We apply our formalism to toroidal oscillations of a NS with a dipole magnetic field and calculate the resulting energy losses. We find that in general relativity the energy loss from the NS is significantly smaller than suggested by the Newtonian treatment.