In the next few years, the first detections of gravity-wave signals using Earth-based interferometric detectors will begin to provide precious new information about the structure, dynamics, and evolution of compact bodies, such as neutron stars and black holes, both isolated and in binary systems. The intrinsic weakness of gravity-wave signals requires a proactive approach to modeling the prospective sources and anticipating the shape of the signals that we seek to detect. Full-blown 3-D numerical simulations of the sources are playing and will play an important role in planning the gravity-wave data-analysis effort. This thesis explores the interplay between numerical source modeling and data analysis, looking closely at three case studies.
1. I evaluate the prospects for extracting equation-of-state information from neutron-star tidal disruption in neutron-star--black-hole binaries with LIGO-II, and I estimate that the observation of disrupting systems at distances that yield about one event per year should allow the determination of the neutron-star radius to about 15%, which compares favorably to the currently available electromagnetic determinations.
2. In collaboration with Lee Lindblom and Joel Tohline, I perform numerical simulations of the nonlinear dynamics of the r-mode instability in young, rapidly spinning neutron stars, and I find evidence that nonlinear couplings to other modes will not pose a significant limitation to the growth of the r-mode amplitude.
3. In collaboration with Alessandra Buonanno and Yanbei Chen, I study the problem of detecting gravity waves from solar-mass black-hole--black-hole binaries with LIGO-I, and I construct two families of detection templates that address the inadequacy of standard post-Newtonian theory to predict reliable waveforms for these systems.
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