Gravitational waves from coalescing binaries: Detection strategies and Monte Carlo estimation of parameters

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Abstract
The detection of gravitational waves from astrophysical sources is probably one of the most keenly awaited events in the history of astrophysics. The paucity of gravitational wave sources and the relative difficulty in detecting such waves, as compared to those in the electromagnetic domain, necessitate the development of optimal data analysis techniques to detect the signal, as well as to extract the maximum possible information from the detected signals. Coalescing binary systems are one of the most promising sources of gravitational waves. This is due to the fact that such sources are easier to model and thus one can design detection strategies particularly tuned to such signals. A lot of attention has been devoted in the literature to studying such techniques and most of the work has revolved around the Weiner filtering and the maximum likelihood estimators of the parameters of the binary system. We investigate such techniques with the aid of differential geometry which provides geometric insight into the problem. Such a formalism allows us to explore the merits and faults of a detection scheme independent of the parameters chosen to represent the waveform. The formalism also generalizes the problem of choosing an optimal set of templates to detect a known waveform buried in noisy data. We stress the need for finding a set of convenient parameters for the waveform and show that even after the inclusion of the second-order post-Newtonian corrections, the waveform can essentially be detected by employing a one-dimensional lattice of templates.