Detecting non-Gaussian stochastic signals, and, Gravitational radiation from test particles bound to black holes

Details Detecting non-Gaussian stochastic signals, and, Gravitational radiation from test particles bound to black holes Detecting non-Gaussian stochastic signals, and, Gravitational radiation from test particles bound to black holes

Nov 2005

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2005phdt.........7d&link_type=abstract

Ph.D dissertation, 2005. Section 0058, Part 0606 224 pages; United States -- New York: Cornell University; 2005. Publication Nu

Computer Science

Performance

Non-Gaussian, Stochastic Signals, Gravitational Radiation, Test Particles, Black Holes

Scientific paper

This thesis describes work concerning two aspects of gravitational wave detection.
Chapter 2 discusses detection methods for a stochastic background of gravitational waves, the gravitational analog of the cosmic microwave background radiation. Today's stochastic background searches use a detection technique (cross-correlation) which is nearly optimal for Gaussian signals. For non-Gaussian signals, other methods generally outperform cross-correlation. I develop a simple model for a non-Gaussian signal and derive a nearly optimal method for its detection. The relative performance of cross-correlation and the more optimal method are compared using Monte Carlo simulations and analytic approximations. For a range in the model's parameter space, the new method is significantly more sensitive.
In chapters 3-5, I discuss gravitational waves produced by the gravitational radiation-driven inspiral of test particles into black holes. Chapter 3 outlines a general strategy for computing waveforms that could be used for the initial detection of such events. The waveforms are computed by treating the inspiral as a sequence of geodesic orbits, computed using black hole perturbation theory. In chapter 4 I develop a formalism to compute the harmonic decomposition of the source for the gravitational waves in terms of the three fundamental frequencies of the orbit. Chapter 5 computes the first waveforms for these generic geodesic orbits. The waveforms can be described as having radial and polar voices, the songs of which can be tuned somewhat independently through the orbit's eccentricity and inclination respectively. That is, if an orbit is made more eccentric, radiation is channeled into harmonics of the radial frequency, and if the orbit is made more inclined, more harmonics of the polar frequency are excited. To describe the complete inspiral, the geodesic orbit waveforms must be spliced together to form an inspiral waveform. This task, which remains to be done, requires an evolution scheme for the three non- trivial constants of geodesic motion: the orbital energy, the axial angular momentum, and Carter's constant. In chapter 5, I perform this evolution for energy and angular momentum. Chapter 3 describes an accurate method for evolving the Carter constant.

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