Graduation Semester and Year




Document Type


Degree Name

Doctor of Philosophy in Physics and Applied Physics



First Advisor

Musielak E Zdzislaw

Second Advisor

Malik Rakhmanov


Multi-messenger astronomy recently added a fundamentally new component to its wide array of observational tools: a gravitational-wave detector. A number of binary black holes mergers have already been detected by gravitational-wave interferometers and the data have been analyzed by the scientific community. Moreover, simultaneous observation of gravitational waves with electromagnetic signals led to the first observation of a binary neutron star merger. Success in gravitational-wave detection motivated the efforts to improve current detectors and initiated the design of future detectors with significantly enhanced sensitivities. The detector improvements will lead to increase of the detection range for binary star mergers and will also allow observation of new sources. One of the most sought-after sources is the core-collapse supernova. According to extensive numerical simulations, gravitational-wave signals emitted during the core collapse can have frequencies in the kilohertz range, approaching the free spectral range of \FP/ arms of future detectors. The long-wavelength approximation, commonly used in the analysis of gravitational-wave interferometers, is not applicable in this regime. Therefore, it is necessary to develop new approaches to calculate waveform deformations, to analyze interferometer responses, and to estimate their implications for calibration for these large-scale detectors. We utilize the time-domain interferometer impulse response and Fourier-Laplace domain transfer function of gravitational wave detectors without any limitation on the maximum frequency of the signal. These tools will allow us to develop a general theory for waveform deformations as the signal propagates through the interferometer arms. In particular, we analyze the time of arrival of the gravitational wave and show that in addition to the geometrical delay due to the detector location on Earth, it has an additional contribution originating from the interferometer transfer function. Accurate calculation of the signal arrival time is important for the determination of the source position on the sky. We analyze this intrinsic delay for different interferometer configurations and present the results as sky-maps for two polarizations of the gravitational wave. In this work we give the classification of various waveform distortions of the signal for applications to searches of gravitational waves from core-collapse supernovae. We analyzed in detail three different features commonly present in numerical waveforms of the supernova. These features are the core bounce, the SASI modes, and the core oscillations. For each of these features we analyze the time delays, the frequency shifts, signal-envelope broadening, and the signal-frequency chirps. In addition to the analytical calculations, we developed numerical simulations of the interferometric gravitational-wave detection to assess accuracy of analytical approximations we used. Good agreement found in almost all cases we considered. Moreover, we found that the detector properties and waveform deformations are largely controlled by the complex zeros of the interferometer response. The significance of the zeros motivated the development of algorithms for effective calculations of the zeros (real and imaginary parts) as functions of the sky location. Substantial difficulty in these calculations comes from the transcendental nature of the characteristic equation. Therefore, an algorithm was built on combination of analytical and numerical methods and used recursive techniques to attain the necessary precision. The results of this work can be used for understanding the waveform deformations of the core-collapse supernova signals, in the development of search algorithms for detection of supernovae gravitational-wave emissions, and for optimization of future gravitational-wave detectors.


Gravitational waves, Gravitational-wave detectors, Gravitational-wave detectors optimization, Core-collapse supernova, gravitational-wave signal


Physical Sciences and Mathematics | Physics


Degree granted by The University of Texas at Arlington

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