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Item Global analysis for space-based gravitational wave observatories(Montana State University - Bozeman, College of Letters & Science, 2018) Robson, Travis James; Chairperson, Graduate Committee: Neil J. Cornish; Nicolas Yunes (co-chair); Neil Cornish and Chang Liu were co-authors of the article, 'The construction and use of LISA sensitivity curves' submitted to the journal 'Classical and quantum gravity' which is contained within this thesis.; Neil Cornish was a co-author of the article, 'Impact of galactic foreground characterization on a global analysis for the LISA gravitational wave observatory' in the journal 'Classical and quantum gravity' which is contained within this thesis.; Neil Cornish, Nicola Tamanini and Silvia Toonen were co-authors of the article, 'Detecting hierarchical stellar systems with LISA' in the journal 'Physical Review D' which is contained within this thesis.; Travis Robson, Blake Moore, Nicholas Loutrel and Nicolas Yunes were all authors of the article, 'A fourier domain waveform for non-spinning binaries with arbitrary eccentricity' in the journal 'Classical and quantum gravity' which is contained within this thesis.; Neil Cornish was a co-author of the article, 'Detecting gravitational wave bursts with LISA in the presence of instrumental glitches' submitted to the journal 'Physical review D' which is contained within this thesis.; Dissertation contains one article of which Travis Robson is not the main author.The Laser Interferometer Space Antenna (LISA) is a space-based gravitational wave detector in development under a joint venture between ESA and NASA. LISA will be sensitive to a wealth of signals from a variety of sources--both astrophysical and instrumental. Since many of these signals will be overlapping we must carry out a global analysis where we model everything believed to be present in the data simultaneously. To analyze the data this way we must understand what types of signals we expect, develop fast signal generators, and develop data analysis algorithms to handle this problem. We must also be flexible to characterize signals that we do not expect such as instrumental glitches of unknown morphology, or exotic astrophysical sources. We employ the Markov Chain Monte Carlo algorithm to address these multiple facets of the global analysis problem through a Bayesian approach. We have developed fast models for a variety of sources, characterized what we can learn about the sources, and assessed the nature of LISA's global analysis problem.Item Detecting a stochastic gravitational wave background with space-based interferometers(Montana State University - Bozeman, College of Letters & Science, 2014) Adams, Matthew Raymond; Chairperson, Graduate Committee: Neil J. CornishThe detection of a stochastic background of gravitational waves could significantly impact our understanding of the physical processes that shaped the early Universe. The challenge lies in separating the cosmological signal from other stochastic processes such as instrument noise and astrophysical foregrounds. One approach is to build two or more detectors and cross correlate their output, thereby enhancing the common gravitational wave signal relative to the uncorrelated instrument noise. When only one detector is available, as will likely be the case with space based gravitational wave astronomy, alternative analysis techniques must be developed. Here we develop an end to end Bayesian analysis technique for detecting a stochastic background with a gigameter Laser Interferometer Space Antenna (LISA) operating with both 6- and 4-links. Our technique requires a detailed understanding of the instrument noise and astrophysical foregrounds. In the millihertz frequency band, the predominate foreground signal will be unresolved white dwarf binaries in the galaxy. We consider how the information from multiple detections can be used to constrain astrophysical population models, and present a method for constraining population models using a Hierarchical Bayesian modeling approach which simultaneously infers the source parameters and population model and provides the joint probability distributions for both. We find that a mission that is able to resolve ~ 5000 of the shortest period binaries will be able to constrain the population model parameters, including the chirp mass distribution and a characteristic galaxy disk radius to within a few percent. This compares favorably to existing bounds, where electromagnetic observations of stars in the galaxy constrain disk radii to within 20%. Having constrained the galaxy shape parameters, we obtain posterior distribution functions for the instrument noise parameters, the galaxy level and modulation parameters, and the stochastic background energy density. We find that we are able to detect a scale-invariant stochastic background with energy density as low as Omega gw= 2x10 -13 for a 6-link interferometer and Omega gw = 5x10 -13 for a 4-link interferometer with one year of data.