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Item Studies in alternative theories of gravity and advanced data analysis(Montana State University - Bozeman, College of Letters & Science, 2024) Gupta, Toral; Chairperson, Graduate Committee: Neil J. Cornish; This is a manuscript style paper that includes co-authored chapters.The field of gravitational wave astronomy is generating groundbreaking findings, yielding unique insights on some of the most extraordinary phenomena in the universe and providing invaluable information on testing the principles of general relativity. All gravitational wave signals detected so far appear to come from compact binaries - black holes and neutron stars. We use information from these sources to probe strong fields of gravity and to constrain modified theories of gravity. However, solely relying on template- based searches for known astrophysical sources biases our gravitational wave signal search towards well-modeled systems, potentially overlooking unpredicted sources with limited theoretical models, hindering the extraction of new physics. Further work in this thesis focuses on building improved signal and noise models to enhance our capability of detecting gravitational signals of all within and beyond the constraints of theoretical predictions. This includes introduction of new basis functions with added modifications to develop a signal-agnostic waveform reconstruction model using Bayesian inference. Additionally, this study discusses improvements in the speed and performance of the BayesWave trans-dimensional Bayesian spectral estimation algorithm, which includes implementing a low-latency analysis and various enhancements to the algorithm itself. In essence, this study is centered on developing a comprehensive understanding, both theoretical and observational, of astrophysical objects along with the spacetime that governs their dynamics.Item Exploring the low-frequency gravitational-wave universe with pulsar timing arrays(Montana State University - Bozeman, College of Letters & Science, 2022) Becsy, Bence; Chairperson, Graduate Committee: Neil J. Cornish; This is a manuscript style paper that includes co-authored chapters.Pulsar timing arrays monitor millisecond pulsars to detect gravitational waves with nanohertz frequencies. They provide valuable information about various astophysical processes inaccessible to electromagnetic observations. In particular, they could shed light on unsolved problems related to the formation and evolution of supermassive black holes. We present several new methods which will help us fully realize the detection potential of pulsar timing arrays. We explore how the large collection of supermassive black hole binaries in the Universe can appear as a stochastic gravitational wave background, and how it might also result in a few individually detectable binaries. We describe a new method to efficiently search for such individual binaries, and also how we can detect multiple binaries in the presence of the confusion noise from the stochastic background. Finally, we introduce a new approach to search for generic gravitational-wave bursts, which enables us to hunt for unexpected new types of sources on the nanohertz gravitational-wave sky.Item Eccentric gravitational waves: modeling and data analysis implications(Montana State University - Bozeman, College of Letters & Science, 2020) Moore, Blake Carroll; Chairperson, Graduate Committee: Nicolas Yunes and Neil J. Cornish (co-chair); Travis Robson, Nicholas Loutrel and Nicolas Yunes were co-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 dissertation.; Nicholas Loutrel was a co-author of the article, 'A 3PN Fourier domain waveform for non-spinning binaries with moderate eccentricity' in the journal 'Classical and quantum gravity' which is contained within this dissertation.; Nicolas Yunes was a co-author of the article, 'Data analysis implications of moderately eccentric gravitational waves' submitted to the journal 'Classical and quantum gravity' which is contained within this dissertation.; Nicolas Yunes was a co-author of the article, 'Constraining gravity with eccentric gravitational waves: projected upper bounds and model selection' submitted to the journal 'Classical and quantum gravity' which is contained within this dissertation.The ground based advanced Laser Interferometer Gravitational wave Observatory (LIGO) has now made numerous detections of compact objects, ushering in an era of gravitational wave astronomy. Soon the Laser Interferometer Space Antenna (LISA) will become operational and allow for even more detections of gravitational waves. With these detections we are able to characterize the physical properties of the sources - the nature of the orbit, the parameters of the individual compact object, and the parameters of the final merged object. Beyond these source measurements, gravitational waves have proven an important test bed for validating General Relativity, as well as testing theoretical astrophysical formation scenarios of these compact binaries. In order to reach these ends, we require accurate and efficient models for the gravitational waves as seen in the detector. While current detections by ground based detectors are consistent with compact binaries in quasi-circular orbits, there are formation scenarios which suggest that some small number of detectable events will be from compact objects in eccentric orbits, and certainly a healthy number of sources detectable by LISA will be in eccentric orbits. We have derived, validated, and explored the data analysis properties of a waveform model for compact objects in eccentric orbits. In the derivation of the waveform we have employed a truncated sum of harmonics, the stationary phase approximation, and a bivariate expansion in eccentricity and orbital velocity. To explore the data analysis implications of this model we have implemented Markov Chain Monte Carlo algorithms to produce the posterior distributions on the waveform parameters. We find that our model is highly accurate for the inspiral phase of compact objects in orbits with eccentricity as high as 0.8, and very computationally efficient - taking only 90ms to evaluate on average. System parameters are best measured when the source eccentricity is about 0.4, sometimes providing two orders of magnitude better measurement than its quasi-circular counterpart, and eccentric signals can provide more stringent constraints on alternative theories of gravity.Item Testing general relativity through the computation of radiative terms and within the neutron star strong-field regime(Montana State University - Bozeman, College of Letters & Science, 2019) Saffer, Alexander; Chairperson, Graduate Committee: Nicolas Yunes; Kent Yagi and Nicolas Yunes were co-authors of the article, 'The gravitational wave stress-energy (pseudo)-tensor in modified gravity' in the journal 'Classical and quantum gravity' which is contained within this thesis.; Nicolas Yunes was a co-author of the article, 'Angular momentum loss for a binary system in Einstein-aether theory' in the journal 'Physical review D' which is contained within this thesis.; Hector O. Silva is an author and Nicolas Yunes is a co-author of the article, 'The exterior spacetime of relativistic stars in scalar-Gauss-Bonnet gravity' submitted to the journal 'Physical review D' which is contained within this thesis.The recent detection of coalescing black holes by the Laser Interferometer Gravitational-wave Observatory has brought forth the era of gravitational wave astronomy. Physicists are only now beginning to probe the mergers of compact objects that send ripples through space and time. These distortions carry with them the information from the system where they originated. The dynamics of black hole collisions and neutron star mergers are new and exciting events which were undetectable just a few years ago. Einstein's theory of General Relativity has done an excellent job of describing gravity and the information that can be extracted from gravitational systems. However, his theory contains several anomalies such as the inability to explain the inflation of the universe, the effects of dark matter and energy, the presence of singularities, as well as a failure to reconcile with quantum mechanics. Modified theories of gravity have been proposed to answer any remaining questions about gravitation while prescribing solutions to the problems General Relativity still has. The work within this thesis describes how we may study modified theories of gravity in the strong field regime through two different means. The first, is through the calculation of the rate of gravitational radiation from binary systems. This rate varies depending on the theory of gravity being studied. Comparing the theoretical predictions of these rates from alternative theories to astronomical observation will allow us to place better constraints on modified gravity and test General Relativity like never before. The second way is through the investigation of the spacetime surrounding a neutron star. Unlike black holes which emit no light, we are able to see neutron stars (more specifically pulsars) through their light curve as they rotate. The shape of the light curve is dictated by the theory of gravitation used to describe the spacetime around the neutron star. My goal of constructing such a spacetime for neutron stars in modified gravity allows for future scientists to study the light curves to be detected and place constraints on the particular theory.Item Testing alternative theories of gravity using low frequency gravitational waves(Montana State University - Bozeman, College of Letters & Science, 2019) O'Beirne, Logan Tyler; Chairperson, Graduate Committee: Neil J. Cornish; Bennett Link (co-chair); Logan O'Beirne, Stephen R. Taylor and Nicolas Yunes were co-authors of the article, 'Constraining alternative theories of gravity using pulsar timing arrays' in the journal 'Physical review letters' which is contained within this thesis.; Neil J. Cornish were co-authors of the article, 'Constraining the polarization content of gravitational waves with astrometry' in the journal 'Physical review D' which is contained within this thesis.; Neil J. Cornish, Sarah J. Vigeland and Stephen R. Taylor were co-authors of the article, 'Constraining alternative polarizations of continuous gravitational waves using pulsar timing arrays' submitted to the journal 'Physical review D' which is contained within this thesis.General Relativity aptly describes current gravitational observations. However, there is great theoretical interest in its validity in untested regimes. Alternative theories of gravity attempt to relax some of the assumptions made, leaving distinct signatures that are absent in Einstein's theory, namely the presence of alternative polarizations of gravitational waves that manifest from the emission of gravitational scalar and vector dipole radiation in black hole binaries. To study this lower order multipole of radiation, it is desirable to work in a regime where the quadrupolar tensor radiation of general relativity is as quiet as possible. This motivates working with supermassive black hole binaries in their slowly evolving inspiral phase, when they are well separated from merger, emitting low frequency gravitational waves. Using a frequentist framework, we study the detectability of a stochastic background of each polarization using pulsar timing arrays, which is currently the most technically developed and viable method for studying low frequency gravitational waves, correlating the observed time delays of pulsars. We also find that astrometry, which measures transverse displacements of the apparent position of stars, turns out to have a very similar correlation structure as the time delays measured by pulsar timing arrays. We lastly study how effective using a pulsar timing array is at studying a loud, foreground binary with these alternative polarizations, using a Bayesian framework. Low frequency gravitational wave astronomy proves advantageous for studying these exotic signatures.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 and characterizing gravitational waves with minimal assumptions(Montana State University - Bozeman, College of Letters & Science, 2018) Millhouse, Margaret Ann; Chairperson, Graduate Committee: Neil J. CornishAfter many years of preparation and anticipation, we are finally in the era of routine gravitational-wave detection. All of the detected signals so far have come from merging compact objects-- either black holes or neutron stars. These are signals for which we have very good waveform models, but there still exist other more poorly modeled sources as well as the possibility of completely new gravitational-wave sources. Because of this, it is important to have the ability to confidently detect gravitational-waves from a wide variety of sources. In this Thesis I will describe one particular algorithm used to detect and characterize gravitational-wave signals using Bayesian inference techniques, and minimal assumptions on the source of the gravitational wave. I will report on the methods and results of the implementation of this search in the first two observing runs of advanced LIGO. I will also discuss developments to this algorithm to improve waveform reconstruction, and target certain signals without using full waveform templates.Item Eccentric compact binaries: modeling the inspiral and gravitational wave emission(Montana State University - Bozeman, College of Letters & Science, 2018) Loutrel, Nicholas Peter; Chairperson, Graduate Committee: Neil J. CornishThe modeling of the inpsiral and subsequent gravitational wave emission from black hole binary systems has been a long outstanding problem in astrophysics and relativity. Astrophysical models predict that most binaries will have low orbital eccentricity by the time the gravitational wave emission enters the detection band of ground based detectors, and significant success has been made by restricting attention to the this limit, where the binary's orbit is approximately circular. However, exotic formation channels in globular clusters and galactic nuclei predict a small, but non-negligible, fraction of systems will enter the detection band of ground-based detectors with significant orbital eccentricity. In this thesis, we present new methods of modeling eccentric binaries under the influence of gravitational wave emission, focusing on two regimes: (i) the early inspiral of highly eccentric binaries, and (ii) the late inspiral of generic eccentric binaries.Item Spin-precessing compact binaries : gravitational wave modeling and information extraction(Montana State University - Bozeman, College of Letters & Science, 2016) Chatziioannou, Katerina; Chairperson, Graduate Committee: Nicolas YunesIn this dissertation we study the effect of spin-precession on gravitational waves emitted by quasicircular compact binary systems. In their most generic configuration, compact objects in a binary system are subject to interactions between the spin and the orbital angular momenta. These interactions give rise to precessional effects that add rich structure to the emitted gravitational waveforms. We study this spin-induced structure with an emphasis on extracting the information it encodes. In particular, we construct gravitational wave models that accurately capture spin-precessional effects. We then use them to study how much information relevant to astrophysics and nuclear physics we can extract from future observations of gravitational waves from compact binary coalescences.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.