Thesis (Ph. D.)--Massachusets Institute of Technology (MIT), 2006. / PDF copy of thesis. Includes bibliograpy.

Thesis (M.S.)--Baylor University, 2006. / Includes bibliographical references (p. 74-76).

Astronomy with gravitational-wave observations is now a reality. Much of the theoretical research in this field falls under three broad themes: the mathematical description and physical understanding of gravitational radiation and its effects; the construction of accurate and computationally efficient waveform models for astrophysical sources; and the improved statistical analysis of noisy data from interferometric detectors, so as to extract and characterise source signals. The doctoral thesis presented in this dissertation is an investigation of various topics across these themes. Under the first theme, we examine the direct interaction between gravitational waves and electromagnetic fields in a self-contained theoretical study; this is done with a view to understanding the observational implications for highly energetic astrophysical events that radiate in both the gravitational and electromagnetic sectors. We then delve into the second theme of source modelling by developing and implementing an improved waveform model for the extreme-mass-ratio inspirals of stellar-mass compact objects into supermassive black holes, which are an important class of source for future space-based detectors such as the Laser Interferometer Space Antenna. Two separate topics are explored under the third theme of data analysis. We begin with the procedure of searching for gravitational-wave signals in detector data, and propose several combinatorial compression schemes for the large banks of waveform templates that are matched against putative signals, before studying the usefulness of these schemes for accelerating searches. After a gravitational-wave source is detected, the follow-up process is to measure its parameters in detail from the data; this is addressed as we apply the machine-learning technique of Gaussian process regression to gravitational-wave data analysis, and in particular to the formidable problem of parameter estimation for extreme-mass-ratio inspirals.

Um Detector de Ondas Gravitacionais tipo Massa-Ressonante Esférico é otimizado. Primeiramente um modelo matemático para o detector com seis transdulatores indutivos supercondutivos de dois modos é usado para simular o desempenho de tal detector. Depois disso, um conjunto completo de experimentos para melhorar os fatores de qualidade mecânico e elétrico do transdutor e dos acoplamentos entre suas partes é mostrado e os resultados, discutidos. / A Spherical Resonant-Mass Detector of Gravitational Waves is optimized. First, a mathematical model for the detector with six inductive superconducting two-mode transducers is used to simulate the performance of such detector. After that, a complete set of experiments to improve the mechanical and the electrical quality factors of the materials and the transducer attachments is shown, and the results are discussed.

In the formation of galaxy groups and clusters, the dark matter haloes containing satellite galaxies are expected to be tidally stripped in gravitational interactions with the host. We use galaxy-galaxy weak lensing to measure the average mass of dark matter haloes of satellite galaxies as a function of projected distance to the centre of the host, since stripping is expected to be greater for satellites closer to the centre of the cluster. We further classify the satellites according to their stellar mass: Assuming that the stellar component of the galaxy is less disrupted by tidal stripping, stellar mass can be used as a proxy of the infall mass. We study the stellar-to-halo mass relation of satellites as a function of the cluster-centric distance to measure tidal stripping. We use the shear catalogues of the Dark Energy Survey (DES) science verification archive, the Canada-France-Hawaii Lensing Survey (CFHTLenS) and the CFHT Stripe 82 surveys, and we select satellites from the redMaPPer catalogue of clusters. For galaxies located in the outskirts of clusters, we find a stellar-to-halo mass relation in good agreement with the theoretical expectations from Moster et al. for central galaxies. In the centre of the cluster, we find that this relation is shifted to smaller halo mass for a given stellar mass. We interpret this finding as further evidence for tidal stripping of dark matter haloes in high-density environments.

The motivation of this thesis is to look for a signature of Lorentz violation, hopefully observable, in the gravitational waves emitted by cosmic strings. Aspects of cosmic strings are reviewed, in particular how focused bursts of gravitational radiation are emitted when a cusp forms on the string. The same phenomenon is then studied in an effective field theory with Lorentz violation called Einstein-aether theory. This is a simple theory with a dynamic preferred frame, but it retains rotational and diffeomorphism invariance. The linearized version of the theory produces five wave modes. We study the usual transverse traceless modes which now have a wave speed that can be lower or greater than the speed of light. This altered speed produces distinctive features in the waves. They depend on two free parameters: roughly the wave speed and the acceleration of the string cusp. The profile of the wave is analyzed in detail for different values of the parameters and explained by close comparison with the string motion. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

Strong gravitational lensing provides an independent measurement of the Hubble parameter (H-0). One remaining systematic is a bias from the additional mass due to a galaxy group at the lens redshift or along the sightline. We quantify this bias for more than 20 strong lenses that have well-sampled sightline mass distributions, focusing on the convergence kappa and shear gamma. In 23% of these fields, a lens group contributes >= 1% convergence bias; in 57%, there is a similarly significant line-of-sight group. For the nine time-delay lens systems, H-0 is overestimated by 11(-2)(+3)% on average when groups are ignored. In 67% of fields with total kappa >= 0.01, line-of-sight groups contribute greater than or similar to 2x more convergence than do lens groups, indicating that the lens group is not the only important mass. Lens environment affects the ratio of four (quad) to two (double) image systems; all seven quads have lens groups while only 3 of 10 doubles do, and the highest convergences due to lens groups are in quads. We calibrate the gamma-kappa relation: log(kappa(tot)) = (1.94 +/- 0.34)log(gamma(tot)) + (1.31 +/- 0.49) with an rms scatter of 0.34 dex. Although shear can be measured directly from lensed images, unlike convergence, it can be a poor predictor of convergence; for 19% of our fields, kappa is greater than or similar to 2 gamma. Thus, accurate cosmology using strong gravitational lenses requires precise measurement and correction for all significant structures in each lens field.

Einstein’s general theory of relativity has withstood 100 years of testing and will soon be facing one of its toughest challenges. In a few years we expect to be entering the era of the first direct observations of gravitational waves. These are tiny perturbations of space-time that are generated by accelerating matter and affect the measured distances between two points. Observations of these using the laser interferometers, which are the most sensitive length-measuring devices in the world, will allow us to test models of interactions in the strong field regime of gravity and eventually general relativity itself. I apply the tools of Bayesian inference for the examination of gravitational wave data from the LIGO and Virgo detectors. This is used for signal detection and estimation of the source parameters. I quantify the ability of a network of ground-based detectors to localise a source position on the sky for electromagnetic follow-up. Bayesian criteria are also applied to separating real signals from glitches in the detectors. These same tools and lessons can also be applied to the type of data expected from planned space-based detectors. Using simulations from the Mock LISA Data Challenges, I analyse our ability to detect and characterise both burst and continuous signals. The two seemingly different signal types will be overlapping and confused with one another for a space-based detector; my analysis shows that we will be able to separate and identify many signals present. Data sets and astrophysical models are continuously increasing in complexity. This will create an additional computational burden for performing Bayesian inference and other types of data analysis. I investigate the application of the MOPED algorithm for faster parameter estimation and data compression. I find that its shortcomings make it a less favourable candidate for further implementation. The framework of an artificial neural network is a simple model for the structure of a brain which can “learn” functional relationships between sets of inputs and outputs. I describe an algorithm developed for the training of feed-forward networks on pre-calculated data sets. The trained networks can then be used for fast prediction of outputs for new sets of inputs. After demonstrating capabilities on toy data sets, I apply the ability of the network to classifying handwritten digits from the MNIST database and measuring ellipticities of galaxies in the Mapping Dark Matter challenge. The power of neural networks for learning and rapid prediction is also useful in Bayesian inference where the likelihood function is computationally expensive. The new BAMBI algorithm is detailed, in which our network training algorithm is combined with the nested sampling algorithm MULTINEST to provide rapid Bayesian inference. Using samples from the normal inference, a network is trained on the likelihood function and eventually used in its place. This is able to provide significant increase in the speed of Bayesian inference while returning identical results. The trained networks can then be used for extremely rapid follow-up analyses with different priors, obtaining orders of magnitude of speed increase. Learning how to apply the tools of Bayesian inference for the optimal recovery of gravitational wave signals will provide the most scientific information when the first detections are made. Complementary to this, the improvement of our analysis algorithms to provide the best results in less time will make analysis of larger and more complicated models and data sets practical.

We have performed a blind search for a gamma-ray transient of arbitrary duration and energy spectrum around the time of the LIGO gravitational-wave event GW150914 with the six-spacecraft interplanetary network (IPN). Four gamma-ray bursts were detected between 30 hr prior to the event and 6.1 hr after it, but none could convincingly be associated with GW150914. No other transients were detected down to limiting 15-150 keV fluences of roughly 5 x10-(8) -5 x 10(-7) erg cm(-2). We discuss the search strategies and temporal coverage of the IPN on the day of the event and compare the spatial coverage to the region where GW150914 originated. We also report the negative result of a targeted search for the Fermi-GBM event reported in conjunction with GW150914.

In his theory of General Relativity, Einstein describes gravity as a geometric property of spacetime, which deforms in the presence of mass and energy. The accelerated motion of masses produces deformations, which propagate outward from their source at the speed of light. We refer to these radiated deformations as gravitational waves. Over the past several decades, the goal of the Laser Interferometer Gravitational-wave Observatory (LIGO) has been the search for direct evidence of gravitational waves from astrophysical sources, using ground based laser interferometers. As LIGO moves into its Advanced era (aLIGO), the direct detection of gravitational waves is inevitable. With the technology at hand, it is imperative that we have the tools to analyze the detector signal and examine the interesting astrophysical properties of the source. Some of the main targets of this search are coalescing compact binaries. In this thesis, I describe and evaluate bhextractor, a data analysis algorithm that uses Principal Component Analysis (PCA) to identify the main features of a set of gravitational waveforms produced by the coalescence of two black holes. Binary Black Hole (BBH) systems are expected to be among the most common sources of gravitational waves in the sensitivity band of aLIGO. However, the gravitational waveforms emitted by BBH systems are not well modeled and require computationally expensive Numerical Relativity (NR) simulations. bhextractor uses PCA to decompose a catalog of available NR waveforms into a set of orthogonal Principal Components (PCs), which efficiently select the major common features of the waveforms in the catalog and represent a portion of the BBH parameter space. From these PCs, we can reconstruct any waveform in the catalog, and construct new waveforms with similar properties. Using Bayesian analysis and Nested Sampling, one can use bhextractor to classify an arbitrary BBH waveform into one of the available catalogs and estimate the parameters of the gravitational wave source.