The first direct detection of gravitational waves in 2015, and the multiple detections that followed ushered in the era of gravitational-wave astronomy. With these developments, the focus of the gravitational-wave community shifted from detection to precision measurement, requiring a factor of ten improvement in calibration accuracy to maximize the astrophysical information that can be extracted from these detected signals. This dissertation discusses the implementation and characterization of a radiation-pressure-based calibration system called the Photon calibrator that is used as the primary calibration reference for the Advanced LIGO detectors. It also discusses the techniques and procedures used to realize sub-percent accuracy calibration of absolute displacement fiducials introduced using the Photon calibrator system during Advanced LIGO’s first and second observing runs. Using the Photon calibrator systems, frequency dependent calibration of the interferometer responses was achieved at the level of 2-3% in magnitude and 3- 5 degrees in phase across the LIGO detection band. This level of calibration accuracy has already played a significant role in extracting astrophysical parameters from LIGO’s detections. With the LIGO and Virgo detectors operating at design sensitivity, updated rate estimates indicate that measurement of the Hubble constant with gravitational waves with 1% accuracy will be possible within the next decade. This will require absolute amplitude calibration of the detectors at the sub-1% level. This dissertation also discusses the improvements that have been implemented in the Photon calibrator systems that will reduce the uncertainty in absolute displacement to below 0.5%. The gravitational waves from the post-merger phase of binary neutron stars are expected to contain interesting features at frequencies up to few kHz, carrying rich information about neutron-star astrophysics. This dissertation discusses the calibration errors introduced by test mass deformations caused by calibration forces at frequencies above 1 kHz. The errors, estimated using Finite Element Analysis, is in reasonable agreement with measurement results in the 1 to 5 kHz band. These investigations have enabled the reduction of calibration uncertainty at these frequencies, which should enhance our ability to decipher the neutron star astrophysics encoded in the gravitational wave signals from the post-merger phase. This dissertation includes previously published co-authored material.

京都大学 / 新制・課程博士 / 博士(理学) / 甲第24404号 / 理博第4903号 / 新制||理||1700(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 田中 貴浩, 准教授 久徳 浩太郎, 教授 橋本 幸士 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

Gravitational waves are detected, analyzed and matched filtered based on an approximation of General Relativity called the Post Newtonian theory. This approximation method is based on the assumption that there is a weak gravity field both inside and around the body. However, scientists cannot justify why Post-Newtonian theory (meant for weak fields) works so well with strong fields of black hole mergers when it really should have failed [C. Will 2011]. Yunes and Pretorius gave another approach called parameterized post-Einsteinian (ppE) theory that uses negligible assumptions and promises to identify any deviation on the parameters through post-processing tests. This thesis project proposes to develop a method for the parametric detection and testing of gravitational waves by computation of ppE for the inspiral phase using ChirpLab. A set of templates will be generated with ppE parameters that can be used for the testing. / Master of Science / Electromagnetic waves were discovered in the 19th century and have changed our lives with various applications. Similarly, this new set of waves, gravitational waves, will potentially alter our perspective of the universe. Gravitational waves can help us understand space, time and energy from a new and deeper perspective. Gravitational waves and black holes are among the trending topics in physics at the moment, especially with the recent release of the first image of a black hole in history. The existence of black holes was predicted a century ago by Einstein in the well defined theory, “Theory of General Relativity”. Current approaches model the chaotic phenomenon of a black hole pair merger by the use of approximation methods. However, scientists Yunes and Pretorius [69] argue that the approximations employed skew the estimation of the physical features of the black hole system. Hence, there is a need to approach this problem with methods that don’t make specific assumptions about the system itself. This thesis project proposes to develop a computational method for the parametric2 detection and testing of gravitational waves.

A network of laser interferometer gravitational waves detectors spread across the globe is currently running and steadily improving. After complex data analysis from the output signal of the present detectors, astrophysical results begin to emerge with upper limits on gravitational wave sources. So far, however no direct detection has been announced. To increase the sensitivity of current detectors, a second generation of interferometers is planned which will make gravitational wave astronomy a reality within one decade. The advanced generation of interferometers will represent a substantial upgrade from current detectors. Especially, very high optical power will circulate in the arm cavities in order to reduce by one order of magnitude the shot noise limited sensitivity in high frequency. However, the theoretical shot noise limit will only be achieved after implementation of complex thermal lensing compensation schemes. Thermal lensing is direct consequence of the residual optical absorption inside the substrate and coating of the test masses and could have tragic consequences for the functionality of the interferometer. The Australian Consortium for Interferometric Gravitational Astronomy (ACIGA) in collaboration with LIGO will run a series of high optical power tests to understand the characteristics and effects of thermal lensing. During these tests, techniques to compensate thermal lensing will be experimented. This thesis mainly focused on the first high optical power test in Gingin, Australia. The first test will consist of a Fabry Perot cavity with the sapphire substrate of the input mirror inside the cavity. Due to the high optical circulating power a strong convergent thermal lens will appear in the input mirror substrate. Because of the presence of the thermal lens inside the cavity, the size of the cavity waist will be reduced and the cavity circulating power will decrease. Simulations using higher order mode expansion and FFT propagation code were completed to estimate ways to compensate strong thermal lensing for the Gingin first test. The term `strong thermal lensing? is used because the thermal lens focal length is comparable to the design focal length of the optical components. The expected performance of a fused silica compensation plate is presented and advantages and limits of this method are discussed. Experimental results on small scale actuators which can potentially compensate thermal lensing are detailed. The knowledge gained from these experiments was valuable to design the real scale compensation plate which was used in the first Gingin test. This test was carried at the end of 2005. The thermal lens due to 1 kW of optical power circulating in the sapphire substrate was successfully compensated using a fused silica plate. Yet, thermal lensing compensation may only be required for room temperature advanced interferometer. Indeed, we showed that cooling the interferometer mirror to cryogenic temperature can eliminate the thermal lensing problem and also substantially decrease the mirror thermal noise.

[No abstract supplied with this thesis - The first page (of three) of the Introduction follows] ¶ This thesis is largely concerned with the changing representations of 'boundary' or 'ideal' points of a pseudo-Riemannian manifold -- and our primary interest is in the space-times of general relativity. In particular, we are interested in the following question: What assumptions about the 'nature' of 'portions' of a certain 'ideal boundary' construction (essentially the 'abstract boundary' of Scott and Szekeres (1994)) allow us to define precisely the topological type of these 'portions', i.e., to show that different representations of this ideal boundary, corresponding to different embeddings of the manifold into others, have corresponding 'portions' that are homeomorphic? ¶ Certain topological properties of these 'portions' are preserved, even allowing for quite unpleasant properties of the metric (Fama and Scott 1995). These results are given in Appendix D, since they are not used elsewhere and, as well as representing the main portion of work undertaken under the supervision of Scott, which deserves recognition, may serve as an interesting example of the relative ease with which certain simple results about the abstract boundary can be obtained. ¶ An answer to a more precisely formulated version of this question appears very diffcult in general. However, we can give a rather complete answer in certain cases, where we dictate certain 'generalised regularity' requirements for our embeddings, but make no demands on the precise functional form of our metrics apart from these. For example, we get a complete answer to our question for abstract boundary sets which do not 'wiggle about' too much -- i.e., they satisfy a certain Lipschitz condition -- and through which the metric can be extended in a manner which is not required to be differentiable (C[superscript1]), but is continuous and non--degenerate. We allow similar freedoms on the interior of the manifold, thereby bringing gravitational wave space-times within our sphere of discussion. In fact, in the course of developing these results in progressively greater generality, we get, almost 'free', certain abilities to begin looking at geodesic structure on quite general pseudo-Riemannian manifolds. ¶ It is possible to delineate most of this work cleanly into two major parts. Firstly, there are results which use classical geometric constructs and can be given for the original abstract boundary construction, which requires differentiability of both manifolds and metrics, and which we summarise below. The second -- and significantly longer -- part involves extensions of those constructs and results to more general metrics.

This thesis describes two main projects; the first one is the optimization of a hierarchical search strategy to search for unknown pulsars. This project is divided into two parts; the first part (and the main part) is the semi-coherent hierarchical optimization strategy. The second part is a coherent hierarchical optimization strategy which can be used in a project like Einstein@Home. In both strategies we have found that the 3-stages search is the optimum strategy to search for unknown pulsars. For the second project we have developed a computer software for a coherent Multi-IFO (Interferometer Observatory) search. To validate our software, we have worked on simulated data as well as hardware injected signals of pulsars in the fourth LIGO science run (S4). While with the current sensitivity of our detectors we do not expect to detect any true Gravitational Wave signals in our data, we can still set upper limits on the strength of the gravitational waves signals. These upper limits, in fact, tell us how weak a signal strength we would detect. We have also used our software to set upper limits on the signal strength of known isolated pulsars using LIGO fifth science run (S5) data. / Diese Dissertation besteht aus zwei Projekten: Im ersten Projekt wird die Optimierung einer hierarchischen Strategie zum Auffinden von 'unbekannten' Pulsaren beschrieben. Der erste Teil besteht dabei aus einer semi-kohärenten und der zweite Teil aus einer kohärenten Optimierungsstrategie, wie sie in Projekten wie Einstein@Home verwendet werden kann. In beiden Ansätzen erwies sich eine 3-Stufensuche als optimale Suchstrategie für 'unbekannte' Pulsare. Für das zweite Projekt entwickelten wir eine Software für eine kohärente Multi-IFO (Interferometer Observatory) Suche. Zum Validieren der Software verwendeten wir sowohl simulierte Daten als auch Hardware induzierte Signale von Pulsaren aus dem vierten 'LIGO Science run' (S4). Wir erwarten nicht, mit der aktuellen Empfindlichkeit unserer Detektoren echte GW- Signale aufzunehmen, können jedoch obere Grenzen für die Stärke der Gravitationswellen-Signale bestimmen. Diese oberen Grenzen geben uns an, wie schwach ein gerade noch detektierbares Signal werden kann. Ferner benutzten wir die Software um eine obere Grenze für bekannte, isolierte Pulsare zu bestimmen, wobei wir Daten aus dem fünften 'LIGO Science run (S5) verwendeten.

[Truncated abstract] Advanced laser interferometer gravitational wave detectors require an extremely high optical power in order to improve the coupling between the gravitational wave signal and the optical field. This high power requirement leads to new physical phenomena arising from nonlinear interactions associated with radiation pressure. In particular, detectors with multi-kilometer-long arm cavities containing high density optical fields suffer the possibility of 3-mode opto-acoustic interactions. This involves the process where ultrasonic vibrations of the test mass cause the steady state optical modes to scatter. These 3-mode interactions induce transverse optical modes in the arm cavities, which then can provide positive feedback to the acoustic vibrations in the test masses. This may result in the exponential growth of many acoustic mode amplitudes, known as Parametric Instability (PI). This thesis describes research on 3-mode opto-acoustic interactions in advanced interferometric gravitational wave detectors through numerical investigations of these interactions for various interferometer configurations. Detailed analysis reveals the properties of opto-acoustic interactions, and their dependence on the interferometer configuration. This thesis is designed to provide a pathway towards a tool for the analysis of the parametric instabilities in the next generation interferometers. Possible techniques which could be helpful in the design of control schemes to mitigate this undesirable phenomenon are also discussed. The first predictions of parametric instability considered only single interactions involving one transverse mode and one acoustic mode in a simple optical cavity. ... In Chapter 6, I was able to make use of a new analytical model due to Strigin et al., which describes parametric instability in dual recycling interferometers. To make the solution tractable, it was necessary to consider two extreme cases. In the worst case, recycling cavities are assumed to be resonant for all transverse modes, whereas in the best cases, both recycling cavities are anti-resonant for the transverse modes. Results show that, for the worst case, parametric gain values as high as ~1000 can be expected, while in the best case the gain can be as low as ~ 3. The gain is shown to be very sensitive to the precise conditions of the interferometer, emphasising the importance of understanding the behaviour of the detectors when the cavity locking deviates from ideal conditions. Chapter 7 of this thesis contains work on the observation of 3-mode interactions in an optical cavity at Gingin, which confirms the analysis presented here, and also a paper which shows how the problem of 3-mode interactions can be harnessed to create new devices called opto-acoustic parametric amplifiers. In the conclusions in Chapter 8, I discuss the next important steps in understanding parametric interactions in real interferometers – including the need for more automated codes relevant to the design requirements for recycling cavities. In particular, it is pointed out how the modal structure of power and signal recycling cavities must be understood in detail, including the Gouy phase for each transverse mode, to be able to obtain precise predictions of parametric gain. This thesis is organised as a series of papers which are published or have been submitted for publication. Such writing style fills the condition for Ph.D. thesis at the University of Western Australia.

L'existence des ondes gravitationnelles, fluctuations de l'espace-temps lui-même, a été prédite sans, pour l'instant, qu'une détection directe n'ait été encore possible. A l'heure actuelle, des méthodes consistant en des détecteurs interférométriques de plusieurs kilomètres de long sont à l'oeuvre pour permettre une première détection. Nous proposons, dans cette thèse, d'étudier une autre méthode : la chronométrie d'un réseau de pulsars milliseconde. Elle consiste en l'observation régulière et la datation précise des impulsions radio en provenance de pulsars ultrastables. L'onde gravitationnelle produisant retards ou avances des impulsions sur Terre, nous recherchons sa présence sous forme d'un signal corrélé entre les observations faites des différents pulsars du réseau. Dans un premier temps, nous détaillons les processus d'observation et de chronométrie des pulsars, pour nous pencher sur un cas particulier avec le pulsar J1614-2230. Puis, nous présentons les ondes gravitationnelles et leurs sources ainsi que les différentes méthodes de détection. Nous décrivons tout particulièrement la méthode de chronométrie d'un réseau de pulsars appliquée à la recherche d'un signal en provenance d'un système binaire de tous noirs supermassifs. Ensuite, après avoir détaillé les outils statistiques et numériques utilisés, nous appliquons notre méthode à l'injection d'un tel signal dans les observations réelles faites dans le cadre de l'EPTA. Enfin, nous présentons les limites supérieures sur l'amplitude d'un signal en provenance d'un système binaire obtenues sur ces données sans injection grâce à notre méthode en fonction de la fréquence et de la position de la source. / The existence of gravitational waves, ripples in space-time itself, has been predicted but their detection remains elusive. Multiple techniques exist for searching for them, including ground-based kilometer long inteferometers. In this thesis, we present an alternative approach, based on the monitoring and precise timing of radio pulses from an array of millisecond pulsars. A gravitational wave will perturb the propagation of those radio pulses, causing them to reach the Earth with a certain delay. By searching for correlations in the arrival times of the pulsations from different pulsars, we can in principle infer the presence of gravitational waves from observations. We begin by giving an overview of pulsar observations and timing. We illustrate those principles with a practical example : the study of the millisecond pulsar J1614-2230. In the second part we describe gravitational waves, the sources that create them, and the various detection methods. Then, we focus on the pulsar timing array technique, and its potential application to the search for gravitational waves from supermassive black hole binary system. We pursue with a detailed description of the statistical and numerical tools that we used in the present work, and present the results of a search ofr an injected signal in the real EPTA data set. Finally, we employ our new method to derive upper limits on the amplitude of a putative signal in the same EPTA data set, as a function of the frequency and sky location of the supermassive black hole binary system.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第20909号 / 理博第4361号 / 新制||理||1626(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 柴田 大, 教授 井岡 邦仁, 教授 川合 光 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

Ground-based gravitational wave detectors are evolving at a rapid pace. In the five minutes that followed the first direct detection of gravitational waves, the Advanced LIGO and Advanced Virgo experiments have been subject to substantial upgrades, increasing their sensitivities by many times and allowing them to detect dozens of other gravitational wave signals. Third-generation ground-based interferometers (Einstein Telescope and Cosmic Explorer) and spaaace-based detectors (such as LISA) are being researched and planned to enter into function in the second half of the next decade. If successful, these experiments will allow the detection of thousands of signals coming from an ever-increasing range of cosmological sources. In the meantime, second-generation interferometers are approaching the conclusion of ambitious upgrades started with the end of the third observing run “O3” in march 2020. The work of this thesis revolves around the planning and the commissioning of the “Advanced Virgo plus” upgrade project, which aims to increase the detector’s sensitivity by a factor of two, allowing a ten times higher detection rate than the previous configuration. In particular, the main topic is the update of the interferometer longitudinal sensing and control scheme required by the upgrade in the detector’s optical configuration. The design and simulation of the new control scheme catried out in constant collaboration with the “Interferometer Sensing and Control” team, started minutes before the actual implementation of the upgrades. Following that, I participated in the full-time commissioning of the upgraded configuration, which started in January 2021 and is currently ongoing. We will first explain the new interferometer configuration, then go into the details of the lock-acquisition procedure, presenting the results of the related simulation studies and the commissioning. A particular focus will also be given to the simulations of the interferometer’s state at the end of the lock acquisition, called “steady-state”. In addition to the study and implementation of the current lock-acquisition procedure, the thesis will present simulation activities to study an alternative lock-acquisition technique that has not yet been implemented.