According to general relativity, appropriately accelerated masses emit gravitational radiation. With the gravitational-wave detectors reaching sufficient sensitivities for detecting astrophysical gravitational-waves, a new messenger for observing the astrophysical events has become available. However, with the current number of gravitational-wave detections, there are many unanswered questions whose answers are waiting to be discovered. Analogous to the Malmquist bias in other astronomical observation techniques, gravitational-wave detections also have an observation bias. In order to infer astrophysical distribution of the properties of gravitational-wave events from detections, this bias needs to be well understood. In this collection of studies, by investigating statistical and physical properties of gravitational-wave detection, an efficient semi-analytical method for calculating the bias was found. Further, the estimated bias was used for doing the first unmodelled inference on the mass distribution of binary black holes which showed additional structures not found by modelled inferences. Vast majority of gravitational-wave detections are binary black hole mergers. One of the mysteries of binary black holes is their formation channels. There are several proposed formation scenarios none of which is strongly favored by data. One of these channels is the so-called hierarchical triple mergers which is an dynamical formation scenario expected to have in dense environments such as globular clusters. This scenario considers a bound three black hole system which gives two consecutive mergers. In this collection of studies, it was directly tested with the detections from the three observing runs of Advanced LIGO and Advanced Virgo detectors. No significant evidence for this scenario was found, individually interesting event pairs were identified for further investigation and upper limits on the occurrence of the scenario were obtained. Gravitational-wave detectors have sensitivity on the significant portion of the sky. However, the localizations of the gravitational-wave detections are not very precise. Multi-messenger follow-ups guided by gravitational-wave detections can precisely locate the astrophysical source and gather more information by probing it with different messengers. The multi-messenger searches are done with statistical methods and it is necessary to have powerful statistical methods not to miss the valuable multi-messenger events. In the final parts of this collection of studies, optimal statistical methods for multi-messenger searches were developed and joint gravitational-wave and high-energy neutrino events were searched, both in realtime and with archival data.

The most promising technique for the direct, ground-based detection of gravitational waves is the use of advanced interferometric gravitational wave detectors. These detectors use long-baseline Michelson interferometers, where the critical enabling component is the laser. The laser required for these interferometers must provide a low noise, single frequency, diffraction limited, high power TEM₀₀ beam. Very importantly, the laser beam must be available continuously and without the need for operator intervention. In this thesis I describe the development and characterisation of injection-locked 10 W Nd:YAG lasers, designed specifically for use at the Australian Consortium for Interferometric Gravitational Astronomy (ACIGA) High Power Test Facility (HPTF) in Western Australia, and on the Japanese TAMA 300 gravitational wave interferometer (GWI). The starting point was a 5 W laboratory laser that had demonstrated the proof-of-principle; however this laser had insufficient power, inadequate reliability, and was not suitable for deployment to a remote site. I describe the development of this laser technology and design to realise reliable, longterm operation and field deployability, while satisfying the requirements for a GWI, with the final laser system bearing little resemblance to the proof-of-principle system. Injection-locked lasers were successfully installed at the ACIGA HPTF and at TAMA 300 in June 2004 and September 2005 respectively. The 10 W laser uses a Nd:YAG Coplanar Pumped Folded Slab (CPFS) gain medium. The slab is side-pumped using a temperature controlled, fast-axis collimated, custom laser diode array, and conduction cooled in the orthogonal direction. Interferometry is used to measure the thermal lensing within the gain medium; these measurements are used to design a single-mode, travelling-wave slave resonator. The entire slave laser is temperature controlled and mounted on an integrated, air-cooled base. The thermal design is validated by extensive thermal testing. Long-term and robust injection-locking is achieved by using a servo system based on the Pound-Drever-Hall technique. I describe the development of a split feedback servo system to provide increased frequency stabilisation loop bandwidth and show that long-term injection-locking of the slave laser to a low power non-planar ring oscillator (NPRO) master laser produces a single frequency output at ~ 10 W with M²[subscript]x.y approx ≤ 1.1. Finally, the noise of the injection-locked laser is characterised. Relative intensity noise measurements demonstrate stability comparable to current GWI laser sources, while the results of a heterodyne beat measurement show that the 10 W injectionlocked laser output has frequency noise limited by the NPRO input. The laser installed at the ACIGA HPTF has been used to investigate the effects of increased intracavity laser powers on next-generation interferometers, with the laser described in this thesis being the key enabling component of this research. / http://proxy.library.adelaide.edu.au/login?url= http://library.adelaide.edu.au/cgi-bin/Pwebrecon.cgi?BBID=1349763 / Thesis (Ph.D.) - University of Adelaide, School of Chemistry and Physics, 2009

[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.

The most promising technique for the direct, ground-based detection of gravitational waves is the use of advanced interferometric gravitational wave detectors. These detectors use long-baseline Michelson interferometers, where the critical enabling component is the laser. The laser required for these interferometers must provide a low noise, single frequency, diffraction limited, high power TEM₀₀ beam. Very importantly, the laser beam must be available continuously and without the need for operator intervention. In this thesis I describe the development and characterisation of injection-locked 10 W Nd:YAG lasers, designed specifically for use at the Australian Consortium for Interferometric Gravitational Astronomy (ACIGA) High Power Test Facility (HPTF) in Western Australia, and on the Japanese TAMA 300 gravitational wave interferometer (GWI). The starting point was a 5 W laboratory laser that had demonstrated the proof-of-principle; however this laser had insufficient power, inadequate reliability, and was not suitable for deployment to a remote site. I describe the development of this laser technology and design to realise reliable, longterm operation and field deployability, while satisfying the requirements for a GWI, with the final laser system bearing little resemblance to the proof-of-principle system. Injection-locked lasers were successfully installed at the ACIGA HPTF and at TAMA 300 in June 2004 and September 2005 respectively. The 10 W laser uses a Nd:YAG Coplanar Pumped Folded Slab (CPFS) gain medium. The slab is side-pumped using a temperature controlled, fast-axis collimated, custom laser diode array, and conduction cooled in the orthogonal direction. Interferometry is used to measure the thermal lensing within the gain medium; these measurements are used to design a single-mode, travelling-wave slave resonator. The entire slave laser is temperature controlled and mounted on an integrated, air-cooled base. The thermal design is validated by extensive thermal testing. Long-term and robust injection-locking is achieved by using a servo system based on the Pound-Drever-Hall technique. I describe the development of a split feedback servo system to provide increased frequency stabilisation loop bandwidth and show that long-term injection-locking of the slave laser to a low power non-planar ring oscillator (NPRO) master laser produces a single frequency output at ~ 10 W with M²[subscript]x.y approx ≤ 1.1. Finally, the noise of the injection-locked laser is characterised. Relative intensity noise measurements demonstrate stability comparable to current GWI laser sources, while the results of a heterodyne beat measurement show that the 10 W injectionlocked laser output has frequency noise limited by the NPRO input. The laser installed at the ACIGA HPTF has been used to investigate the effects of increased intracavity laser powers on next-generation interferometers, with the laser described in this thesis being the key enabling component of this research. / http://proxy.library.adelaide.edu.au/login?url= http://library.adelaide.edu.au/cgi-bin/Pwebrecon.cgi?BBID=1349763 / Thesis (Ph.D.) - University of Adelaide, School of Chemistry and Physics, 2009

[Truncated abstract] The research described in this thesis investigated optical spring interactions and instabilities in a macroscopic opto-mechanical resonator. The thesis describes an experiment designed to model an optical spring `tranquiliser’ cavity which has been proposed to suppress the predicted parametric instabilities in the next generation of interferometric gravitational wave detectors. In a series of experiments, the optical spring effect was observed in macroscopic optical cavities through measured changes in mechanical stiffness, and measured changes in mechanical loss. The optical spring effect was further characterised through investigation of its dependent parameters. Two pairs of identical, low optical loss mirrors were bonded to a mechanical structure using a novel low mechanical loss technique, forming an opto-mechanical composite resonator. The technique uses the naturally occurring resin Yacca gum as a bonding agent. This resulted in the formation of two optical cavities with a length of l = 0.100±0.001m, only one of which was used in experiments. Using finite element modelling, the resonator?s two lowest modes, with frequencies of fm1 = 722.8Hz and fm2 = 747.9Hz, and an effective mass 0.0323±0.0001kg, were found to be subject to the optical spring effect. ... The instabilities are expected to have a parametric gain factor of up to 100 in the frequency range of 15-120kHz. Therefore, if optical spring damping can be made large enough to reduce the Q-factor of the Advanced LIGO test-masses by a factor of 100, all parametric instabilities should be eliminated. For a simple servo loop and an optical cavity with the practically achievable finesse of F = 30,000, a tranquiliser cavity length of 1.3cm was found to produce optimum enhanced damping. This configuration only requires 1.47W of input power, resulting in an intra-cavity power of 5.72kW. The cavity mirrors were assumed to have optical coatings with a damage threshold of 1MW/cm2, which limited the spot size to a minimum area of 0.572mm2, or a radial beam waist of w = 0.427mm. This nearly flat-flat cavity has a stability g-factor of 0.9997. Even given these technical challenges, suppression of the parametric instabilities predicted to occur in the next generation of interferometric detectors is possible to achieve practically using enhanced optical spring damping. A possible design for such a tranquiliser cavity is also suggested.

Advanced Laser Interferometric Gravitational Wave Detectors, based on current infrastructure (in particular, the Advanced LIGO detectors), are being planned to significantly increase the sensitivity to gravitational wave strain in the near future. To upgrade the existing detectors requests implementing very high optical power, as well as very high circulating power in the arm cavities; these measures will increase the sensitivity at the shot noise floor by one order of magnitude. However, such extremely high power circulation in the cavities will cause optical distortions in the test masses. Thermal distortions arise from the optical power absorption by defects or inhomogeneities in test masses, resulting in wavefront deformations, which have important consequences for the power buildup of the Radio-Frequency (RF) sidebands in the recycling cavities, thus degrading the performance of the detectors. The degree of this sensitivity degradation in the shot noise floor, due to optical distortions induced by defects or inhomogeneities (i.e. imperfections) in test masses in Advanced Laser Interferometric Gravitational-wave Detectors, is dependent on the test mass optical quality; while the sensitivity degradation in the thermal noise floor is dependent on the test mass mechanical properties. For this reason, it is compulsory to use high optical and mechanical quality test mass materials in the advanced interferometer detectors. Fused silica has been used for test masses in detectors, while sapphire has been planned to be used for test mass substrates in the proposed Large-scale Cryogenic Gravitational-wave Telescope (LCGT) project. Other materials, such as calcium fluoride (CaF2), are also attractive, especially for cryogenic detectors. However, for the state-of-theAbstract II art facilities, it is difficult to manufacture very uniform, defect-free, inhomogeneity-free, high-quality, and large-size samples. Thus, the qualities of sapphire and calcium fluoride single crystal samples were investigated and evaluated, to ensure that they have suitable properties for use in interferometer detectors, i.e. with an adequately low level of imperfections, but also with high mechanical quality factor (Q-factor). This thesis describes research done in the endeavour to investigate bulk defects or inhomogeneities in test masses, as well as their induced thermal distortions, which appear at a high optical power in Laser Interferometric Gravitational-wave Detectors. An Automatic Rayleigh Scattering Mapping System (ARSMS) to examine the optical property of large-size test masses is described. This ARSMS enables quantitative high-resolution 3D mapping of defects or inhomogeneities in optical materials. The measured 3D defect distribution mapping of optical materials can assist in the design of suitable configurations of test masses in high optical power interferometers. In addition, a very sensitive Hartmann wavefront sensor was used to actively monitor the thermal distortions due to bulk and coating absorption in test masses. A very strong thermal distortion in these test masses was observed in the Gingin facility, demonstrating that thermal distortions could be a critical issue in advanced interferometer detectors. A negative thermo-optical coefficient material, to be used in a thermal distortion compensation method, was investigated for the compensation of very localised distortions due to imperfections. This thesis also includes experimental and theoretical studies of the scattering, absorption, and birefringence mechanisms, thermal distortion effects, and optimal compensation methods for test masses.

[Truncated abstract] As gravitational wave detectors approach sensitivities that will allow observations to become routine, astrophysics lies on the cusp of an exciting new era. Potential sources will include transients such as merging neutron stars and black holes, supernova explosions or the engines that power gamma-ray bursts. This thesis will be devoted to the astrophysical gravitational wave background signal produced by cosmological populations of such transient signals. Particular attention will be devoted to the observation-time dependence imposed on the individual sources that accumulate to produce a gravitational wave background signal. The ultimate aim is to determine what information is encoded in the temporal evolution of such a signal. To lay the foundations for further investigation, the stochastic gravitational wave background signal from neutron star birth throughout the Universe has been calculated. In view of the uncertainties in both the single-source emissions and source rate histories, several models of each are employed. The results show that that the resulting signals are only weakly dependent on the source-rate evolution model and that prominent features in the single-source spectra can be related to the background spectra. In comparison with previous studies, the use of relativistic single-source gravitational wave waveforms rather than Newtonian models and a more slowly evolving source-rate density results in a 1 { 2 order of magnitude reduction in signal. ... A comparison with the more commonly used brightness distribution of events shows that when applying both methods to a data stream containing a background of Gaussian distributed false alarms, the brightness distribution yielded lower standard errors, but was biased by the false alarms. In comparison, a fitting procedure based on the time evolution of events was less prone to errors resulting from false alarms, but as fewer events contributed to the data, had a lower resolution. In further support of the time dependent signature of transient events, an alternative technique is fiapplied to the same source population. In this case, the local rate density is probed by measuring the statistical compatibility of the filtered data against synthetic time dependent data. Although this method is not as compact as the fitting procedure, the rate estimates are compatible. To further investigate how the observation time dependence of transient populations can be used to constrain global parameters, the method is applied to Swift long gamma-ray burst data. By considering a distribution in peak °ux rather than a gravitational wave amplitude, gamma-ray bursts can be considered as a surrogate for resolved gravitational wave transients. For this application a peak °ux{observation time relation is described that takes the form of a power law that is invariant to the luminosity distribution of the sources. Additionally, the method is enhanced by invoking time reversal invariance and the temporal cosmological principle. Results are presented to show that the peak °ux{observation time relation is in good agreement with recent estimates of source parameters. Additionally, to show that the intrinsic time dependence allows the method to be used as a predictive tool, projections are made to determine the upper limits in peak °ux of future gamma-ray burst detections for Swift.

[Truncated abstract] Interferometric gravitational wave detectors are being built around the world with continually improving measurement sensitivities. Noise levels from sources that are intrinsic to these detectors must be reduced to a level below the gravita- tional wave signal. Seismic noise in the low frequency range, which is within the gravitational wave detection bandwidth, is a concern for earth-based detectors. This thesis presents research and development of a high performance vibration isolation system that is designed to attenuate seismic noise. The final design will be used as part of a fully working interferometer at the Australian International Gravitational Observatory (AIGO). Pendulums and springs are conventionally used for the horizontal and vertical vibration isolation components respectively. A complete system comprises of a cascade of these components, each stage dramatically improving the level of isola- tion. The residual motion at the test mass level is thus reduced but is dominated by the normal mode resonances of the chain. A simple and effective method to reduce residual motion further is to add ultra-low frequency pre-isolation stages which suspend the chain. The Roberts Linkage is a relatively new and simple geometrical structure that is implemented in the pre-isolation stages. Here we present experimental results of improving isolation based on mathematical mod- elling. The attenuation of seismic noise in the vertical direction is almost as important as that in the horizontal direction, due to cross-coupling between the two planes. To help improve the vertical performance a lightweight Euler spring that stores no static energy was implemented into the AIGO suspension system. ... Theoretical and experimental results are presented and discussed. Currently the AIGO laboratory consists of two 80 m length arms. They are aligned along the east and south directions. One of AIGO's top priorities is the installation of two complete vibration isolators in the east arm to form a Fabry-Perot cavity. Assembling two suspension systems will enable more accurate performance measurements of the tuned isolators. This would significantly reduce the measurement noise floor as well as eliminate the seismic noise spectrum due to referencing with the ground motion. The processes involved in preparing such a task is presented, including clean room preparation, tuning of each isolator stage, and local control schematics and methods. The status of the AIGO site is also presented.