Low-frequency sensitivity of next generation gravitational wave detectors

Transcription

1 Low-frequency sensitivity of next generation gravitational wave detectors Mark G. Beker

2 ISBN: Cover: designed by the author, featuring surface Rayleigh wave simulations. Reverse: The author and J. Harms digging a hole in the Homestake mine, South Dakota. Photo courtesy of Jaret Heise, Sanford lab. Printed in Amsterdam by Ipskamp Drukkers This work is part of the research program of the Foundation for Fundamental Research on Matter (FOM), which is part of The Netherlands Organisation for Scientific Research (NWO).

3 VRIJE UNIVERSITEIT Low-frequency sensitivity of next generation gravitational wave detectors ACADEMISCH PROEFSCHRIFT ter verkrijging van de graad Doctor aan de Vrije Universiteit Amsterdam, op gezag van de rector magnificus prof.dr. F.A. van der Duyn Schouten, in het openbaar te verdedigen ten overstaan van de promotiecommissie van de Faculteit der Exacte Wetenschappen op vrijdag 28 juni 2013 om uur in het auditorium van de universiteit, De Boelelaan 1105 door Mark Gerrit Beker geboren te Pretoria, Zuid Afrika

4 promotor: prof.dr. J.F.J. van den Brand copromotor: dr. H.J. Bulten

5 To my parents and big brother.

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7 Contents Introduction 1 1 Background and theory Gravity, general relativity and gravitational waves Ripples in space Observable effects of gravitational waves Sources of gravitational waves Supernova core collapse Compact binary coalescence Continuous waves Stochastic background Mathematical principles of seismic motion Theory of seismic waves Seismic correlation Linear control and the Kalman filter State space model State observation and the Kalman filter Linear quadratic regulator Gravitational wave detection Interferometric detection Interferometric principles i

8 Contents Limitations to sensitivity Advanced Virgo Design and optical layout Thermal compensation Angular alignment and control noise Sensitivity evolution Global detector network Einstein Telescope Design concept and sensitivity Noise budget Site and infrastructure Seismic noise Introduction Ambient seismic motion Seismic characterization studies Measurement procedure and data analysis Measurement sites Results from candidate sites Summary of seismic measurement results Virgo seismic correlation measurements Correlation measurements Correlation results and analysis Discussion Summary Newtonian noise Introduction Mathematical background Newtonian noise derivation for numerical analysis Surface detector models New methods for Newtonian noise modeling ii

9 Contents 4.4 Numerical ambient Rayleigh wave model Model description and method Analysis and results Newtonian noise and Advanced Virgo Finite element models Comparison with surface detector models Finite element simulations of local excitations Newtonian noise from local excitations Ambient Newtonian noise subtraction Wiener filter subtraction Newtonian noise subtraction results Discussion Summary Vibration isolation Vibration isolation for Advanced Virgo Vibration isolation with anti-spring technology The inverted pendulum The geometric anti-spring MultiSAS design Mechanical overview Sensors and actuators System modeling Vertical model Horizontal model System characterization Vertical transfer functions Magic wand performance Control system Coordinate system transformation and pre-filtering Actuator diagonalization iii

10 Contents Vertical control and the state observer Control performance Top stage horizontal control Vertical proportional integral derivative control Vertical linear quadratic gaussian control Comparative results Summary Valorization opportunities Introduction Sensor networks Seismic data surveying Current status Other applications MEMS accelerometers Low-noise optical readout Inertial sensor with interferometric readout Applications Vibration isolation Summary Conclusions, discussions and future work 183 A Seismic survey results 189 References 193 Summary 203 Samenvatting 209 Acknowledgements 215 iv

11 Introduction For millennia mankind has admired and studied the skies and in doing so has learned more and more about the nature of the cosmos. It led to the rejection of the Earth s central position in the Universe and the adoption of the heliocentric model in the 16 th century, placing the Sun at the center of the Universe. With the advent of the optical telescope early day astronomers could further refine their models and discover new planets and even their moons. Finally these developments led, in the 19 th century, to the notion that our Sun was not at the center of the Universe but one of billions of stars that make up the Milky Way. By the middle of the 1900s astronomy was experiencing a golden age thanks to a range of new technologies that expanded the observational scope beyond that of visible light. This included radio and infrared astronomy which provided whole new ways of observing the skies. Probing the entire spectrum of electromagnetic radiation, physicists continued to unravel the mysteries of the cosmos and our existence within it. Yet a number of fundamental questions still remain unanswered, these include: why is there an apparent asymmetry in the amount of matter and antimatter? What is the nature of dark energy and dark matter? What is the origin of the Universe and what will be its ultimate fate? Gravity plays a role the dynamics of all matter and energy. The most successful theory of gravity we have is general relativity. It predicts the motion of the planets, the deflection of light around the Sun and even governs the evolution of the entire Universe. This theory, published by Albert Einstein in 1915, describes gravity as the curvature of spacetime, and paved the way to the notion of gravitational waves: one of the last predictions of general relativity yet to be directly observed. Gravitational waves are minute ripples in the curvature of spacetime that are produced by violent astrophysical events. They propagate through space like the waves in a pond after a pebble is thrown onto its surface. Because the curvature of spacetime and gravity are interconnected, a gravitational wave will change the way freely falling objects interact with curved spacetime. We can therefore measure gravitational waves by accurately monitoring the motion of freely suspended test masses. This is done by using laser interferometers. The study of gravitational waves will open up a whole new window on the Universe and expose it in a way never seen before. This will enable us to test general relativity under the most 1

12 Introduction extreme conditions and develop a firmer understanding of the Universe and its origins. More importantly, entirely new discoveries and insights await us in this fledgling field of astronomy. We are on the verge of making the first direct detection of gravitational waves. The technology required to make such precision measurements has been under development for the last few decades and excellent sensitivity was demonstrated during the operation of the first generation of kilometer scale interferometric detectors: Virgo in Italy, LIGO in the USA and GEO600 in Germany. Currently these detectors are being upgraded to so-called second generation or advanced configurations, and the international network will be reinforced by new detectors in Japan (KAGRA) and India (LIGO-India). Advanced Virgo and Advanced LIGO will begin operation in with an ultimate sensitivity 10 times better than that of their first generation predecessors. Design studies are underway to develop concepts for future generation detectors that would improve on advanced detector sensitivity by another factor of ten and extend the detection bandwidth to even lower frequencies. Einstein Telescope is such a project that envisages a gravitational observatory capable of sensing spacetime disturbances from the furthest extremities of the Universe and the earliest moments of the Big Bang. To achieve the sensitivities needed to hunt for gravitational waves, detectors push the boundaries of our technological capabilities. This thesis describes a number of insights and technologies that will improve the low-frequency performance of advanced and future generation ground-based detectors. In the following, these will collectively be referred to as next generation detectors. An overview of detector generations, their approximate timelines and corresponding experiments, is given in Fig First generation Initial LIGO, Initial Virgo GEO600 Second generation Advanced LIGO, Advanced Virgo GEO-HF, KAGRA, LIGO-India Next generation Future generation Einstein Telescope,... LISA Pathfinder Pulsar timing arrays elisa, DECIGO Big Bang Observer Figure 1: Timeline and generations of ground and space based gravitational wave detectors. 2

13 Introduction Other projects are under development that would explore the lower frequency spectrum of gravitational radiation. One such project is elisa/ngo that proposes to place three satellites in triangular formation in orbit around the Sun, with the satellites separated by several million kilometers. The technology required for such a detector will first be piloted by LISA pathfinder, a single satellite test mission, due for launch in A similar project, but with a separation distance of one thousand kilometers, is the proposed Japanese gravitational space antenna DECIGO, while an elisa/nso successor has been proposed and is known as Big Bang Observer. In addition, astronomers accurately monitor the timing residuals of consistently pulsating stars. An array of so called radio pulsars is used to search for ultra low frequency gravitational waves. Thesis outline Chapter 1 provides a short introduction to general relativity and shows how the linearization of the Einstein field equations gives rise to gravitational waves. Furthermore, the various sources of gravitational radiation are addressed with an emphasis on the importance of low-frequency detection. This is followed by the mathematical description of two concepts that are relied on in subsequent chapters: seismic motion and linear control. The principles of gravitational wave detection are outlined in Chapter 2 with a more detailed account of the Advanced Virgo detector. The current status of all detectors across the globe is briefly discussed, followed by an outline of Einstein Telescope. Having established that seismic motion is a key factor in low-frequency sensitivity, Chapter 3 will discuss the various sources of seismic activity and presents an analysis of data from European seismometer arrays. This chapter also presents a site study performed in order to characterize underground motion in Europe and at various sites around the world. Chapter 4 provides an in depth discussion of Newtonian noise, a noise source connected to seismic motion and expected to limit the sensitivity of next generation detectors. New techniques for the modeling of Newtonian noise are presented along with an optimal filtering technique that promises efficient subtraction of Newtonian noise from the detector output. Chapter 5 then presents vibration attenuation systems designed to isolate parts of the Advanced Virgo detector from seismic induced vibrations. This chapter features a novel approach to the feedback control of such an isolation system. A number of technological solutions developed for the research discussed here, may find useful application in areas outside of gravitational astronomy. The opportunities for the commercialization of this technology are addressed in Chapter 6. Finally, Chapter 7 summarizes all ideas presented in this thesis and draws conclusions from the results. Ideas for future work and further development of the presented research will be given. 3

14 Introduction 4