The Search for Gravitational Wave Bursts in Data from the Second LIGO Science Run

The search for gravitational wave bursts in data from the second LIGO science run Shourov Keith Chatterji S.B. Physics Massachusetts Instititute of Technology, 1995 S.B. Electrical Engineering Massachusetts Instititute of Technology, 1995 Submitted to the Department of Physics in partial fulfillment of the requirements for the degree of Doctor of Philosophy at tlie MASSACHUSETTS INSTITUTE OF TECHNOLOGY September 2005 @ Shourov Keith Chatterji, MMV. All rights reserved. The author hereby grants to MIT permission to reproduce and distribute publicly paper and electronic copies of this thesis document in whole or in part. /1 Ad--, 4 Author ..................................../b. - eb.... Department of Physics June 10, 2005 \ Certified by. ..........................w2 .......... .%. \ Erotokritos ~:dt=nid; Assistant Professor of Physics Thesis Supervisor. - Accepted by ........................ .- +~on2as~eytak Professo f Physics Associate Department Head for Education The search for gravitational wave bursts in data from the second LIGO science run by Shourov Keith Chatterji Submitted to the Department of Physics on June 10, 2005, in partial fulfillment of the requirements for the degree of Doctor of Philosophy Abstract The network of detectors comprising the Laser Interferometer Gravitational-wave Observatory (LIGO) are among a new generation of detectors that seek to make the first direct observation of gravitational waves. While providing strong support for the General Theory of Relativity, such observations will also permit new tests of physical theory in regions of strong space-time curvature and high matter-energy density. However, the observed signals are expected to occur near the limit of detector sensitivity. The problem of identifying such small signals is the primary focus of this work. This work presents a novel method for the identification of astrophysically unmodeled bursts of gravitational radiation in data from networks of interferometric detectors. The method is based on the Q transform, a multiresolution time-frequency transform that efficiently targets waveforms within a finite region of time, frequency, and Q space. The ]:nethod is also based on a modification of linear prediction that greatly simplifies the resulting statistical analysis by whitening interferometric detector data prior to Q transform analysis. Together, these techniques form the basis of a complete analysis pipeline that is equivalent to a template-based matched filter search for minimum uncertainty waveforms in the whitened data stream. This method is then applied to search for gravitational-wave bursts with duration less than 1 second and frequency content between 64 and 1024 Hz in coincident data from two detectors during second LIGO science run. Although no gravitational- wave bursts are identified, upper bounds are reported for the rate of gravitational- wave bursts as a function of signal strength for isotropic and galactic populations of sources with both abstract and astrophysically motivated waveform. The results indicate a maximum of 0.09 events per day at the 90% confidence level for bursts with characteristic strain amplitude in excess of to lo-'' strain HZ-'/~ depending on waveform. A comparison with previous searches demonstrates that this search is one of the most sensitive to date for gravitational-wave bursts of unknown waveform, and is inconsistent with recent indications for an statistical excess of events by the ROG collaboration at above the 99% confidence level. Thesis Supervisor: Erotokritos Katsavounidis Title: Assistant Professor of Physics Acknowledgements The completion of this work would not have been possible without the immeasurable support of a large number of people. The sensitivity of this analysis is a testament to the abilities of the many people involved in the design, commissioning, and operation of the LIGO detectors. It is primarily through their effort, in constructing what is arguably the most sensitive net,work of detectors to date, that this work is able to achieve the strictest upper bound on the rate of gravitational-wave bursts to date. I am also ind.ebted to the members of the LIGO Scientific Collaboration, in particular its Burst Analysis Group, for providing an excellent forum for the exchange of ideas, many of which have had a profound impact on this work. In particular. in the MIT LIGO Data Analysis Group, I have had the privilege to work with many extraordinarily talented people who have helped make this work possible. While I have appreciated the countless hours of discussion and assistance they have provided while this research was carried out, above all I have appreciated working in such an enjoyable group. In particular, I would like to thank Laura Cadonati, Katherine Rawlins, Lindy Blackburn, Michele Zanolin, Stefan Ballmer, Keith Bayer, and Marie Woods for their assistance. I look forward to continuing to work with them within the LIGO Scientific Collaboration. On my thesis committee, I was fortunate to have Deepto Chakrabarty and Scott Hughes. Through their careful reading and suggestions, the content, quality, focus and accessibility of this work was greatly improved. In addition, parts of this work have also benefited from careful reading by Patrick Sutton, Rej ean Dupuis, and Katherine Rawlins. I would also like to thank Rai Weiss, who introduced me to the challenge of high precision experimental physics, and who was also instrumental in bringing me into the MIT graduate physics program. I am particularly indebted to Stan Whitcomb and David Shoemaker, who kindly provided much needed support and encouragement during difficult times. The LIGO Laboratory is fortunate to have them. I have had the great privilege of pursuing this research under the guidance of my thesis adviser, Erik Katsavounidis. I cannot thank him enough for the opportunity, support, and guidance he has provided. It was with his arrival at MIT, and his development of a strong gravitational-wave data analysis group here, that I was able to find a research topic which lead to an interesting and challenging thesis project. Since then, he has gone out of his way many times to help ensure the success of this project. And, for that, I am extremely thankful. Finally, I would not have been able to accomplish this monumental task without the support of my family. All of them, particularly my wife Suzanne, have been a constant source of support, understanding, and encouragement throughout this very long process. And, for the last year and 9 months, my daughter Anna, with little effort, has provided more encouragement than she can possibly know. Now that this work is complete, I look forward to spending much more time with them. This work wits supported by the US National Science Foundation under Cooperative Agreement No. PHY-0107417. Contents 1 Introduction 2 Gravitational radiation 2.3 Sources ................................... 38 3 Burst detection 3.1 Parameterization of bursts ........................ 66 3.2 Measurement of bursts .......................... 73 3.3 Dett::ction of bursts ............................ 84 4 Linear E'rediction 4.1 Definition ................................. 92 4.2 Training .................................. 93 9 4.3 Properties ................................. 95 4.4 Application ................................ 98 4.5 Frequency response ............................ 99 4.6 Zero-phase filtering ............................ 102 4.7 Example .................................. 106 5 The Q Transform 5.1 The continuous Q transform ....................... 111 5.2 The discrete Q transform ......................... 113 5.3 Analysis window ............................. 117 5.4 Normalization ............................... 122 5.5 Statistics .................................. 138 5.6 Identification of events .......................... 155 5.7 The Q pipeline .............................. 157 5.8 The coherent Q pipeline ......................... 161 5.9 Example .................................. 167 6 Simulation 6.1 Well localized bursts 6.2 Stationary white noise .......................... 177 6.3 Simulated detector noise ......................... 186 7 All sky search 195 7.1 Data selection ............................... 197 7.2 Analysis pipeline ............................. 202 7.3 Event rates ................................ 205 7.4 Can.didate events ............................. 213 7.5 Statistical analysis ............................ 234 7.6 Detection efficiencies ........................... 237 7.7 Systematic errors ............................. 245 7.8 Upper limits ................................ 246 7.9 Comparison of results ........................... 251 8 Conclusion 8.1 Summary ................................. 268 8.2 Future investigations ........................... 273 Bibliography Chapter 1 Introduction Gravita,tiona,l waves are linear perturbations of space and time, caused by the mo- tion of matter, that travel outward through the universe at the speed of light. The existence of gravitational waves follows as a direct consequence of Einstein's General Theory of Relativity. As a result, the direct detection of their interaction with matter would constitute an important confirmation of theory. There is alrefady strong indirect evidence in support of the existence of gravitational waves. Pulsatr timing observations of the relativistic binary system PSR 1913+16 by Hulse, Taylor, and colleagues indicate that the orbit of the system is decaying at a rate that is in very good agreement

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