A SEARCH FOR ASTRONOMICAL GRAVITATIONAL RADIATION WITH AN INTERFEROMETRIC BROAD BAND ANTENNA by DANIEL DEWEY B.S., Massachusetts Institute of Technology (1979) SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY IN PHYSICS at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY February, 1986 @ Massachusetts Institute of Technology 1986 Signature redacted Signature of Author .. .. .. ,w . - ... epartment of Physics Signature redacted January 17, 1986 Certified by . v . ....... ..... Rainer Weiss Thesis Supervisor redacted AcceptedAcce by..........Signature tedby.. g .- n . \. .. /. , -. .x . George Koster Chairman, Department Committee FEB 1 4 198& Archive'1 A SEARCH FOR ASTRONOMICAL GRAVITATIONAL RADIATION WITH AN INTERFEROMETRIC BROAD BAND ANTENNA by DANIEL DEWEY Submitted to the Department of Physics on January 17, 1986 in partial fulfillment of the requirements for the Degree of Doctor of Philosophy in Physics ABSTRACT This thesis describes and implements a data analysis scheme designed to detect short, burst-like gravity waves in the output of the interferometric antennas. This represents a first attempt at integrating the astrophysical predictions of expected waveshapes with a data analysis scheme for their detection. An experimental program was carried out involving the construction of a proto- type gravitational radiation antenna, the diagnosis of some of its noise sources, the study of expected astronomical sources of radiation, and the collection and analysis of data from the instrument. Construction included the implementation of a system to damp the motions of the test masses, the design of a servo system to hold the interferometer to a dark fringe and the assembly of a microcomputer-A/D system to record data and instrument parameters. Diagnosis of noise sources identified noise due to scattered light as a problem, and methods to suppress this noise through external phase modulation of the input laser beam were devised and implemented. The results of the analysis are encouraging from an instrument performance perspective; the noise obeys Gaussian statistics to signal-to-noise ratios of 5.5, and the number of events in the non-Gaussian tail is not excessive, ~ 500 per day. As a detector of gravity waves, the sensitivity of the prototype is very low due to its size, remaining noise sources, and low light power. Detected burst events with amplitudes of ho ~ 5 x 10- 4 correspond to the signal expected from an optimisti- cally large source at the distance of Proxima Centauri, the closest star beyond our Sun. Thesis Supervisor: Dr. Rainer Weiss Title: Professor of Physics -2- Scientific Acknowledgments This work is greatly indebted to Prof. Rainer Weiss for both its scientific content and flavor. A project of this size is the work of many people and this work owes much to each of them. In June of 1985, the MIT gravity group consisted of Rai Weiss, Paul Linsay, Peter Saulson, Andrew Jeffries, Jeff Livas and Richard Benford, with past member David Shoemaker. Specifics of the division of labor are given at the end of the Introduction. Thanks to Steve Meyer for introducing noise into my work. Paul Linsay introduced and addicted me to servo systems. It was a pleasure to share the intensive week of data taking with Jeff Livas and the egg timer. Thanks also to Andrew Jeffries for several days and nights of helpful organization during this period-lots of orange juice. Interactions with the MPQ Garching group has been a source of pleasure and scientific advance. The task of putting together this thesis was made infinitely easier and more satisfying through pretty plot programs and TEX, both due to Ed Cheng. Thanks to David Shoemaker for a crash course in TEX. Nearly as essential were the XEROX machine and two wonderful Rapidograph pens. Thanks to Ed Cheng, David Shoemaker and Claude Canizares for proof reading this thesis. All errors, however, are the author's. This work supported through NSF grant PHY 8109581. -3- Personal Acknowledgments Graduate studies and research can be hazardous to both body and mind. To all who have added joy, from the passing smiling stranger to the closest of friends, I acknowledge my debt and offer my thanks. In particular, the early years of graduate study were positively fun thanks to Luz Martinez-Miranda, Steve Evangelides, Mehran Kardar, Bruce McClain, and Mary-Lou Powers. The warm, friendly atmosphere of the Ashdown House Coffee Hours, under the care of Prof. and Mrs. Hulsizer, contributed immensely to the enjoyment of these years. Very special thanks to Chris for many shared years of love. Thanks to all in "the lab" for the sense of community and the knowledge that they're always there. Special thanks to Richard Benford for providing much of this lab spirit and overlooking gross incompetence in the machine shop. Thanks to Kathreen Gimbrere, a.k.a. "the neighborhood pest", for several fun evenings when they were needed most. Lyman Page aided in the writing of this thesis by making periodic visits to the author's office, instilling humor, confidence and determination. The "extended family" provided by Steve Meyer, Sharon Salveter, and Ed Cheng provided essential and appreciated support during the writing of this the- sis. Special thanks to Ed for an altogether not unpleasurable living arrangement, including habitually "yummy" meals and leftovers. Tony Patera provided his hard-boiled egg recipe and many crazy ideas that have pleasantly punctuated the past ten years. Thanks to Mehran for the five thousand six hundred and sixteen sweaty games of squash, and as many locker room conversations, which kept the body in shape and saved the mind from many an abyss. A smiling wink to David Shoemaker, who introduced me to homemade pasta, cloth napkins, dBs and BDs, the fun of working together, carburetors, the "slap" bass, black jeans, the National Audio-Radio Handbook, Italy, the END DO, empty letters, and most recently TEX. Thank you, David. The love and faith of my family has sustained me for the past 28 years. A heartfelt thanks to Dan, Jean, Tim, Bill, John and Kate. -4- TO MY GRANDPARENTS Daniel and Georgia Gray Dewey William and Jean Long Moyles - 5- Table of Contents 1 Introduction 10 2 Theory of Gravity Waves 18 2.1 Introduction 18 2.2 Propogation and Polarization of Gravity Waves 18 2.3 Generation of Gravity Waves 20 2.4 Detection of Gravity Waves 21 2.4.1 Resonant ("Bar") Antenna Operation 21 2.4.2 Free-mass ("Interferometric") Antenna Operation 22 2.4.3 Comparison of Antenna Sensitivities to Burst Sources 23 3 Astrophysical Sources 24 3.1 Introduction 24 3.2 System of Units 24 3.3 Detectability of Burst Events 25 3.4 Particle-Blackhole Events 26 3.5 Stellar Collapse Events 28 3.6 Chirp Events 29 3.6.1 Chirp Source Waveforms and Detectability 30 4 The Instrument 33 4.1 Introduction 33 4.2 Mechanical 33 4.3 A Walk through the Optical Components 36 4.3.1 Laser 36 4.3.2 External Phase Modulator 36 4.3.3 Fiber 37 4.3.4 Central Mass 38 4.3.5 Delay Lines 38 4.3.6 Photodetectors 40 4.4 Electronic Systems 40 4.4.1 Mass Damping System 40 4.4.2 Fringe Servo System 41 4.4.3 Monitoring and Data taking 41 5 Noise Sources and the Prototype Noise Performance 42 5.1 Noise Sources 42 5.2 Prototype Noise Performance 42 5.2.1 Shot Noise 44 5.2.2 Electronic Noise 45 -6- 5.2.3 Laser Amplitude Noise 45 5.2.4 Seismic and Acoustic Noise 46 5.2.5 Scattered Light Noise 47 5.2.6 Laser Frequency Noise 50 5.2.7 Thermal Noise 51 5.2.8 Beam Jitter 53 5.2.9 E/M Fields 54 6 Data Analysis Scheme 55 6.1 Introduction 55 6.2 The Matched Filter 55 6.2.1 Signal to Noise Ratio (SNR) 56 6.2.2 Pulse Height Distribution (PHD) 57 6.3 Practical Considerations 60 6.3.1 Sample Rate and the White Assumption 60 6.3.2 The Effect of Mismatched Templates 60 6.3.3 Multiple Detections 61 6.4 A Set of Templates 62 6.4.1 The N 1 , No, NHC Templates 62 6.4.2 Choosing a Subset of the Templates 63 6.4.3 Implementation 64 7 The Data Taking Run and its Analysis 66 7.1 The Run 66 7.2 Analyzing the Data 66 7.2.1 Introduction and Overview 66 7.2.2 The HKP and PHD files 68 7.2.3 Data Synthesis 84 7.2.4 Windows and the Final Data Set 84 7.2.5 Final PHDs and a List of Events 87 7.3 Examination of the Events 94 7.3.1 Template "102" Events 94 7.3.2 Other Events 97 8 Discussion of the Results 106 8.1 An Instrument Performance Perspective 106 8.2 An Astrophysical Perspective 106 8.3 Conclusions 108 References 111 -7- Appendices A Quadrupole Radiation from Masses in a Circular Orbit 116 B Thermal Limit for a Bar Antenna 117 C Interferometer Response 118 D Comparison of Bar and Interferometer Response to GW Bursts 120 D.1 The Canonical Form of a Burst of Gravitational Radiation 120 D.2 Interferometer Response 120 D.3 Bar Response 121 D.4 Comparing Bar and Interferometer 122 D.5 Comparison for an Arbitrary Wave Shape 123 D.6 Discussion 123 E Mass Damping System 130 E.1 Overview 130 E.1.1 The Sensing Capacitor Plates 133 E.1.2 The HV Drive Plates 133 E.2 Capacitive Displacement Transducer 136 E.2.1 The Capacitance Bridge 138 E.2.2 The Mixer 140 E.2.3 Transfer Functions from x to VCMO and VCMON 141 E.3 Equations of Motion 144 E.3.1 Exact Damping Equations and the Root-Locus 146 E.4 Damping System Noise 148 E.5 Parameter Trade-offs 151 F The RF Modulation/Demodulation Scheme and its Noise Sources 152 F.1 Overview 152 F.2 The Modulation/Demodulation Scheme 152 F.3 Noise Terms 155 F.3.1 Shot Noise 155 F.3.2 Thermal and Mixer Noise 156 F.3.3 RF Amplitude Noise 157 F.3.4 The Total Noise vs.