Search for Gravitational Waves from a nearby neutron star using barycentric resampling Thesis by Pinkesh K. Patel In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy California Institute of Technology Pasadena, California 2010 (Defended Aug 26, 2010) ii c 2010 Pinkesh K. Patel All rights Reserved iii To my Mum and Dad... iv Preface The work presented in this thesis was carried out within the LIGO Scientic Col- laboration (LSC). The methods and results presented here are under review and are potentially subject to change. The opinions expressed here are those of the author and not necessarily those of the LSC. The author gratefully acknowledges the support of the United States National Science Foundation for the construction and operation of the LIGO Laboratory, which provided support for this work. v Acknowledgements It is the memories that remain with you, even after one can’t remember the exact moment, the faces of the people involved or even the year in which they happened. How does one thank all the people involved in creating all the wonderful memories I have had in the past five years? If I miss someone, know that I will remember all the sweet or sour memories that I have shared with you. Sour memories also have their place and make me the person I am. So thank you all the people who thought they were unkind to me or said things I didnt want to hear. You also shaped me, just as much as the people I hold dear. I would like to start by thanking the California Institute of Technology, lov- ingly known as Caltech. It is the best university on the planet. Caltech and its staff are exemplary and I cannot thank them enough. The only sad part about graduating is that I will be leaving Caltech. I will miss its Millikan pond, its sci- entifically minded grafitti, its wonderful easy-going attitude and its efficient and always smiling secretaries among other things. Alan Weinstein is the best advisor that I could have hoped for. He has given me all the freedom that even a postdoc may not hope to have. He has been a wonderful critic of my work and has always had my best interest in heart. He has stood by me when needed and fought for me (he has the blows to show for it). He has stayed up at 5 AM to hear me present in Europe, and has read every word that I have written. Thank you Alan. The LIGO Scientific Collaboration has been a source of wonderful mentors to me. I would like to thank the Continuous Waves working group and the staff at LIGO Hanford for all their efforts in making me a scientist. Three people besides Alan stand out in mentoring me - Rejean Dupuis, Xavier Siemens and Joseph Betzweiser. Thank you guys, you have helped me learn a lot of tricks and made me a better person. I especially remember the day after a customary CW telecon, in which I goofed up something and got scolded by Rejean and Xavier sitting on the bridge of the Millikan pond. Or the night at which I called Joe, thinking that vi I had a detection and a ticket to Stockholm for Rai Weiss. I would like to thank Xavier Siemens, David Hitlin, Christopher Hirata and Curt Cutler for serving as my thesis committee. I have been fortunate to have had some fantastic friends over the past five years. Some of the memories that stand out in my mind are midnight arguments with Devdutt, Setu and Naresh, my first year roommates; going snowboarding with Evan and Berit; driving to glacier national park with Justin and Adam; playing settlers with Jake and Phil; sliding on a trashbin can down the Philadelphia Museum of Art steps with Nachiket; the council “jokes” with Krish and Sujit; filming the Oasis movie with Vikram, Shankar, Chaitanya and Tejaswi; playing mafia with Setu, Mansi, Prabha, Uday, Teja and Mayank; cooking with Harmony, JC and all my roommates. All of these and more memories will remain with me. I thank all my friends for the wonderful times that we have all had. Vaibhav and Sonali have been the elder brother and sister that I have never had. Vaibhav has made me laugh more than anyone else and if I follow only a fraction of all the advise he has given me over the years, I will be wildly successful. Sonali has been a moral compass of sorts and the funnest person to be with. Zeesh has been the perfect companion on my journey through Caltech. He and I studied together for the qualifiers, shared a house for two years and have had numerous good times. Varun has been my partner in crime at Caltech. He has been a close confidant and a stress release valve. I have had a lot of fun going to different national parks and generally driving around with Naresh and Shriharsh. I would also thank Sowmya and Vijay for always being there for me and for all the times that we have cooked together. Last, but by no means least, I would like to thank my parents, Kirit Patel and Jayshree Patel. They are the ones I aspire towards and idolize. My father and mother both came from a poor family and made a name for themselves through hard work and dedication and I can only hope to emulate them. They have en- couraged me to do whatever I want and have been the best friends I have had. I hope our friendship lasts a long time. vii Search for Gravitational Waves from a nearby neutron star using barycentric resampling by Pinkesh K. Patel In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy Abstract Rapidly spinning neutron stars in our Galactic neighborhood are promising sources of quasi-monochromatic continuous gravitational waves observable by the current LIGO detectors. I describe a search done on the LIGO S5 data, looking for an isolated neutron star hypothesized to be at a distance of about 100 parsecs. This kind of search is computationally bound and is made possible by the implemen- tation of barycentric resampling, which is described here as well. I also describe the work done at the Hanford LIGO site, while taking data for the Astrowatch program. viii Contents 1 Thesis overview and introduction to Gravitational Waves 2 1.1 General Relativity and Gravitational Waves . ... 3 1.2 Gravitational Wave Sources . 6 1.2.1 Compact Binary Coalescences . 7 1.2.2 Bursts.............................. 8 1.2.3 StochasticBackground. 9 1.2.4 Continuous Waves . 10 2 LIGO Detectors and their Operation 11 2.1 LIGOoverview ............................. 11 2.1.1 Michelson Interferometers . 14 2.1.2 Fabry-Perot Cavities . 15 2.2 LIGOsubsystems............................ 18 2.2.1 Pre-Stabilized Laser . 18 2.2.2 SuspensionSystem . 18 2.2.3 Length Sensing and Control . 20 2.2.4 Angular Sensing and Control . 21 2.2.5 Thermal Compensation System . 21 2.3 Astrowatch ............................... 22 2.3.1 Astrowatch highlights . 23 2.3.2 AcousticTuning ........................ 24 2.3.3 SGR search data quality . 25 ix 3 Sources of continuous gravitational waves 30 3.1 Introduction............................... 30 3.2 NeutronStars.............................. 31 3.3 Pulsars.................................. 32 3.3.1 Pulsar emission and ages . 35 3.4 Compositionofneutronstars . 41 3.5 MechanismsofEmission . 43 3.5.1 Non-axisymmetric mass tensor . 43 3.5.2 Non-axisymmetric oscillations . 47 3.5.3 Torque-freePrecession . 50 3.5.4 Accretion ............................ 50 4 Finding weak quasi-periodic signals in noisy broadband data 53 4.1 Introduction............................... 53 4.2 Summary of searches for continuous gravitational waves with LIGO data ................................... 54 4.2.1 Knownpulsarsearches. 54 4.2.2 All-skysearches. .. .. .. .. .. .. .. 55 4.2.3 Searches for suspected neutron stars . 57 4.2.4 Binarysystems ......................... 58 4.2.5 Searches directed at a region of the sky . 59 4.3 Coherenttechniques .......................... 59 4.3.1 Frequentist framework . 61 4.3.2 Bayesian framework . 63 4.3.3 Template bank scalings . 65 4.4 Semi-coherenttechniques . 67 5 Implementation of Barycentric Resampling 70 5.1 Preliminaries .............................. 70 5.2 Implementation of barycentric resampling . 74 5.2.1 TimeDomainAnalysis. 75 x 5.2.2 Frequency Domain Analysis . 80 5.3 Results.................................. 88 5.3.1 Speed .............................. 88 5.3.2 Validations ........................... 91 5.4 PracticalConsiderations . 92 5.4.1 Discreteness........................... 92 5.4.2 InterpolationIssue . 93 5.5 Summaryandconclusions . 96 6 Introduction to Calvera 99 6.1 Overview ................................ 99 6.1.1 Observable properties and classification of neutron stars . 99 6.2 Calvera ................................. 103 6.2.1 Observations .......................... 103 6.2.2 ClassifyingCalvera. 104 6.2.3 Properties of Calvera . 107 7 Search for GWs from Calvera 108 7.1 Introduction............................... 108 7.1.1 Possibility of a search . 108 7.1.2 Parameter Selection . 110 7.1.3 Searchpipeline . .. .. .. .. .. .. .. 114 7.2 Probabilities and False Alarm Rates . 117 7.3 Vetoes .................................. 119 7.3.1 KnownLines .......................... 119 7.3.2 Kolmogorov-Smirnov Test Statistic . 120 7.4 SearchResults ............................. 125 7.5 Followup ................................ 130 7.5.1 Criteria for Follow up . 130 7.6 UpperLimitCalculation. 135 7.6.1 Theoretical Predictions . 135 xi 7.6.2 Injections ............................ 140 8 Conclusions 141 xii List of Figures 1.1 The effect of a gravitational wave consisting of only one of the two polarizations “+” and “ ” on a ring of particles. The lines are × just a guide to the eye. The GW would be passing perpendicularly through the page and the figure shows snapshots in time as the wave passes. It shows one whole wavelength for each polarization....