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Searching for Gravitational Waves from Scorpius X-1 with a Cross- Correlation Method: from Mock Data to Advanced LIGO

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Searching for Gravitational Waves from Scorpius X-1 with a Cross- Correlation Method: from Mock Data to Advanced LIGO Rochester Institute of Technology RIT Scholar Works Theses 8-11-2017 Searching for Gravitational Waves from Scorpius X-1 with a Cross- correlation Method: from Mock Data to Advanced LIGO Yuanhao Zhang [email protected] Follow this and additional works at: https://scholarworks.rit.edu/theses Recommended Citation Zhang, Yuanhao, "Searching for Gravitational Waves from Scorpius X-1 with a Cross-correlation Method: from Mock Data to Advanced LIGO" (2017). Thesis. Rochester Institute of Technology. Accessed from This Dissertation is brought to you for free and open access by RIT Scholar Works. It has been accepted for inclusion in Theses by an authorized administrator of RIT Scholar Works. For more information, please contact [email protected]. Rochester Institute of Technology Ph.D. Dissertation Searching for Gravitational Waves from Scorpius X-1 with a Cross-correlation Method: from Mock Data to Advanced LIGO Author: Advisor: Yuanhao Zhang Dr. John T. Whelan A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Astrophysical Sciences and Technology in the College of Science, School of Physics and Astronomy August 11, 2017 Rochester Institute of Technology Ph.D. Dissertation Searching for Gravitational Waves from Scorpius X-1 with a Cross-correlation Method: from Mock Data to Advanced LIGO Author: Advisor: Yuanhao Zhang Dr. John T. Whelan A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Astrophysical Sciences and Technology in the College of Science, School of Physics and Astronomy Approved by Dr. Joel Kastner Date Director, Astrophysical Sciences and Technology Certificate of Approval Astrophysical Sciences and Technologies R I T College of Science · · Rochester, NY, USA The Ph.D. Dissertation of Yuanhao Zhang has been approved by the undersigned members of the dissertation committee as satisfactory for the degree of Doctor of Philosophy in Astrophysical Sciences and Technology. Dr. David S. Ross, Committee Chair Date Dr. John T. Whelan, Dissertation Advisor Date Dr. Joshua Faber Date Dr. Keith Riles Date To our ancestors. ABSTRACT Abstract Gravitational waves (GWs) are propagating ripples of space-time predicted by general relativity. 100 years after Albert Einstein published his theory of GR, the Laser Interferometer Gravitational- Wave Observatory (LIGO) found the first direct detection of GW in the first Advanced LIGO observing run. The GW signal known as GW150914 (Abbott et al., 2016), was the first of a series of binary black hole mergers observed by LIGO. These detections marked the beginning of gravitational-wave astronomy. The continuous wave (CW) signal emitted by fast spinning neutron stars (NSs) is an another interesting source for a detector like LIGO. The low-mass X-ray binary (LMXB) Scorpius X-1 (Sco X-1) is considered to be one of the most promising CW sources. With improving sensitivity of advanced detectors and improving methods, we are getting closer to being able to detect an astrophysically feasible GW signal from Sco X-1 in the coming few years. Searching for CWs from NSs of unknown phase evolution is computationally intensive. For a target with large uncertainty in its parameters such as Sco X-1, the fully coherent search is computa- tionally impractical, while faster algorithms have limited sensitivity. The cross-correlation method combines all data-pairs in a maximum time offset from same and different detectors coherently based on the signal model. We can adjust the maximum coherence time to trade off computing cost and sensitivity. The cross-correlation method is flexible and so far the most sensitive. In this dissertation I will present the implementation of Cross-correlation method for Sco X-1, its test on a Sco X-1 mock-data challenge (MDC) data set and the Advanced LIGO O1 observations. This search gave the best results in the Sco X-1 mock data challenge and recent LIGO Sco X-1 search. In the O1 run, the Cross-correlation search managed to improve the upper limit on GW strain strength from Sco X-1 closer than ever before to the level estimated from a torque balance argument. i CONTENTS Abstract i Declaration iv Acknowledgments v List of published work vii List of Tables ix List of Figures x Notation xii 1 Introduction 1 1.1 Gravitational Waves....................................2 1.1.1 General Relativity.................................2 1.1.2 Linearized Gravity.................................3 1.1.3 Gravitational-wave Sources............................ 15 1.1.4 Gravitational-wave Experiments......................... 16 1.2 Gravitational-wave Data Analysis............................. 19 1.2.1 Response to Interferometer............................ 19 1.2.2 Continuous Wave Signal Model.......................... 26 1.2.3 General Methods.................................. 28 1.2.4 Continuous Wave Searches............................ 29 1.3 Outline........................................... 33 2 CrossCorr Method 35 2.1 Methods........................................... 35 2.1.1 Cross-correlation.................................. 35 ii CONTENTS 2.1.2 Constructing the Cross-Correlation Statistic................... 43 2.2 Statistics and Sensitivity.................................. 56 2.2.1 Mean and variance of cross-correlation statistic................. 56 2.2.2 Impact of spectral leakage on estimated sensitivity............... 60 2.2.3 Sensitivity estimate for unknown amplitude parameters............ 63 2.2.4 SFT Length Limit for LMXB........................... 66 2.2.5 Parameter Metric Estimation........................... 74 2.2.6 Systematic Parameter Offset........................... 77 2.2.7 Parameter space metric.............................. 78 2.2.8 Lag Time Limit of Spin Wandering........................ 89 2.2.9 Probability distribution for cross-correlation statistic in Gaussian noise.... 96 3 Analysis of Mock Data 101 3.1 The Sco X-1 Mock Data Challenge............................ 101 3.2 Implementation for MDC................................. 105 3.2.1 Computing Cost Estimation............................ 105 3.2.2 Search Setups.................................... 106 3.3 MDC Results........................................ 111 3.3.1 Detection Significance............................... 111 3.3.2 Followup procedure................................ 117 3.3.3 Parameter Estimation............................... 119 3.3.4 Results and Comparison.............................. 128 3.4 MDC Conclusion...................................... 133 4 Advanced LIGO O1 Observation 135 4.1 Search Parameters..................................... 135 4.2 Observation Results.................................... 141 4.2.1 Followup of Candidates.............................. 141 4.2.2 Upper Limits.................................... 152 4.3 Outlook for Future Observations............................. 154 4.4 Details of the Upper Limit Method............................ 155 4.4.1 Idealized Bayesian Method............................ 155 4.4.2 Correction for Known Lines............................ 156 4.4.3 Empirical Adjustment from Software Injections................. 156 4.5 Results with Constrained Semimajor Axis........................ 160 5 Discussion 162 5.1 Summary.......................................... 162 5.2 Future Work........................................ 163 Bibliography 165 iii DECLARATION I, Yuanhao Zhang(\the Author"), declare that no part of this dissertation is substantially the same as any that has been submitted for a degree or diploma at the Rochester Institute of Tech- nology or any other University. I further declare that this work is my own. Those who have contributed scientific or other collaborative insights are fully credited in this dissertation, and all prior work upon which this dissertation builds is cited appropriately throughout the text. Fraction of Chapter2 was adapted from my coauthored paper Whelan et al.(2015). Chapter3 was adapted from my paper Zhang et al.(2017) in preparation. The results comparison and MDC information were adapted from my coauthored paper Messenger et al.(2015). Contents of Chapter4 is from the LVC paper The LIGO Scientific Collaboration and the Virgo Collaboration and Abbott, B. P. and Abbott, R. and Abbott, T. D. and Acernese, F. and Ackley, K. and Adams, C. and Adams, T. and Addesso, P. and et al.(2017), where I am an author of the collaboration paper. This dissertation was successfully defended in Rochester, NY, USA on July 11th, 2017. Chapter2 is based on the paper Whelan et al.(2015), entitled Model-based cross-correlation search for gravitational waves from Scorpius X-1 (2015, PRD, 91, 102005), authored by John T. Whelan (the Dissertation adviser), Santosh Sundaresan, Yuanhao Zhang (the author), and Prabath Peiris. Chapter4 is based on the paper The LIGO Scientific Collaboration and the Virgo Collab- oration and Abbott, B. P. and Abbott, R. and Abbott, T. D. and Acernese, F. and Ackley, K. and Adams, C. and Adams, T. and Addesso, P. and et al.(2017), entitled Upper Limits on Gravitational Waves from Scorpius X-1 from a Model-Based Cross-Correlation Search in Advanced LIGO Data (2017 submitted to APJ; arXiv: 1706.03119), authored by the LSC and LVC collaboration and D. Steeghs, L. Wang, including Yuanhao Zhang (the author) and John T. Whelan (the Dissertation adviser). iv ACKNOWLEDGMENTS It has been 5 year since I Joined Rochester Institute of Technology (RIT) Astrophysical Sciences and Technology (AST) family in 2012. I would like to
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