Black hole binaries in our Galaxy: Understanding their population and rapid X-ray variability by Kavitha Arur, M.Phys, M.Sc A Dissertation In Physics Submitted to the Graduate Faculty of Texas Tech University in Partial Fulfillment of the Requirements for the Degree of DOCTOR OF PHILOSOPHY Approved Thomas J. Maccarone Chairperson of the Committee Benjamin Owen Simone Scaringi James F. Steiner Beth Thacker Mark Sheridan Dean of the Graduate School May 2020 c 2020, Kavitha Arur Texas Tech University, Kavitha Arur, May 2020 ACKNOWLEDGMENTS First I would like to thank my advisor, Prof. Tom Maccarone for the many years of support and encouragement, especially when it came to voicing my ideas. Thank you for teaching me so much, and for always believing in me. I could not have asked for a better mentor! I would also like to thank my committee members for participating in my defense and approving this dissertation. This work would not have been possible without the extensive HEASARC data archives, the Astrophysics Database System (ADS), arxiv.org, endless cups of tea and Stackoverflow who have helped me and many other PhD students get their research done. I am also incredibly grateful to the wider X-ray astronomy com- munity, who have been incredibly encouraging throughout my PhD. I also want to thank Adam, Phil and Jack for all their help during the job application process. Coming to TTU has been one of the best decisions I have made, and this is largely because of the wonderful people I have met. A huge thank you to Chris Britt, Paul Sell, Denija Crnojevic, Lennart van Haaften, Michael Holcomb, Rob Coyne, Ra Inta, Liliana Rivera Sandoval, Dario Carbone, Robert Morehead and Anna McLeod for always cheering me on, and always being willing to help me out. An extra spe- cial thank you to the most amazing group of ladies (Denija, Bonnie, Beth, Kris Coyne, Kristen Holcomb, Jess, Pam, Lili, Anna, Nipuni) who kept me going even when things were hard. Thanks for all the laughs, hugs, advice and chocolate. You guys are the best! I also want to thank Manuel, Deven, JP, Matteo, Arvind, Binod, and everyone else in this amazing TTU group - thank you for making Lubbock truly feel like home during these PhD years. I also have to mention the various D&D groups (both in Lubbock and in the UK) that I am fortunate to have been a part of - thank you for all the amazing memories and for keeping me entertained and sane! ii Texas Tech University, Kavitha Arur, May 2020 Huge thanks to my parents, grandparents and other family members for their endless support. Thanks also to Lavanya, Abishek, Samiksha, Sindhuja and Sarah for keeping in touch and cheering me on from thousands of miles away. I would also like to express my gratitude to my fellow TANASTRO members, who have always encouraged me to study the stars. And finally, thank you Paul for your endless love and support. I am so glad that we are a team, and that we could do this together. iii Texas Tech University, Kavitha Arur, May 2020 STATEMENT OF WORK Chapters 2,3 and 4 of this dissertation have been published in the Monthly No- tices of the Royal Astronomical Society as articles co-authored by Kavitha Arur and Thomas Maccarone. Thomas Maccarone and Kavitha Arur worked together to define the scope of the project and on the interpretation of the results. Kavitha Arur performed the data analysis and wrote up the results, with comments from Thomas Maccarone. iv Texas Tech University, Kavitha Arur, May 2020 TABLE OF CONTENTS Acknowledgments . ii Statement of work . iv Abstract . ix List of Figures . xi 1. Introduction ..................................1 1.1 Black Hole X-ray Binaries . .1 1.2 Population of BHXBs . .3 1.3 Properties of BHXBs . .5 1.3.1 Spectral Properties . .5 1.3.2 Timing Properties . 10 1.4 Quasi-Periodic Oscillations . 11 1.4.1 QPO Models . 12 1.5 Non-linear Variability . 14 1.6 Higher Order Statistics . 15 1.6.1 Bispectrum . 16 1.6.2 Biphase . 16 1.6.3 Bicoherence . 17 1.6.4 Calculating the bicoherence . 19 1.7 RXTE . 20 1.8 Outline of this dissertation . 21 2. Selection Effects on the Orbital Period Distribution of Low Mass Black Hole X-ray Binaries ........................ 22 2.1 Abstract . 22 2.2 Introduction . 22 2.3 Data set and correction of selection effects . 25 2.3.1 Galaxy model and data set . 25 2.3.2 Extinction of Optical Counterpart . 26 2.3.3 Detection of the X-ray outburst . 27 2.3.4 Probability of outburst detection . 27 v Texas Tech University, Kavitha Arur, May 2020 2.3.5 Implied Orbital Period Distribution using Observational Data . 31 2.4 Monte Carlo Simulation . 33 2.4.1 Generation of simulated sources . 33 2.4.2 Optical counterpart detection . 35 2.4.3 Probability of an X-ray outburst and its detection . 36 2.4.4 Implied Orbital Period Distribution using Simulated Data 36 2.4.5 Effect of mass transfer on the companion . 36 2.5 Discussion . 38 2.6 Conclusions . 41 3. Nonlinear Variability of Quasi-Periodic Oscillations in GX 339-4 ... 42 3.1 Abstract . 42 3.2 Introduction . 42 3.3 Bicoherence . 44 3.4 Data Overview . 45 3.4.1 QPO Classification . 46 3.5 Results . 46 3.5.1 Bicoherence Patterns . 46 3.5.1.1 The ‘hypotenuse’ pattern . 47 3.5.1.2 The ‘web’ pattern . 47 3.5.2 Type B QPOs . 48 3.5.3 Type A QPOs . 49 3.5.4 Evolution during state transition . 51 3.5.5 Reconstructing the QPO waveforms . 54 3.6 Discussion . 56 3.6.1 Physical Interpretation . 56 3.6.1.1 Is this a reasonable value for τ?............ 59 3.7 Conclusions . 60 4. A Likely Inclination Dependence in the Non-linear Variability of Quasi Periodic Oscillations from Black Hole Binaries ....... 61 4.1 Abstract . 61 4.2 Introduction . 61 vi Texas Tech University, Kavitha Arur, May 2020 4.3 Statistical Methods . 63 4.3.1 Bicoherence . 63 4.3.2 Biphase . 64 4.4 Observations and Data Reduction . 65 4.4.1 Data Sample . 65 4.4.2 Data Reduction and Analysis . 66 4.5 Results . 67 4.5.1 Bicoherence Patterns . 67 4.5.1.1 Hypotenuse . 67 4.5.1.2 Cross . 67 4.5.1.3 Web . 68 4.5.2 Evolution of type C QPOs . 69 4.5.2.1 Low inclination sources . 69 4.5.2.2 High inclination sources . 71 4.5.2.3 Hardening phase of the outburst . 71 4.5.2.4 Intermediate inclination sources . 73 4.5.2.5 Quantifying the inclination dependence . 75 4.5.3 Statistical Significance . 75 4.5.4 Type B QPOs . 77 4.6 Discussion . 77 4.6.1 Low inclination . 77 4.6.2 High inclination . 79 4.6.3 Variation of the optical depth with QPO phase . 80 4.6.4 Optical depth and geometry of the corona . 82 4.6.5 Caveats . 84 4.7 Conclusions . 85 5. Summary and Outlook ............................ 87 5.1 Summary . 87 5.2 Future Work . 89 5.2.1 Black Holes . 89 5.2.2 Neutron stars . 91 5.2.3 Cataclysmic variables . 93 vii Texas Tech University, Kavitha Arur, May 2020 5.2.4 Active Galactic Nuclei . 95 5.2.5 Three wave interactions in the solar wind . 96 5.2.6 Stochastic Gravitational Wave Background . 97 5.3 Current and Future Missions . 97 5.3.1 NICER . 97 5.3.2 STROBE-X . 98 5.3.3 eXTP . 99 5.4 Concluding remarks . 100 Appendix A. Details of Observations Analysed in Chapter 3 ....... 135 Appendix B. Details of Observations Analysed in Chapter 4 ....... 138 Appendix C. Duffing Oscillator ........................ 157 viii Texas Tech University, Kavitha Arur, May 2020 ABSTRACT One of the fundamental problems in the field of high energy astrophysics is con- straining the formation and evolution of compact objects such as black holes and neutron stars in binary systems. The physics of accretion onto compact objects has profound impacts on our understanding of processes such as mergers of binary compact objects, production of type Ia supernovae and the formation of millisec- ond pulsars. On larger scales, the structure and star formation properties of galax- ies can be influenced by accretion onto super-massive black holes. Progress in this field requires both a global study of the X-ray binaries as a population, as well as detailed characterization of individual systems. Population synthesis models predict thousands of black hole binaries in our Galaxy. However, only ∼20 such objects have been confirmed. One potential ex- planation for this discrepancy is the presence of observational biases that prevent a large fraction of these objects from being detected. The work presented in this dis- sertation shows that these selection effects can account for a signification portion of black hole binaries, especially those with short orbital periods, being undetected. Despite these promising results, large uncertainties still exist in our knowledge of the Galactic binary population as details of the accretion physics that govern binary evolution are still not well understood. Studies of rapid X-ray variability provide an excellent method of probing the ge- ometry and the physical processes that dominate in the accretion disks, especially close to the central black hole. In order to properly interpret the observed vari- ability, sophisticated timing analysis techniques are needed. In this dissertation, I present the first systematic analysis of a novel higher order timing analysis tech- nique known as the bispectrum, to understand rapid X-ray variability from black hole binaries.