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Accreting Neutron Stars and Black Holes Zhuqing Wang Department of Physics

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Accreting Neutron Stars and Black Holes Zhuqing Wang Department of Physics Accreting Neutron Stars and Black Holes by Zhuqing Wang Thesis Submitted to the University of Warwick for the degree of Doctor of Philosophy Department of Physics May 2018 “A journey is a person in itself; no two are alike. And all plans, safeguards, policies and coercion are fruitless. We find after years of struggle that we do not take a trip; a trip takes us.” John Steinbeck i Contents List of Tables v List of Figures vi Acknowledgments x Declarations xi Abstract xii Abbreviations xiii Chapter 1 Introduction 1 1.1 Binaries .................................... 2 1.1.1 Roche geometry ........................... 2 1.1.2 Binary evolution ........................... 4 1.1.3 Accretion discs ............................ 6 1.2 Low-mass X-ray binaries ........................... 9 1.2.1 X-ray transients ............................ 10 1.2.2 Neutron stars in low-mass X-ray binaries .............. 10 1.2.3 Millisecond pulsars .......................... 12 1.2.4 Black hole candidates ........................ 15 1.2.5 Dynamical mass measurements ................... 18 1.3 The Bowen fluorescence technique ...................... 20 1.3.1 Detection of the mass donor in Sco X-1 ............... 20 1.3.2 Parameter constraints via the donor signature ............ 21 1.3.3 The Bowen survey .......................... 23 1.4 Gravitational waves .............................. 25 1.5 Goals of this study .............................. 26 ii Chapter 2 Methods 29 2.1 Data analysis ................................. 29 2.1.1 Radial velocity technique ....................... 29 2.1.2 Doppler tomography ......................... 31 2.1.3 Axioms of Doppler Tomography ................... 35 2.1.4 A tomography-based method ..................... 36 2.2 Method development ............................. 41 2.2.1 The Bootstrap test .......................... 41 2.2.2 Bowen diagnostic diagram ...................... 47 2.2.3 Monte-Carlo binary parameter calculations ............. 48 Chapter 3 Bowen survey 51 3.1 4U 1636 536 (=V801 Ara) and 4U 1735 444 (=V926 Sco) ........ 51 − − 3.1.1 Source data .............................. 54 3.1.2 Analysis ............................... 54 3.1.3 Determination of system parameters ................. 59 3.2 4U 1254 69 (=GR Mus) ........................... 67 − 3.2.1 Source data .............................. 68 3.2.2 Analysis ............................... 68 3.2.3 Determination of system parameters ................. 70 3.3 Aql X-1 .................................... 71 3.3.1 Source data .............................. 75 3.3.2 Gaussian fitting ............................ 76 3.3.3 Doppler mapping ........................... 76 3.3.4 Opening angle of the accretion disc ................. 79 3.4 X1822-371 .................................. 80 3.4.1 Introduction .............................. 80 3.4.2 Analysis ............................... 81 3.4.3 Future plan .............................. 83 Chapter 4 XTE J1814-338 86 4.1 Introduction .................................. 86 4.2 Observations and data reduction ....................... 87 4.3 Average spectrum and orbital variability ................... 88 4.4 Radial velocities and the systemic velocity .................. 89 4.5 Analysis .................................... 90 4.5.1 Doppler mapping ........................... 90 4.5.2 Bootstrap Monte-Carlo ........................ 93 iii 4.5.3 The Bowen blend diagnostic ..................... 95 4.6 Discussion ................................... 97 4.6.1 The K-correction ........................... 97 4.6.2 Binary parameter estimation ..................... 99 4.6.3 The nature of the companion .....................105 4.6.4 A hidden ‘redback’? .........................106 Chapter 5 Sco X-1 108 5.1 Introduction ..................................108 5.2 Source data and RV determination ......................109 5.3 Determination of observables .........................110 5.3.1 Circular orbit fit ...........................111 5.3.2 Doppler tomography-based method .................112 5.4 Estimation of binary parameters .......................117 5.4.1 The K-correction ...........................118 5.4.2 Monte-Carlo analysis .........................121 5.4.3 The eccentricity problem .......................125 5.5 Conclusions ..................................126 Chapter 6 Conclusions and future work 129 6.1 Summary of the method ............................129 6.2 Persistent systems ...............................132 6.3 Transients ...................................133 6.4 Future work ..................................134 Appendix A Sco X-1 radial velocity data 137 Appendix B Irradiation modelling 146 iv List of Tables 1.1 A list of observed optically bright, active low-mass X-ray binaries ..... 24 3.1 Observations of V801 Ara and V926 Sco .................. 54 3.2 Revised system parameters for V801 Ara and V926 Sco ........... 64 3.3 Optical observations of GR Mus ....................... 68 3.4 Revised system parameters for GR Mus ................... 75 3.5 System parameters for Aql X-1 ........................ 80 4.1 XTE J1814-338 emission line parameters .................. 88 4.2 XTE J1814-338 system parameters ......................104 5.1 Observations of Sco X-1 ...........................110 5.2 Sco X-1 system parameters ..........................125 6.1 A list of observed optically bright, active low-mass X-ray binaries with updated system parameters ..........................131 A.1 RVs determined from 1999 WHT observations ................137 A.2 RVs determined from 2011 WHT observations ................140 A.3 RVs determined from 2011 VLT observations ................144 B.1 The Vsini-correction factor for ↵ = 0◦ and i = 40◦ ..............149 v List of Figures 1.1 Roche equipotential surfaces in the orbital plane for a binary system .... 3 1.2 Disc instability plot .............................. 8 1.3 An artist’s impression of a typical low-mass X-ray binary .......... 9 1.4 X-ray burst profiles from 4U 1702 42 .................... 12 − 1.5 A cartoon depicting the evolution of a ZAMS binary system that results in a binary millisecond pulsar .......................... 14 1.6 NS mass-radius curves for typical EOSs ................... 15 1.7 An X-ray color-color diagram taken from the High Energy Astronomy Ob- servatory 1 A-2 scanning data. ........................ 16 1.8 Masses of NSs and BHs measured in XRBs ................. 17 1.9 Radial velocity curve of the secondary star in V404 Cygni ......... 19 1.10 Trailed spectrogram of the Bowen blend and He ii λ4686 for Sco X-1 ... 21 1.11 Radial velocity curves of the sharp Bowen emission components and He ii λ4686 emission line .............................. 22 1.12 K-correction as function of the mass ratio for di↵erent disc opening angles . 23 1.13 Estimates for the gravitational wave strain amplitude (h0) for a number of known accreting neutron star sources as a function of frequency ...... 27 2.1 Example spectra from the 2011 VLT observations of Sco X-1 ........ 30 2.2 Trailed spectrogram of the Bowen blend for Sco X-1 and V926 Sco .... 32 2.3 Model contour map of the disc in velocity space ............... 33 2.4 Schematic view of a CV in both Doppler coordinates and spatial coordinates in the binary frame .............................. 35 2.5 Doppler maps of GW Lib and the LMXB X1822-371 ............ 37 2.6 The MEM solution for a 2-pixel image .................... 39 2.7 Doppler maps of ASAS 0025+1217 ..................... 40 2 2.8 χ versus entropy trajectories (constant Caim) ................ 42 2.9 χ2 versus entropy trajectories (constant entropy) ............... 43 vi 2.10 Example bootstrap maps of J1814 338 ................... 44 − 2.11 Number distribution of the peak height of the donor emission spot deter- mined from bootstrapped images of J1814 .................. 44 2.12 Number distribution of the peak height of a potential donor emission spot determined from bootstrapped images of ASAS 0025+1217 ........ 45 2.13 Distribution of the goodness-of-fit level of synthetic maps .......... 46 2.14 Bowen Doppler images of Sco X-1 for an assumed γ parameter of 77, − 113.6 and 150 km s 1 ........................... 48 − − − 2.15 Bowen Diagnostic diagram for Sco X-1 ................... 49 2.16 Plot of synthetic Kcor models for ↵ between 0 and 18◦ as a function of q determined by our code ............................ 50 3.1 Average Doppler corrected spectra of the Bowen region for the systems observed by our team during the period 1999 – 2005 ............ 52 3.2 Toolbox for Bowen data analysis. ....................... 53 3.3 Trailed spectra of the Bowen blend and He ii λ4686 for V801 Ara and V926 Sco ...................................... 55 3.4 Bowen Doppler images of V801 Ara for an assumed γ parameter of 19, 31 and 81 km s 1. ............................. 56 − − − 3.5 Number distributions of the phase shift, peak emission and Kem measured from 2000 bootstrap maps of V801 Ara assuming γ = 31 km s 1 ..... 57 − − 3.6 Bowen Diagnostic diagram for V801 Ara .................. 58 3.7 Bowen Doppler images of V926 Sco for an assumed γ parameter of 90, − 140 and 190 km s 1. ............................ 59 − − − 3.8 Number distributions of the phase shift, peak emission and Kem measured from 2000 bootstrap maps of V926 Sco assuming γ = 140 km s 1 .... 60 − − 3.9 Bowen Diagnostic diagram for V926 Sco .................. 61 3.10 The 68% and 95% confidence regions and projected PDF’s for K2 and q for V801 Ara ................................... 62 3.11 The 68% and 95% confidence regions and
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