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TITLE:Orbital Parameters Estimation for Compact Binary Stars 1 AUTHOR: Penélope Alejandra Longa-Peña, MSc DEGREE: Doctor of Philosophy TITLE: Orbital Parameters Estimation for Compact Binary Stars DATE OF DEPOSIT: . I agree that this thesis shall be available in accordance with the regulations governing the University of Warwick theses. I agree that the summary of this thesis may be submitted for publication. I agree that the thesis may be photocopied (single copies for study purposes only). Theses with no restriction on photocopying will also be made available to the British Library for microfilming. The British Library may supply copies to individuals or libraries. subject to a statement from them that the copy is supplied for non-publishing purposes. All copies supplied by the British Li- brary will carry the following statement: “Attention is drawn to the fact that the copyright of this thesis rests with its author. This copy of the thesis has been supplied on the condition that anyone who consults it is un- derstood to recognise that its copyright rests with its author and that no quotation from the thesis and no information derived from it may be published without the author’s written consent.” AUTHOR’S SIGNATURE: . USER’S DECLARATION 1. I undertake not to quote or make use of any information from this thesis without making acknowledgement to the author. 2. I further undertake to allow no-one else to use this thesis while it is in my care. DATE SIGNATURE ADDRESS ............................................................................................. ............................................................................................. ............................................................................................. ............................................................................................. ............................................................................................. Orbital Parameters Estimation for Compact Binary Stars by Penélope Alejandra Longa-Peña, MSc Thesis Submitted to the University of Warwick for the degree of Doctor of Philosophy Department of Physics December 2015 Contents Contents i List of Figures iv List of Tables viii Acknowledgements ix Declaration and Published Work xi Abbreviations xiii Abstract xv 1 Introduction 1 1.1 Compact Binary Stars . 1 1.1.1 Binary Geometry . 2 1.1.2 Evolution: Common Envelope and Stable Mass Transfer . 4 1.1.3 Accretion Disc . 5 1.1.4 Angular Momentum Loss . 6 1.1.5 Compact Binaries Classification . 8 1.1.6 Orbital Parameters . 15 1.2 Spectral Line Formation . 18 1.2.1 Spectral Features in CBs . 20 1.3 Ca II and the Bowen blend . 23 1.4 Summary and Outline . 26 2 Methods 27 2.1 Spectroscopy . 27 2.1.1 Long Slit Spectroscopy . 28 2.1.2 Echelle spectroscopy . 29 i ii CONTENTS 2.1.3 Data Reduction . 32 2.2 Radial Velocity Analysis . 37 2.2.1 Diagnostic Diagram . 38 2.3 Bootstrap . 40 2.3.1 The bootstrap estimate of standard error . 40 2.4 Indirect Imaging: Doppler Tomography . 40 2.4.1 Profile Formation by Projection . 41 2.4.2 Understanding Doppler maps . 43 2.4.3 Maximum Entropy Inversion . 44 2.4.4 The effect of the systemic velocity γ in Doppler maps . 45 2.4.5 Axioms of Doppler Tomography . 46 2.4.6 Doppler tomography and Bootstrapping . 47 2.4.7 Orbital Parameters with Doppler Tomography . 47 2.4.8 Secondary star and Phase zero from Kem .................... 51 2.5 Summary........................................... 63 3 Emission line tomography of CC Scl and V2051 Oph 65 3.1 Introduction . 65 3.2 Observations and Reduction . 67 3.3 Results . 67 3.3.1 Spectrum . 67 3.3.2 Radial velocities analysis . 68 3.3.3 Doppler tomography . 73 3.4 Discussion and Conclusions . 83 3.4.1 CC Scl . 84 3.4.2 V2051 Oph . 85 3.5 Summary........................................... 86 4 The Low Mass Black Hole Candidate 4U 1957+111 89 4.1 Introduction . 89 4.2 4U 1957+111 . 89 4.3 Instrument Performance on the Bowen blend . 91 4.4 Observation and Data Reduction . 92 4.5 Results . 94 4.5.1 Averaged Spectrum . 94 4.5.2 Radial Velocities . 96 4.5.3 Spectroscopic Period . 96 CONTENTS iii 4.5.4 Doppler Tomography . 99 4.6 Discussions and Conclusions . 104 4.7 Summary........................................... 105 5 Orbital Parameters of four Superhumping CVs 107 5.1 Introduction . 107 5.2 Observations and Data Reduction . 108 5.3 Average Spectra . 109 5.4 Radial Velocities . 116 5.5 Doppler Tomography . 117 5.5.1 Secondary Star and Phase Zero . 123 5.5.2 Systemic Velocity γ ................................. 124 5.5.3 Radial Velocity of the Primary Star . 125 5.5.4 Mass Ratio . 126 5.6 Discussions and Conclusions . 129 5.7 Summary........................................... 132 6 Discussions and Conclusions 135 6.1 Dynamic constraints with Doppler tomography . 135 6.2 CaIIemission ........................................ 136 6.3 4U 1957 and the Bowen blend . 136 6.4 Implications for the ² q relation . 136 ¡ 6.5 Conclusions . 138 6.6 Future Research . 138 6.6.1 Ca II . 138 6.6.2 Short Period CVs . 138 6.6.3 Extending the method . 139 Bibliography 141 List of Figures 1.1 Roche Potential . 3 1.2 Schematic representation of the accretion disc formation. 7 1.3 Schematic of CV evolution. Based on figure from Postnov & Yungelson (2014). Figure not to scale. 9 1.4 Orbital period distribution . 11 1.5 Mass transfer versus orbital period of CVs . 12 1.6 Superhump excess versus mass ratio. 14 1.7 Evolution of NS binaries . 16 1.8 Orbital phases . 18 1.9 Stars of masses M1 and M2 orbiting around their centre of mass. 18 1.10 Sodium spectra . 20 1.11 Blackbody radiation curves. Image created for educational purposes, courtesy of “Darth Kule”................................................. 21 1.12 Disc’s double peaked profile formation . 22 1.13 Cataclysmic variable spectrum . 23 1.14 X-ray binary spectrum . 24 1.15 Trailed spectra of Sco X-1 from Steeghs & Casares (2002) . 25 2.1 Schematic of the essential components of a spectrograph . 29 2.2 MagE spectra of the X-ray binary Sco X-1. 30 2.3 Photograph of MagE installed on the Magellan II telescope. 31 2.4 MagE optical design. 31 2.5 MagE bias frame . 32 2.6 MagE flat field frame. 34 2.7 MagE ThAr lamp frame . ..
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