Mass Determinations of Cataclysmic Variables Christopher D.J. Savoury Department of Physics & Astronomy A dissertation submitted in candidature for the degree of Doctor of Philosophy at the University of Sheffield February 2013 “Space is big. You just won’t believe how vastly, hugely, mind-bogglingly big it is. I mean, you may think it’s a long way down the road to the chemist’s, but that’s just peanuts to space.” Douglas Adams, The Hitchhiker’s Guide to the Galaxy i Declaration I declare that no part of this thesis has been accepted, or is currently being submitted, for any degree or diploma or certificate or any other qualification at this University or elsewhere. This thesis is the result of my own work unless otherwise stated. The following Chapters have been based on publications: • Chapter 4 – Savoury et al. (2011) • Chapter 5 – Savoury et al. (2011) • Chapter 6 – Savoury et al. (2012) • Chapter 7 – Savoury & Littlefair (2013) ii Summary Cataclysmic variables (CVs) are a class of closely interacting binary system that un- dergo mass transfer from a Roche lobe filling secondary star to a white dwarf primary star, usually via a gas stream and an accretion disc. A bright spot is formed where the gas stream meets the edge of the accretion disc. The light curves of CVs can be complex, with the accretion disc, white dwarf and bright spot all being eclipsed in rapid succession. When observed with time resolutions of the order of a few seconds, this eclipse structure allows the system parameters to be determined to a high degree of precision, with relatively few assumptions. In this thesis I present new, high-speed photometry of 20 eclipsing CVs. For 6 objects, I am able to determine the system parameters by fitting a parameterised model to the observed eclipse light curve (the photometric method). In addition, I perform an updated analysis of 11 CVs that were previously analysed by my group, bringing the total sample size of eclipsing CVs with precise mass determinations in this thesis to 17. I find the secondary stars in CVs are oversized in comparison to standard models. I show that this can be explained by either enhancing the mass-transfer rate, or by modifying the stellar physics of the secondary stars. Distinguishing between these two possibilities is not possible given the available data. I perform an independent check of the photometric method by deriving system pa- rameters for one object using well known spectroscopic methods. The parameters iii derived are found to be consistent with the photometric method, thus supporting its accuracy and validity. Finally, I look at the infrared spectra of a short period CV. I am able to make a direct detection of the secondary star and place some constraints on the spectral type of the secondary star. iv Acknowledgements There are many people I wish to thank, without whom the following work would not have been possible. In no particular order: • My supervisor, Stuart Littlefair: Thank you for all of your patience and guid- ance over the last three and a half years, and thank you too for providing me with some great opportunities that have been both thoroughly enjoyable and educational. • Vik Dhillon and Tom Marsh: If only more people took your attitude towards data acquisition and analysis, then astronomy would be a far richer place. • Paul ‘Pablo’ Kerry: Your I.T skills are second to none. Thank you for all of your invaluable I.T support and advice, both inside the department and out. • Marvin Rose, Darren White and Emile Doran: Legendary. • Joanne Bibby, Richard Parker, Richard Allison, Krisada Rawiraswattana, Edgar Ramirez, Cristina Ramos Almeida, Patrica Bessiere, David Hubber, David Sah- man, Chris Rosslowe, Pavel Lee; We’ve had plenty of laughs, some good of banter and many a great time. Thanks for all of your support, and good luck. • David Maltby and Emma Bradshaw: It’s been an incredible journey, but we made it! v • Charlotte Angus: I don’t know where to even start. Thank you for putting up with me, for being there everyday, and generally being so amazing. Love you. • Mum & Dad: Thank you for all of your patience, support and encouragement over the years, no matter what. Without you, I would not have made it this far. vi Contents 1 Introduction 1 1.1 Cataclysmic Variables .......................... 1 1.1.1 What is a CV? .......................... 1 1.1.2 Roche Lobe Geometry ...................... 2 1.2 Types of Cataclysmic Variable ...................... 5 1.2.1 Classical and Recurrent Novae .................. 5 1.2.2 Dwarf Novae ........................... 7 1.2.3 Nova-Like Variables ........................ 8 1.2.4 Magnetic CVs . ......................... 9 1.3 Disc Instability Model .......................... 9 1.4 Origins and Evolution .......................... 12 1.4.1 Progenitors of CVs . ..................... 12 1.4.2 Common Envelope Phase .................... 13 1.4.3 Pre-CV Evolution ......................... 14 1.4.4 Direct Formation from a White Dwarf-Brown Dwarf Binary . 15 1.4.5 Response to Mass Loss ...................... 16 1.5 Angular Momentum Loss ......................... 20 1.5.1 Magnetic Braking of the Secondary Star ............ 20 1.5.2 Gravitational Radiation ..................... 20 vii 1.6 The Secondary Stars in CVs ....................... 21 1.7 The Distribution of Orbital Periods ................... 22 1.7.1 The Long Period Cut-Off ..................... 23 1.7.2 The Period Gap . ....................... 24 1.7.3 The Period Minimum ....................... 26 1.8 The Importance of Secondary Star Properties ............. 28 1.8.1 Superhumps ............................ 29 1.8.2 Empirical Donor Sequences ................... 31 1.9ThisThesis................................ 31 2 Observations and Data Reduction 33 2.1 Observations ................................ 33 2.1.1 ULTRACAM Photometry .................... 33 2.1.2 X-Shooter Spectroscopy ..................... 35 2.1.3 NIRI Spectroscopy ........................ 41 2.2 Data Reduction .............................. 42 2.2.1 Pipelines .............................. 42 2.2.2 Bias Subtraction ......................... 42 2.2.3 Flat Fielding ........................... 44 2.2.4 Dark Frames ........................... 47 2.2.5 NIRI Nodding ........................... 49 2.3 Aperture Photometry ........................... 50 2.4 Flux Calibration ............................. 53 2.4.1 Extinction ............................. 53 2.4.2 Instrumental Response ...................... 54 2.4.3 Absolute Flux Calibration .................... 55 2.5 X-Shooter Extraction ........................... 55 viii 2.5.1 Flexure Correction ........................ 57 2.5.2 Flux Calibration and Telluric Correction ............ 58 2.6 NIRI Extraction .............................. 59 2.6.1 Wavelength Calibration ..................... 61 2.6.2 Flux Calibration and Telluric Correction ............ 62 3 Techniques of Data Analysis 66 3.1 Data Phasing and Ephemerides ..................... 66 3.2 A Physical Model of the Binary System ................. 68 3.2.1 White Dwarf Model Atmospheres ................ 74 3.3 Markov Chain Monte Carlo ....................... 75 3.3.1 Bayes Theorem and MCMC ................... 75 3.3.2 Conditions of MCMC ....................... 76 3.3.3 Metropolis-Hastings ........................ 76 3.3.4 MCMC in Practice ........................ 78 3.4 Photometric Mass Determinations .................... 80 3.5 Radial Velocity Measurements ...................... 83 3.5.1 Cross-Correlation of the Secondary Star ............ 83 3.5.2 Skew Mapping .......................... 85 3.6 Rotational Broadening and Spectral Type of the Secondary Star . 86 3.7 Spectroscopic Mass Determinations ................... 86 3.8 The K2 Correction ............................ 87 3.9 Spectroscopic Distance Estimation ................... 89 3.10 Doppler Tomography ........................... 89 3.10.1 Line Formation .......................... 90 3.10.2 Back Projections ......................... 91 3.10.3 Interpretation of Doppler Maps ................. 93 ix 3.10.4 Limitation of Doppler Tomography ............... 95 4 Orbital Ephemerides and Light Curve Morphology 96 4.1 Introduction ................................ 96 4.2 Orbital Ephemerides ........................... 98 4.3 Light Curve Morphology and Variations ................ 99 4.3.1 CTCV J1300-3052 ........................ 99 4.3.2 CTCV J2354-4700 ........................ 101 4.3.3 SDSS J1152+4049 ........................ 102 4.3.4 CSS080623:140454-102702 .................... 102 4.3.5 SDSS J0901+4809 ........................ 102 4.3.6 PHL 1445 ............................. 103 4.3.7 SDSS J1325+2100 ........................ 103 4.3.8 SDSS J0750+1411 ........................ 104 4.3.9 SDSS J1524+2209 ........................ 104 4.3.10 SDSS J1250+6655 ........................ 104 4.3.11 SDSS J1555-0010 ......................... 105 4.3.12 CSS080227:112634-100210 .................... 105 4.3.13 1RXS J1808+1010 ........................ 106 4.3.14 SDSS J0920+0042 ........................ 106 4.3.15 GAL0035 ............................. 106 4.3.16 SDSS J1006+2337 ........................ 107 4.3.17 SDSS J0924+0801 ........................ 107 4.3.18 SDSS J0932+4725 ........................ 108 4.3.19 SDSS J0935+1619 ........................ 108 4.4 Systems for Modelling .......................... 108 x 5 Mass Determinations of 17 Eclipsing Systems 115 5.1 Introduction ................................ 115 5.2 Results ................................... 116 5.2.1 System Parameters .......................