Ultracam photometry of eclipsing cataclysmic variable stars William James Feline Department of Physics and Astronomy The University of Sheffield arXiv:0806.0797v1 [astro-ph] 4 Jun 2008 July, 2005 A thesis submitted to the University of Sheffield in partial fulfilment of the requirements of the degree of Doctor of Philosophy ii iii Declaration I declare that no part of this thesis has been accepted, or is currently being sub- mitted, for any degree or diploma or certificate or any other qualification in this University or elsewhere. This thesis is the result of my own work unless otherwise stated. iv v Summary The accurate determination of the masses of cataclysmic variable stars is critical to our understanding of their origin, evolution and behaviour. Observations of cataclysmic variables also afford an excellent opportunity to constrain theoretical physical models of the accretion discs housed in these systems. In particular, the brightness distributions of the accretion discs of eclipsing systems can be mapped at a spatial resolution unachievable in any other astrophysical situation. This thesis addresses both of these important topics via the analysis of the light curves of six eclipsing dwarf novæ, obtained using ultracam, a novel high-speed imaging photometer. The physical parameters of the eclipsing dwarf novæ OU Vir, XZ Eri and DV UMa are determined from timings of the white dwarf and bright spot eclipses. For XZ Eri and DV UMa the physical characteristics are also calculated using a parameterized model of the eclipse, and the results from the two techniques critically compared. This work marks the first accurate determination of the system parameters of both OU Vir and XZ Eri. The mass of the secondary star in XZ Eri is found to be close to the upper limit on the mass of a brown dwarf. The brightness distributions of the accretion discs of the six eclipsing dwarf novæ OU Vir, XZ Eri, DV UMa, GY Cnc, IR Com and HT Cas are determined using an eclipse mapping technique. The accretion discs of the first five objects are undetected in the observations, as expected for short-period quiescent dwarf novæ with low mass transfer rates. The observations of HT Cas, however, show significant changes in the brightness distribution of the quiescent accretion disc between 2002 September and 2003 October, which are related to the overall system brightness. These differences are caused by variations both in the rate of mass transfer from the secondary star and through the accretion disc. The disc colours indicate that it is optically thin in both its inner and outer regions. I estimate the white dwarf temperature of HT Cas to be 15 000 ± 1000 K in 2002 and 14 000 ± 1000 K in 2003. vi Contents Declaration . iii Summary . v List of Figures . xiii List of Tables . xix Acknowledgments xxi 1 Introduction 1 Context . 1 1.1 The canonical scheme . 2 1.2 The Roche-lobe . 4 1.3 Classification of cataclysmic variables . 8 1.3.1 Classical and recurrent novæ . 8 1.3.2 Dwarf novæ . 9 1.3.3 Novalikes . 10 1.3.4 Magnetic CVs . 12 1.4 Cataclysmic variable evolution . 12 vii viii CONTENTS 1.4.1 Angular momentum loss . 13 1.4.2 Pre-common envelope evolution . 15 1.4.3 Common envelope evolution . 16 1.4.4 Pre-cataclysmic variable evolution . 17 1.4.5 Cataclysmic variable evolution . 17 1.4.6 The orbital period distribution . 18 1.4.7 The disrupted magnetic braking model . 22 1.5 The gas stream and accretion disc . 23 1.5.1 Gas stream dynamics . 23 1.5.2 The radial temperature profile . 26 1.5.3 Outbursts and the disc instability model . 29 1.5.4 Superoutbursts and superhumps: SU UMa stars . 35 1.5.5 Spiral shocks . 35 1.6 Methods of mass determination . 37 1.6.1 Mass-orbital period relations . 37 1.6.2 Radial velocity mass determination . 38 1.6.3 The photometric method of mass determination . 44 1.7 This thesis . 46 2 Observations and data reduction 47 2.1 Ultracam ................................ 47 2.2 Journal of observations . 52 ULTRACAM PHOTOMETRY OF ECLIPSING CVS ix 2.3 Data reduction . 52 2.3.1 Bias frames . 55 2.3.2 Flat fielding . 56 2.3.3 Dark frames . 57 2.3.4 Extraction . 57 2.3.5 Flux calibration . 62 3 Analysis techniques 67 3.1 Phasing the data . 67 3.2 Derivative method . 68 3.3 Lfit method . 74 3.4 Comparing the derivative and lfit methods . 78 3.5 Mass determination . 96 3.6 White dwarf model atmospheres . 96 3.7 Eclipse mapping . 97 3.7.1 Theory . 99 3.7.2 Practice . 101 4 OU Vir 113 4.1 Light curve morphology . 114 4.2 Eclipse contact phases . 115 4.3 Orbital ephemeris . 115 4.4 System parameters . 118 4.5 Eclipse mapping . 123 x CONTENTS 5 XZ Eri and DV UMa 131 5.1 Light curve morphology . 134 5.2 Orbital ephemerides . 134 5.3 Light curve decomposition . 136 5.3.1 The derivative method . 136 5.3.2 A parameterized model of the eclipse . 142 5.3.3 Comparison of methods . 149 5.4 Eclipse mapping . 151 6 GY Cnc, IR Com and HT Cas 157 6.1 Orbital ephemerides . 159 6.2 GY Cnc . 162 6.3 IR Com . 165 6.4 HT Cas . 167 6.4.1 Light curve morphology . 167 6.4.2 Eclipse mapping . 170 6.4.3 Temperature maps . 173 7 Discussion, conclusions and future work 181 7.1 Discussion and conclusions . 181 7.1.1 OU Vir . 181 7.1.2 XZ Eri and DV UMa . 183 ULTRACAM PHOTOMETRY OF ECLIPSING CVS xi 7.1.3 GY Cnc, IR Com and HT Cas . 185 7.2 Overview . 189 7.3 Future work . 192 Bibliography 195 xii CONTENTS List of Figures 1.1 An artist's impression of a non-magnetic CV. 3 1.2 The Cartesian co-ordinate system used throughout this thesis. 5 1.3 Roche potentials. 6 1.4 Types of close binary system. 7 1.5 The ten-year light curve of SS Cyg. 9 1.6 An artist's impression of a polar. 11 1.7 An artist's impression of an intermediate polar. 11 1.8 A schematic demonstrating the important stages in the evolution of aCV. ................................... 19 1.9 The orbital period distribution of CVs. 20 1.10 The trajectory of the gas stream for q = 0:15. 27 1.11 A sequence of eclipse maps of the dwarf nova EX Dra through the outburst cycle. 30 1.12 The Σ − T relation and the resulting thermal limit cycle for dwarf novæ. 34 1.13 The superhump light distribution across the disc of Z Cha during superoutburst. 36 xiii xiv LIST OF FIGURES 1.14 The relationship between the mass ratio q and orbital inclination i for grazing eclipses of the bright spot and white dwarf. 40 1.15 An eclipse of OY Car, illustrating the distinct eclipses of the white dwarf and bright spot. 45 2.1 A ray-trace through ultracam...................... 48 2.2 A CAD image of the opto-mechanical design of ultracam. 49 2.3 A photograph of ultracam in the test focal station of the WHT just prior to commissioning on the telescope. 49 2.4 Transmission profiles of the ultracam optical components. 50 3.1 Phase arcs at different orbital phases. 70 3.2 The horizontal and vertical structure of the bright spot of Z Cha and the definition of Ajk and Zjk. ...................... 71 3.3 Deconvolution of the white dwarf light curve of Z Cha from the mean light curve. 74 3.4 The model grid used to produce the fake data for comparing the results of the derivative and lfit techniques. 80 3.5 Fake light curve produced and fitted as described in the text using the parameters given in table 3.1 for model 1. 88 3.6 Fake light curve produced and fitted as described in the text using the parameters given in table 3.1 for model 2. 89 3.7 Fake light curve produced and fitted as described in the text using the parameters given in table 3.1 for model 3a. 90 3.8 Fake light curve produced and fitted as described in the text using the parameters given in table 3.1 for model 3b. 91 ULTRACAM PHOTOMETRY OF ECLIPSING CVS xv 3.9 Fake light curve produced and fitted as described in the text using the parameters given in table 3.1 for model 4a. 92 3.10 Fake light curve produced and fitted as described in the text using the parameters given in table 3.1 for model 4b. 93 3.11 Fake light curve produced and fitted as described in the text using the parameters given in table 3.1 for model 5a. 94 3.12 Fake light curve produced and fitted as described in the.