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Rotation and Magnetism in Massive Stars Adrian Thomas Potter

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Rotation and Magnetism in Massive Stars Adrian Thomas Potter University of Cambridge Institute of Astronomy A dissertation submitted for the degree of Doctor of Philosophy Rotation and magnetism in massive stars Adrian Thomas Potter arXiv:1205.6491v1 [astro-ph.SR] 29 May 2012 Pembroke College Under the supervision of Dr. Christopher A. Tout Submitted to the Board of Graduate Studies 10 May, 2012 i For everyone who helped to get me here ii CONTENTS iii Contents Contents iii Declaration vii Acknowledgements ix Summary xi List of Tables xiii List of Figures xv 1 Introduction 1 1.1 Stellar evolution . 1 1.1.1 The mechanical equilibrium of stars . 2 1.1.2 Themainsequence .......................... 3 1.2 Rotationinmassivestars........................... 7 1.2.1 Changes in stellar structure . 7 1.2.2 TheVonZeipelparadox . .. .. 11 1.2.3 The Kelvin–Helmholtz instability . 13 1.2.4 Observations of rotational velocities . 18 1.2.5 Chemical mixing in massive stars . 21 1.3 Stellar magnetism . 22 1.3.1 Observations of magnetism in massive stars . 22 1.3.2 Stellar dynamos . 24 1.3.3 Fossil fields . 26 1.4 Commonenvelopeevolution . 27 1.5 Dissertation outline . 33 2 Modelling rotation and magnetic fields in stars 35 2.1 Stellar structure and evolution . 35 2.2 The Cambridge stellar evolution code . 37 2.3 Modelling stellar rotation . 39 iv CONTENTS 2.3.1 Structureequationsforrotatingstars . 39 2.3.2 Meridional circulation . 40 2.3.3 Mass loss with rotation . 42 2.3.4 Rotation in convective zones . 42 2.3.5 Angularmomentumtransport . 42 2.3.6 Numerical implementation of rotation . 43 2.4 Modelling stellar magnetism . 46 2.4.1 Magnetic field evolution . 46 2.4.2 Angular momentum evolution with a magnetic field . 48 2.4.3 Magnetic diffusion . 49 2.4.4 Dynamomodel ............................ 50 2.4.5 Magnetic braking . 50 2.4.6 Freeparameters............................ 51 2.4.7 Numerical implementation . 52 2.5 Simulating stellar populations . 52 3 Comparison of stellar rotation models 55 3.1 Introduction.................................. 55 3.2 Models of stellar rotation . 56 3.3 Angularmomentumtransport . 57 3.3.1 Testcases ............................... 57 3.4 Results..................................... 61 3.4.1 Evolution of a 20 M⊙ starincases1,2and3 . 61 3.4.2 EffectonHertzsprung–Russelldiagram . 65 3.4.3 Nitrogen enrichment . 67 3.4.4 Helium–3 enrichment . 69 3.4.5 Metallicity dependence . 69 3.4.6 Surfacegravitycut–off . 71 3.4.7 Alternative models for convection . 74 3.5 Conclusions .................................. 74 4 Model–dependent characteristics of stellar populations 79 4.1 Introduction.................................. 79 4.2 Inputphysics ................................. 80 4.2.1 Case1................................. 82 4.2.2 Case2................................. 83 4.2.3 Stellar populations . 84 4.3 Results..................................... 84 4.3.1 TheHertzsprung–Russelldiagram . 84 4.3.2 Velocity distribution evolution . 86 4.3.3 TheHunterdiagram ......................... 86 CONTENTS v 4.3.4 Effective surface gravity and enrichment . 89 4.3.5 Recalibration . 93 4.3.6 Effects of metallicity . 93 4.3.7 Selection effects in the VLT–FLAMES survey . 98 4.4 Conclusions .................................. 101 5 Stellar evolution with an alpha–omega dynamo 105 5.1 Introduction.................................. 105 5.2 Magneticrotatingmodel ........................... 107 5.3 Results..................................... 108 5.3.1 Magnetic field evolution . 110 5.3.2 Effect on angular momentum distribution . 113 5.3.3 Mass–rotation relation of the main–sequence field strength . .. 117 5.3.4 EffectontheHertzsprung–Russel diagram . 121 5.3.5 The lifetime of fossil fields . 123 5.3.6 Effect on surface composition . 124 5.3.7 Variation with different parameters . 128 5.4 Conclusions .................................. 129 6 WD magnetic fields in interacting binaries 133 6.1 Introduction.................................. 133 6.2 CEEvolutionandenergyconstraints . 134 6.3 Governing equations for magnetic field evolution . 136 6.4 NumericalMethods.............................. 139 6.5 Results..................................... 140 6.5.1 Consequences of CE lifetime . 141 6.5.2 Effect of randomly varying the magnetic field orientation . 146 6.6 Conclusions .................................. 152 7 Conclusions 155 7.1 Populationsofrotatingstars . 155 7.2 Populations of magnetic, rotating stars . 158 7.3 Highly magnetic white dwarfs . 159 7.4 Futurework.................................. 159 A Stellar structure derivations 161 A.1 The structure parameter, fP ......................... 161 A.2 The structure parameter, fT ......................... 163 A.3 TheVonZeipelTheorem........................... 164 Bibliography 167 vi CONTENTS vii Declaration I hereby declare that my dissertation entitled Rotation and magnetism in mas- sive stars is not substantially the same as any that I have submitted for a degree or diploma or other qualification at any other university. I further state that no part of my thesis has already been or is being concurrently submitted for any such degree, diploma or other qualification. This dissertation is the result of my own work and includes nothing which is the outcome of work done in collaboration except where specifically indicated in the text. Those parts which have been published or accepted for publication are: Material from chapter 1 is largely intended as a literature review and so • draws heavily on the references contained therein. Material from section 1.4 was submitted for the Certificate of Postgraduate Study to the University of Cambridge. Material from chapters 2 and 3 has been published as: Potter A. T., • Tout C. A. and Eldridge J. J., 2012, “Towards a unified model of stellar rotation”, Monthly Notices of the Royal Astronomical Society, 419, 788-759 and was completed in collaboration with these authors. Material from chapters 2 and 4 has been accepted for publication as: Pot- • ter A. T., Brott I. and Tout C. A., “Towards a unified model of stellar ro- tation II: Model-dependent characteristics of stellar populations”, Monthly Notices of the Royal Astronomical Society and was completed in collabo- ration with these authors. Material from chapters 2 and 5 has been accepted for publication as: Pot- • ter A. T., Chitre S. M. and Tout C. A., “Stellar evolution of massive stars with a radiative alpha–omega dynamo”, Monthly Notices of the Royal As- tronomical Society and was completed in collaboration with these authors. Material from chapter 6 has been published as: Potter A. T. and Tout C. A., • 2010, “Magnetic field evolution of white dwarfs in strongly interacting bi- nary star systems”, Monthly Notices of the Royal Astronomical Society, 402, 1072-1080 and was completed in collaboration with that author. This dissertation contains fewer than 60, 000 words. Adrian Potter June 1, 2018 viii DECLARATION ix Edmund: It’s taken me seven years, and it’s perfect... My magnum opus, Baldrick. Every- body has one novel in them, and this is mine. Baldrick: And this is mine. My magnificent octopus. (Blackadder the Third, Ink and Incapability) Acknowledgements For this piece of work I am indebted to the invaluable help and support of countless people over the past four years. Without their time and effort none of this work would have been possible. First and foremost I would like to give the greatest of thanks to my supervisor, Christopher Tout. His hard work, knowledge and guidance have been an abso- lutely essential for driving this work forwards and I am thoroughly grateful. I am also particularly thankful for the support of John Eldridge who stepped in to fill the void whilst Christopher was on sabbatical. Not only that but his firm knowledge of the Cambridge stellar evolution code has allowed me to overcome countless hurdles. I would also like to thank Ines Brott and Shashikumar Chitre for their ongoing support. The success of a PhD is dependent on all of those people behind the scenes who make things possible. Firmly at the top of that list is Andrea Kuesters who has always been there when I needed her the most. I have always been able count on her regardless of what life sent my way and for that I am eternally grateful. More than that we’ve had some fantastic times and even when she tried to break my hand one Christmas, I treasure every moment we’ve spent together. I also couldn’t have asked for a better year group at the Institute of Astronomy. Amy, Becky, Ryan, Warrick, Steph, Alex, Jon, James, other James, Dom and Yin-Zhe, you’ve been fantastic, thank you. I’d also like to thank Chrissie, Amy, Natasha, Barny, Sam, Mark C, James, Samantha, Mark W, Simon, Bahar, Sophie and Lucy for all the great times during the past four years. In addition I’d like to thank Sian Owen, Margaret Harding and Becky Coombs for their tireless administrative efforts. My family have also been a constant source of support. They shouldered the financial burden of my degrees and have always been just a phone call away whenever I needed them. Finally I’d like to give my thanks to Christine whose love, support and en- couragement has been unwavering. Her time and understanding has been so important in helping me to cope with pressure of finishing my eight years in Cambridge and I’m very thankful for everything she’s given me. x ACKNOWLEDGEMENTS xi ...so smart it’s got a PhD from Cambridge. (Blackadder Goes Forth, Private Plane) Summary Rotation has a number of important effects on the evolution of stars. Apart from struc- tural changes because of the centrifugal force, turbulent mixing and meridional circulation can dramatically affect a star’s chemical evolution. This leads to changes in the surface temperature and luminosity as well as modifying its lifetime. Rotation decreases the surface gravity, causes enhanced mass loss and leads to surface abundance anomalies of various chemical isotopes all of which have been observed. The replication of these physical effects with simple stellar evolution models is very difficult and has resulted in the use of numerous different formulations to describe the physics. We have adapted the Cambridge stellar evolution code to incorporate a number of different physical models for rotation, including several treatments of angular momentum transport in convection zones.
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