Post-Main Sequence Evolution of Planetary Systems
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Post-main Sequence Evolution of Planetary Systems Amy Bonsor Institute of Astronomy St. John’s College University of Cambridge A thesis submitted for the degree of Doctor of Philosophy October 2011 Declaration I hereby declare that my thesis entitled The post-main sequence evolution of planetary systems 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. Furthermore, the work presented in this dissertation is my own and contains nothing which is the outcome of work done in collaboration with others, except as specifically indicated clearly in the text and acknowledgments. Whilst all writing was generated by myself, I have asked others (credited in the acknowledgments) for their aid in editing and revision. I note that Chapters 1 and 2 are intended as reviews, and as such contain little, if any, original work. They contain a number of images and plots extracted from other published works, all of which are clearly cited in the appropriate caption. Those parts of this thesis which have been published or accepted for publica- tion are as follows: Much of the work contained in Chapter 3 formed the basis of the work • published as Bonsor, A. & Wyatt, M., Post-main-sequence evolution of A star debris discs, MNRAS, 2010, 409, 1631-1646 and was completed in collaboration with the named authors. Much of the work contained in Chapter 4 forms the basis of the paper • Bonsor, A.; Mustill, A. J. & Wyatt, M. C. Dynamical effects of stellar mass- loss on a Kuiper-like belt mnras, 2011, 414, 930-939 and was completed in collaboration with the named authors. A. J. Mustill was responsible for the encounter map analysis and producing Fig.4.4 Much of the work contained in Chapter 5 forms the basis of the work to • be published as Bonsor, A. & Wyatt, M., The scattering of small bodies in planetary systems, 2011, that is currently in preparation with collaboration with the named authors. This thesis contains fewer than 60,000 words. Amy Bonsor Cambridge, 7th October, 2011 i Acknowledgements I would like to begin by fully acknowledging the support of my supervisor, Dr. Mark Wyatt. Without him none of this work would have been possible. With his help and support I have been able to develop from a naive undergraduate into a confident researcher. I am indebted to Mark for his guidance, helpful comments, ability to point me in the right direction and patient re-reading of endless paper drafts. Next, I would like to thank the rest of our group at the IoA. Laura, my office mate and friend, Alex, my on-call mathematician, Dimitri, Grant, Alan, Matt and Mark. Further thanks go to Alex for his contribution to (Bonsor et al., 2011) or Chapter 4. On a technical level, thanks also to Jim Pringle, Jay Farihi, John Debes, Mike Jura, Richard Alexander, Alexander Krivov and many others, for their continued interest and comments on my work. Within the department a massive thank you goes out to Margeret Harding and Sian Owen, for their friendly help with all the practical aspects of being a graduate student. Further thanks to Paul Hewett for his practical help behind the scenes and for always having time to give me good advice. I also acknowledge the support of STFC in funding my PhD. And of course I couldn’t forget all my fellow PhD students for making my time at the IoA so much fun! How would I have coped without all those tea breaks? A particular mention to Ryan, Becky, Adrian and Pierre, for all their support. On a more personal note, I wouldn’t be here today without the continued love and support of Jon, my parents and my sister, Poppy. iii Summary Post-main Sequence Evolution of Planetary Systems Planetary systems are common around main sequence stars. There are hun- dreds of detections of planets and analogues to the Solar System’s Kuiper belt, known as debris discs, around stars on the main sequence. However, there are very few observations of such systems around evolved stars. An important link has been made between observations of metal pollution and circumstellar discs around white dwarfs and evolved planetary systems. The hypothesis is that as- teroids or comets from an outer belt are scattered in close to the star, where they are tidally disrupted and accrete on to the star. The focus of this thesis is on the evolution of planetary systems beyond the main sequence, with relevance to the observations. Starting from the main sequence, the effects of stellar evolution on debris discs are outlined and it is determined that although such belts of rocks and dust survive the star’s evolution, their detectability decreases as the star evolves. A cold, undetected population of outer discs around white dwarfs may supply the observed accretion. Investigations into the effects of stellar mass loss on such a disc find that for Solar System analogues sufficient material is scattered inwards in order to produce the observations. This is, however, highly dependent on the planets’ orbits. The conservation of the Tisserand parameter is used to confirm that many planetary systems, with sufficient planets, can scatter particles from an outer belt onto star-grazing orbits. The conservation of the Tisserand parameter in this manner can also be used to describe the scattering of small bodies by planets in any system. I consider both our Solar System and main sequence stars with two belts of rocks and dust, an inner warm belt and an outer cold belt. All the work presented in this thesis develops our understanding of planetary systems as they evolve beyond the main sequence. Vital evidence is provided in support of a link between main sequence planetary systems and the observations of evolved stars linked with planetary systems, in particular metal polluted white dwarfs and white dwarfs with circumstellar discs. Amy Bonsor, 7th October 2011 Contents Contents vii List of Figures xi 1 Introduction 1 1.1 Main Sequence planetary systems . 2 1.1.1 Planets............................. 2 1.1.2 Planetesimal belts around main-sequence stars . 5 1.2 Thestarevolves............................ 6 1.2.1 Giants ............................. 6 1.2.2 Core-helium burning or horizontal branch stars . 9 1.2.2.1 Extreme horizontal branch stars . 9 1.2.3 Asymptotic giant branch (AGB) . 10 1.2.4 Whitedwarfs ......................... 11 1.2.5 Neutronstarsandpulsars . 12 1.2.6 Binarystars.......................... 12 1.3 Observations of evolved stars associated with planetary systems . 14 1.3.1 Colddustdiscs ........................ 14 1.3.2 Metalpollutedwhitedwarfs . 16 1.3.3 White dwarfs with close-in, circumstellar discs . 18 1.3.4 White dwarfs with gaseous discs . 20 1.4 Summary ............................... 21 2 Debris disc theory 23 2.1 Dynamics ............................... 23 vii 2.1.1 Circular restricted three-body problem . 25 2.1.2 Resonance........................... 27 2.1.3 MassLoss ........................... 29 2.2 Debrisdiscmodelling. 31 2.2.1 Thermalemission . 32 2.2.2 Collisions ........................... 34 2.2.3 Removalofsmallgrains . 38 2.2.3.1 Radiativeforces. 38 2.2.3.2 Poynting-Robertsondrag . 39 2.2.3.3 Stellarwind. 41 2.2.4 Planets............................. 42 2.2.5 Models............................. 42 2.3 Summary ............................... 43 3 Post-main sequence evolution of A star debris discs 45 3.1 Summary ............................... 45 3.2 Introduction.............................. 46 3.3 StellarEvolution ........................... 48 3.4 Models of debris discs around post-main sequence A stars ..... 52 3.4.1 Evolution of an individual disc . 52 3.4.2 PopulationofdiscsaroundAstars . 54 3.5 Models of debris discs around post-main sequence A stars ..... 56 3.5.1 Radiusevolution . 58 3.5.2 Mass in the disc and the collisional lifetime . 58 3.5.3 Temperatureofthedisc . 60 3.5.4 Smallest particles in the disc . 62 3.5.4.1 Radiationpressure . 62 3.5.4.2 Poynting-RobertsonDrag . 66 3.5.4.3 Stellar wind pressure . 67 3.5.4.4 Stellarwinddrag . 68 3.5.4.5 Sublimation. 69 3.5.4.6 Summary ...................... 71 3.6 Observations.............................. 72 3.6.1 Evolution of a 100AU disc around a 2.9M star at a dis- ⊙ tanceof10pc ......................... 73 3.6.1.1 Dependence on disc parameters . 76 3.6.1.2 Dependence on stellar parameters . 76 3.6.1.3 Dependence on wavelength of observations . 77 3.6.2 Populationmodels . 78 3.6.2.1 Giantstars ..................... 79 3.6.2.2 Core-helium burning stars . 83 3.6.2.3 Whitedwarfs . 83 3.6.2.4 Post-AGBorpre-WDstars . 87 3.7 Conclusions .............................. 87 4 Dynamical effects of stellar mass loss on a Kuiper-like belt. 91 4.1 Summary ............................... 91 4.2 Introduction.............................. 92 4.3 Setup ................................. 94 4.4 Main-Sequence evolution . 96 4.4.1 Baseline simulation . 96 4.4.2 Setting up the initial conditions in the belt . 97 4.4.3 The effect of varying the definition of ‘scattered in’ or ain . 98 4.4.4 Comparison to analytic prescription . 100 4.4.5 Results ............................ 102 4.5 Post-main sequence evolution . 104 4.5.1 Analyticformulation . 104 4.5.2 Scatteredinorejected?. 106 4.6 The relationship between these simulations and observations of metalrichwhitedwarfs. 108 4.7 Conclusions .............................. 116 5 Scattering in planetary systems 119 5.1 Summary ............................... 119 5.2 Introduction.............................. 120 5.3 Scatteringofplanetesimals . 122 5.4 Scatteringbyasingleplanet . 124 5.4.1 Orbitalconstraints . 124 5.4.2 Minimumpericentre . 127 5.4.3 Ejection ............................ 127 5.5 Scatteringbytwoplanets. 128 5.5.1 Orbitalconstraints .