The Evolution and Nucleosynthesis of Thermally Pulsing Asymptotic Giant Branch Stars Richard James Stancliffe Churchill College Institute of Astronomy University of Cambridge Thesis submitted for the Degree of Doctor of Philosophy at the University of Cambridge · 2005 · Declaration I hereby declare that my thesis entitled The Evolution and Nucleosynthesis of Thermally Pulsing Asymptotic Giant Branch 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 of this thesis which have been published or accepted for publication are as follows: • Material from chapters 2 and 3 has been published as: Stancliffe R. J., Tout C. A., Pols O. R., 2004, “Deep dredge-up in intermediate-mass thermally pulsing asymptotic giant branch stars”, Monthly Notices of the Royal Astronomical Society, 352, 984-992 and was completed in collaboration with these authors. • Material from chapter 4 has been published as: Stancliffe R. J., Izzard R. G., Tout C. A., 2005, “Third dredge-up in low-mass: solving the Large Magellanic Cloud carbon star mystery”, Monthly Notices of the Royal Astronomical Society, 356, L1-L5 and was completed in collaboration with these authors. • Material from chapter 5 has been published as: Stancliffe R. J., Lugaro M. A., Ugalde C., Tout C. A., G¨orres J., Wi- escher M., 2005, “The effect of the 19F(α, p)22Ne reaction rate uncer- tainty on the yield of fluorine from Wolf-Rayet stars”, Monthly Notices of the Royal Astronomical Society, 360, 375-379 and was completed in collaboration with these authors. This thesis contains fewer than 60,000 words. R. J. Stancliffe Cambridge, October 23, 2005 2 Abstract The thermally pulsing asymptotic giant branch (TP-AGB) is a computa- tionally demanding phase of evolution. This work presents a set of models that have been computed fully simultaneously – i.e. by solving the equations of stellar structure, nuclear burning and mixing together for each iteration of each timestep. It details the development of a viscous mesh technique in order to deal with some of the numerical problems that occur during the TP-AGB. Models have been created at solar metallicity (Z = 0.02) and metallici- ties appropriate to the Large and Small Magellanic Clouds (Z = 0.008 and Z = 0.004). These are evolved without mass loss. The solar metallicity models display important differences from those computed using other codes including deeper third dredge-up. The Large and Small Magellanic Cloud models are used to investigate the problem of the carbon star luminosity function. TP-AGB stars are also important sites for stellar nucleosynthesis. In or- der to investigate nucleosynthesis on the TP-AGB a set of subroutines have been developed to track the evolution of isotopes from deuterium to sulphur plus important iron group elements. These have been used to calculate the evolution of minor isotopes in TP-AGB stars of 1.5, 3 and 5 M at metal- licities of Z = 0.02, 0.008 and 0.004 evolved with mass loss. The results of these calculations are compared to known constraints from spectroscopic observations and measurements of pre-solar grains. At the end of the TP-AGB the star makes the transition to a white dwarf. In the course of trying to calculate this evolution it was found that numerical diffusion could substantially affect the evolution and that this phase has to be treated with great care. Contents Acknowledgments xi 1 Introduction 1 1.1 Stellar Evolution . 1 1.1.1 The Main-sequence . 1 1.1.2 The Red Giant Branch . 3 1.1.3 The Asymptotic Giant Branch . 5 1.2 A Brief History of the Thermally Pulsing Asymptotic Giant Branch . 6 1.2.1 The Discovery of Thermal Pulses . 6 1.2.2 Third Dredge-up . 10 1.3 TP-AGB Nucleosynthesis and the s-process . 12 1.3.1 Light Element Nucleosynthesis . 13 1.3.2 Nucleosynthesis via the s-process . 14 1.3.3 Mass Loss . 15 1.4 Observational Constraints . 17 1.4.1 Direct Observations . 17 1.4.2 Pre-solar Grains . 19 2 stars: a Stellar Evolution Code 21 i 2.1 Input Physics . 21 2.2 Implementation . 25 2.2.1 Convective Mixing and the Choice of σ . 26 2.3 Overview of the stars Code Structure . 27 2.4 Numerical Instability . 29 2.4.1 Mixing . 29 2.4.2 Viscous Mesh . 30 2.4.3 Timestep Control . 32 2.5 Making Stellar Models . 33 3 TP-AGB Stars of Solar Metallicity 35 3.1 Initial Attempt – a 5 M star . 35 3.2 General Properties . 38 3.3 Model-by-model . 38 3.3.1 1 M ............................ 39 3.3.2 1.5 M ........................... 40 3.3.3 2 M ............................ 41 3.3.4 3 M ............................ 43 3.3.5 4 M ............................ 45 3.3.6 6 M ............................ 49 3.3.7 7 M ............................ 49 3.4 Model Comparisons . 51 3.4.1 Models with Convective Overshooting . 55 3.5 Summary . 57 4 TP-AGB Stars of Low Metallicity 58 4.1 The Z = 0.008 Models – TP-AGB Stars in the LMC . 58 4.2 The Z = 0.004 Models – TP-AGB Stars in the SMC . 62 ii 4.3 The Carbon Star Luminosity Function . 65 4.3.1 LMC Models . 66 4.3.2 SMC models . 67 4.3.3 Population Synthesis . 67 4.4 Detailed Model Comparison . 72 4.4.1 Evolutionary Properties . 73 4.4.2 Focusing on a Pulse . 76 4.5 Summary . 82 5 Nucleosynthesis on the TP-AGB 83 5.1 Updating the Algorithms . 83 5.1.1 Charged Particle Reaction Rates . 86 5.1.2 Neutron Capture Rates . 86 5.2 Light Isotope Nucleosynthesis . 90 5.2.1 Nucleosynthesis During a Thermal Pulse . 90 5.2.2 Surface Composition Evolution . 91 5.3 The 13C Pocket: a Warning on Numerical Diffusion . 105 5.4 Summary . 108 6 Post-AGB Stars 110 6.1 The End of the TP-AGB . 110 6.2 Producing a Post-AGB Model . 111 6.3 Modelling a Late Thermal Pulse . 118 6.4 Summary . 121 7 Summary and Future Directions 122 7.1 Evolution . 122 7.2 Nucleosynthesis . 126 iii A Derivation of Gravothermal Specific Heat Capacity and Thermal Stability Criterion 137 A.1 The Gravothermal Specific Heat Capacity . 137 A.2 The Thermal Stability Criterion . 139 B Details of the Solar Metallicity Models 141 C Details of the LMC Metallicity Models 150 D Details of the SMC Metallicity Models 156 Bibliography 156 iv List of Figures 1.1 Hertzsprung-Russell diagram for a 1 M star of Z=0.008, showing its transition from the main sequence to the red giant branch. This model is evolved without mass loss. 4 1.2 Hertzsprung-Russell diagram for a 1 M star of Z=0.008, showing its transition from core helium burning to the AGB. 6 1.3 Interior structure of a typical AGB star. 7 1.4 The ubiquitous AGB TDUP figure . 11 2.1 Schematic depiction of the connections of the various subrou- tines in the stars code. 28 3.1 Evolution of the helium luminosity of the 5 M model. 36 3.2 Evolution of the core masses of the 5 M model. 37 3.3 Evolution of the CNO abundances of the 5 M model. 37 3.4 Evolution of the helium luminosity of the 1 M model. 39 3.5 Evolution of the core masses of the 1 M model. 40 3.6 Evolution of the helium luminosity of the 1.5 M model. 41 3.7 Evolution of the core masses of the 1.5 M model. 42 3.8 Evolution of the CNO abundances of the 1.5 M model. 42 3.9 Evolution of the helium luminosity of the 2 M model. 43 3.10 Evolution of the core masses of the 2 M model. 44 v 3.11 Evolution of the CNO abundances of the 2 M model. 44 3.12 Evolution of the helium luminosity of the 3 M model. 45 3.13 Evolution of the core masses of the 3 M model. 46 3.14 Evolution of the CNO abundances of the 3 M model. 46 3.15 Evolution of the helium luminosity of the 4 M model. 47 3.16 Evolution of the core masses of the 4 M model. 48 3.17 Evolution of the CNO abundances of the 4 M model. 48 3.18 Evolution of the helium luminosity of the 6 M model. 49 3.19 Evolution of the core masses of the 6 M model. 50 3.20 Evolution of the CNO abundances of the 6 M model. 50 3.21 Evolution of the helium luminosity of the 7 M model. 51 3.22 Evolution of the core masses of the 7 M model. 52 3.23 Evolution of the CNO abundances of the 7 M model. 52 4.1 Evolution of the core masses for the Z = 0.008 1 M model . 60 4.2 Evolution of the CNO abundances for the Z = 0.008 1 M model . 60 4.3 Evolution of the helium luminosity for the Z = 0.008 1.5 M model . 61 4.4 Evolution of the CNO abundances for the Z = 0.008 4 M model .