Combining stellar structure and evolution models with multi-dimensional hydrodynamic simulations Andreas Christ Sølvsten Jørgensen M¨unchen2019 Combining stellar structure and evolution models with multi-dimensional hydrodynamic simulations Andreas Christ Sølvsten Jørgensen Dissertation an der Fakult¨atder Physik der Ludwig{Maximilians{Universit¨at M¨unchen vorgelegt von Andreas Christ Sølvsten Jørgensen aus Fredericia, D¨anemark M¨unchen, den 23. August 2019 Erstgutachter: Professor Dr. Achim Weiss Zweitgutachter: Professor Dr. Jochen Weller Tag der m¨undlichen Pr¨ufung:23.10.2019 Contents Zusammenfassung xv Abstract xvii 1 Introduction1 1.1 Overview of the Content of this Thesis....................3 1.1.1 The Lower Convective Boundary...................4 1.1.2 The Upper Convective Boundary...................5 1.1.2.1 Dealing with 3D Simulations................5 1.1.2.2 Post-Evolutionary Patching.................6 1.1.2.3 Coupling 1D Stellar Models with 3D Envelopes......6 2 Stellar Structure and Evolution9 2.1 Introduction...................................9 2.2 Simplifying Assumptions............................ 10 2.3 The Stellar Structure Equations........................ 11 2.3.1 Convective Instability......................... 13 2.3.2 Parameterizations of Superadiabatic Convection........... 15 2.3.3 Entropy................................. 16 2.4 Solving the Stellar Structure Equations.................... 16 2.4.1 The Henyey Scheme and Time Integration.............. 17 2.4.2 Setting the Inner Boundary Conditions................ 18 2.4.3 Setting the Outer Boundary Conditions................ 18 2.5 Solar Calibration Models............................ 21 2.6 From Cradle to Grave............................. 23 2.6.1 Early Phases.............................. 23 2.6.2 The Main Sequence........................... 26 2.6.3 Late Evolutionary Stages........................ 26 3 Stellar Pulsations 29 3.1 The Pulsation Equations............................ 32 3.1.1 Perturbation Theory.......................... 33 3.1.2 Dealing with Turbulent Pressure................... 33 vi CONTENTS 3.2 Inversion Techniques.............................. 34 3.3 The Surface Effect............................... 35 4 Lithium Depletion and the Tachocline Anomaly 39 4.1 The Role of Overshooting........................... 40 4.2 Overshooting Approaches........................... 42 4.3 Lithium Depletion............................... 44 4.4 Helioseismic Properties............................. 48 4.5 Summary.................................... 54 5 3D Simulations of Stellar Envelopes 57 5.1 Terminology................................... 57 5.2 Multi-Dimensional Stellar Envelope Simulations............... 58 5.3 Interpolation.................................. 60 5.3.1 Interpolation in Teff and log g ..................... 60 5.3.2 Interpolation in [Fe=H]......................... 67 5.3.2.1 Testing the Interpolation Scheme.............. 68 5.4 Turbulent Pressure............................... 70 6 Post-Evolutionary Patching 75 6.1 Constructing Patched Models......................... 77 6.1.1 The Patching Procedure........................ 77 6.1.2 Choosing the 3D -Envelope...................... 79 h i 6.2 The Solar Case................................. 80 6.2.1 Patched Solar Models.......................... 81 6.2.2 Testing the Interpolation Scheme................... 85 6.2.3 Selecting Envelope Parameters..................... 88 6.3 Stars in the Kepler Field............................ 90 6.3.1 Selecting UPMs............................. 90 6.3.2 Selecting Envelopes........................... 91 6.3.3 Asteroseismic Analyses of Patched Models.............. 93 6.3.3.1 KIC 9025370......................... 93 6.3.3.2 KIC 9955598......................... 94 6.3.3.3 KIC 11133306......................... 94 6.3.3.4 KIC 11772920......................... 94 6.4 Discussion.................................... 94 6.5 Summary.................................... 101 7 Parameterizations of Patched Models and the Surface Effect 103 7.1 The Patching Procedure............................ 104 7.2 The Surface Effect............................... 105 7.2.1 The Stellar Model Grid......................... 106 7.2.2 Parameterizations............................ 109 CONTENTS vii 7.2.3 Reconstructing the Sun......................... 113 7.3 Best-Fitting Models............................... 116 7.3.1 Maximum Likelihood Estimation................... 116 7.3.2 The Stellar Model Grid......................... 118 7.3.3 Comparisons.............................. 119 7.3.4 Hare and Hound Exercise....................... 121 7.3.5 Kepler Stars............................... 127 7.3.6 Patched Models of Kepler Stars.................... 132 7.4 Summary.................................... 135 8 Coupling: Improving the Outer Boundary Conditions 137 8.1 A New Standard Solar Model......................... 137 8.1.1 Coupling 1D Models with 3D -Envelopes.............. 138 h i 8.1.2 A Solar Calibration........................... 140 8.1.2.1 The Structure of the Outermost Layers........... 143 8.1.2.2 Oscillation Frequencies.................... 146 8.1.2.3 The Matching Depth..................... 148 8.2 Stellar Evolution and Asteroseismic Applications............... 148 8.2.1 Further Investigations of the Sun................... 150 8.2.1.1 The Matching Depth..................... 150 8.2.1.2 The Trampedach Grid.................... 151 8.2.2 A Grid Search.............................. 155 8.2.2.1 The Structure of Different Evolutionary Stages...... 156 8.2.3 Modelling Kepler Stars......................... 158 8.2.3.1 Best-Fitting Models..................... 158 8.3 Summary.................................... 161 9 Inference of Stellar Parameters 163 9.1 Bayesian Statistics............................... 164 9.1.1 MCMC Algorithms........................... 165 9.1.2 Defining a Likelihood for Stellar Modelling.............. 166 9.1.3 Priors.................................. 168 9.1.4 Specification of Priors......................... 169 9.1.5 Initial Conditions, Convergence and Burn-in............. 170 9.2 Stellar Parameter Estimates.......................... 170 9.2.1 Alpha Centauri A............................ 171 9.2.2 Alpha Centauri B............................ 178 9.3 Discussion.................................... 181 9.4 Summary.................................... 185 viii Table of Contents 10 Turbulent Pressure 187 10.1 Including and Calibrating Turbulent Pressure................ 187 10.2 A Complete Solar Model............................ 188 10.2.1 The Turbulent Pressure Profile.................... 192 10.2.2 The Sound Speed Profile........................ 195 10.2.3 Solar Oscillations............................ 197 10.2.4 Evolution of the Sun.......................... 199 10.3 Summary.................................... 201 11 Conclusions 203 12 Outlook 207 12.1 Extending Grids of 3D Stellar Envelopes................... 208 12.2 Alternative Approaches............................. 209 12.3 Non-adiabatic Effects.............................. 209 12.4 A Bigger Picture................................ 210 A Acronyms and Nomenclature 213 A.1 Jargon...................................... 215 B Advection and Convective Settling 217 B.1 Implementation................................. 217 B.2 Results and Discussion............................. 219 Bibliography 225 Acknowledgement 247 List of Figures 2.1 Temperature stratification of the solar atmosphere.............. 20 2.2 Temperature gradient of the Sun....................... 22 2.3 The Kiel diagram................................ 25 3.1 The surface effect for the present-day Sun.................. 36 4.1 Change in the surface lithium abundance with time............. 47 4.2 Squared sound speed difference for models with different overshooting ap- proaches..................................... 50 4.3 Equivalent to Fig. 4.2 but only including diffusion of H, 4He, 7Li and 9Be. 50 4.4 Hydrogen abundance as a function of radius for different overshooting ap- proaches..................................... 51 4.5 The gradient of the squared sound speed for models with different overshoot- ing approaches................................. 53 4.6 Equivalent to Fig. 4.2 but for AGSS09.................... 53 5.1 Mean opacity of a 3D stellar envelope..................... 59 5.2 Scaled density stratification for simulations in the Stagger grid....... 61 5.3 Pressure scaling factor.............................. 63 5.4 Residuals of an interpolated solar 3D -envelope............... 64 h i 5.5 Kiel diagram showing the residuals in the interpolated density for the Stagger grid....................................... 66 5.6 Kiel diagram corresponding to Fig. 5.5 but for the Trampedach grid.... 67 5.7 Residuals for the reconstruction of the density at the base of stellar 3D - envelopes by interpolation in metallicity...................h i 69 5.8 Residuals for the reconstruction of the turbulent pressure at the base of stellar 3D -envelopes by interpolation at solar metallicity in T and log g 71 h i eff 5.9 Residuals for the reconstruction of the turbulent pressure as a function of the scaled pressure by interpolation in Teff and log g ............. 72 6.1 Comparison between the structures of a patched and un-patched model of the present-day Sun............................... 78 6.2 Comparing different 3D envelope grids..................... 81 6.3 Comparing patched models, using MLT and full spectrum theory...... 83 x LIST OF FIGURES 6.4 Comparing patching criteria..........................