Exploring the Dynamics of Near-Surface Solar Convection with Helioseismology by Benjamin J. Greer B.S., Carnegie Mellon University, 2010 M.S., University of Colorado, 2012 A thesis submitted to the Faculty of the Graduate School of the University of Colorado in partial fulfillment of the requirements for the degree of Doctor of Philosophy Department of Astrophysical and Planetary Sciences 2015 This thesis entitled: Exploring the Dynamics of Near-Surface Solar Convection with Helioseismology written by Benjamin J. Greer has been approved for the Department of Astrophysical and Planetary Sciences Prof. Bradley Hindman Prof. Juri Toomre Prof. Mark Rast Prof. Benjamin Brown Prof. Keith Julien Date The final copy of this thesis has been examined by the signatories, and we find that both the content and the form meet acceptable presentation standards of scholarly work in the above mentioned discipline. iii Greer, Benjamin J. (Ph.D., Astrophysics) Exploring the Dynamics of Near-Surface Solar Convection with Helioseismology Thesis directed by Prof. Bradley Hindman I present a new implementation of local helioseismology along with observations of near-surface solar convection made with this method. The upper 5% of the solar radius (35 Mm) is known as the Near-Surface Shear Layer (NSSL) and is characterized by strong rotational shear. While the physical origin of this layer remains unknown, current theories point to convective motions playing an important role. In this thesis I investigate the properties of convection in the NSSL using a newly-developed high-resolution ring-diagram analysis. I present measurements of the speeds and spatial scales of near-surface flows and from these infer that the degree of rotational constraint on convective flows varies significantly across this layer. In-depth analysis of the convective patterns reveals the pervasive influence of coherent downflow plumes generated at the photosphere. These structures link the convective pattern of supergranulation seen in surface observations with the deeper motions found within the NSSL and further hint at the importance of rotation in this layer. These observations of transient, small-scale convective motions are enabled by the use of improved local helioseismic techniques. Local helioseismology relies on observations of the solar wavefield to produce measurements of plasma flows beneath the surface. In general, this has the capability to map out the subsurface convective flows in three-dimensions, but is often limited in accuracy, resolution, and depth range by the specifics of the analysis procedure. Here, I focus on a particular implementation of local helioseismology called ring-diagram analysis that involves analyzing small patches of the solar surface to build up three-dimensional maps. I will present a new analysis scheme for ring-diagram helioseismology that produces maps of the subsurface flow fields with higher fidelity and vastly higher resolution than previously possible. This is achieved through a combination of novel tools including a robust nonlinear fitting procedure and a highly efficient linear inversion technique. I present these new methods and demonstrate how they enable a new class of high-resolution helioseismic observations. The scientific results made possible with these methods display the power of the new techniques and aid our understanding of near-surface solar dynamics. iv Acknowledgements I would like to thank my advisor Brad Hindman for providing guidance and continually urging me to write things down. Thanks to his dedication and patience, I have learned to be a better scientist. I would also like to thank Juri Toomre for explaining the big picture and asking the big questions. His encouragement has lead me to new and exciting areas of research. I thank Douglas Gough for the suggestion which initiated the expansion of my work into high-resolution helioseismology. Finally, I gratefully acknowledge the University of Colorado’s George Ellery Hale Graduate Student Fellowship, which has supported my scientific endeavors for a large fraction of my graduate career. v Contents Chapter 1 Introduction 1 1.1 Overview of Solar Dynamics . ...... 1 1.2 Near-Surface Convection . ...... 4 1.2.1 Supergranules . ... 6 1.2.2 Convective Amplitudes . ... 8 1.3 Observing the Solar Interior . ....... 8 1.3.1 Global Helioseismology . ....... 10 1.3.2 LocalHelioseismology ............................. ....... 11 1.3.3 Scientific Results from Local Helioseismology . ........ 14 1.4 Thesis Overview . 17 2 Helioseismic Ring-Diagram Methods 19 2.1 Overview of Standard Processing Steps . 20 2.2 Photospheric Observations of the Solar Wavefield . ...... 23 2.2.1 DopplergramData .................................. 23 2.2.2 TileTracking ................................... ...... 24 2.2.3 TileApodization ................................. ...... 25 2.2.4 TileSets........................................ 27 2.3 Representation in Spectral Space . ..... 30 vi 2.3.1 Flow-Induced Perturbation to the Wavefield . 30 2.3.2 Perturbations to the Power Spectrum . 31 2.4 Measuring Shifts in Spectral Power . ...... 32 2.4.1 Sensitivity Kernels . 37 2.5 High-Resolution Data Sets and Their Properties . ....... 38 3 Multi-Ridge Fitting 42 3.1 Introduction....................................... ....... 43 3.2 FittingMethods ...................................... ..... 45 3.2.1 Single-Ridge Fitting (SRF) . 45 3.2.2 Multi-RidgeFitting(MRF) . ...... 47 3.3 Comparison....................................... ....... 49 3.3.1 High Phase-Speed Modes . 50 3.3.2 Approaching the Solar Limb . 52 3.3.3 Frequency Shift Accuracy . 57 3.3.4 Post-Processing of Frequency Shift Measurements . 61 3.4 Discussion........................................ ....... 66 3.4.1 Improvements in Depth for Inversions . ...... 66 3.4.2 Spatial Variability and General Implications . ........ 67 4 Helioseismic Inversions 69 4.1 Introduction....................................... ....... 69 4.2 Mathematical Background . ....... 72 4.2.1 Frequency Shift Measurements . 72 4.2.2 Methods of Solution . 73 4.3 One-Dimensional Depth Inversions . 81 4.3.1 TwoBoxKernels..................................... 81 4.3.2 Solar Wave Mode Kernels . 84 vii 4.3.3 Summary of Depth Inversion Behavior . ..... 88 4.4 Horizontal Inversions with Spatial Invariance . ............. 88 4.4.1 Solution in Spectral Space . 90 4.4.2 Regularization Tuning . 92 4.5 Three-Dimensional Helioseismic Inversions with MORDI . ......... 94 4.5.1 Multi-Dimensional Localization . ....... 97 4.5.2 Regularization Tuning . 98 4.5.3 Selected Averaging Kernels . 106 4.5.4 Conclusions....................................... 108 5 Convective Amplitudes and Rotational Influence 110 5.1 Introduction....................................... ....... 111 5.2 Methods............................................ 114 5.2.1 Measurement Procedure . 114 5.2.2 Inversions...................................... 115 5.3 Convective Amplitudes . 118 5.4 RossbyNumber...................................... 120 5.5 Discussion........................................ ....... 123 5.5.1 Comparison of Convective Amplitudes . 123 5.5.2 Rotational Influence on Convective Motions . 126 6 Imaging Supergranular Flows in the Near-Surface Shear Layer 129 6.1 Introduction....................................... ....... 129 6.1.1 Supergranulation.................................. 129 6.1.2 Near-Surface Shear Layer . 133 6.2 Matching to Independent Observations . 134 6.2.1 Direct Doppler Imaging . 137 6.2.2 Advection of Magnetic Field . 137 viii 6.2.3 RotationRate .................................. 139 6.3 Propagation of Convective Patterns . ........... 142 6.3.1 Structure Similarity . 148 6.3.2 Inferred Vertical Velocities . 150 6.4 Discussion........................................ ....... 152 6.4.1 Self-Consistent Flow Fields . 152 6.4.2 Supergranular Flows and Surface-Driven Convection . 153 6.4.3 Rotational Influence on Convection in the NSSL . 155 7 Conclusions and Future Directions 158 7.1 Thesis Conclusions . 158 7.1.1 Improvements to Ring-Diagram Helioseismology . ......... 158 7.1.2 Properties of Near-Surface Solar Convection . ....... 159 7.1.3 Influence of Rotation on Convection . 160 7.2 Future Directions in High-Resolution Ring-Diagram Analysis . ........... 161 7.2.1 Spatial Extent of Analysis Regions . ....... 161 7.2.2 HorizontalResolution ............................. ....... 162 Bibliography 164 Appendix A Center-to-Limb Velocity Systematic 173 A.1 Introduction....................................... ....... 173 A.2 Temporally-Averaged Frequency Shift Data . 174 A.3 Fitting Procedure . 175 A.4 Results&Analysis ................................... ....... 177 A.5 Discussion & Conclusions . 178 ix B Averaging Kernels for Three-Dimensional OLA Inversion 181 C Code Listing 186 x Tables Table 2.1 List of analysis periods used in this thesis. ........... 40 Figures Figure 1.1 Observations of solar granulation and magnetic activity . ............. 2 1.2 Fundamental observations from global helioseismology . ........... 2 1.3 Magnetic butterfly diagram . ..... 3 1.4 Solar simulations of global dynamics and magnetic structure . .......... 5 1.5 Direct Doppler imaging of supergranulation . ......... 6 1.6 Images of the Sun captured by SDO . 10 1.7 Ring diagrams from a 16◦ tile. ................................... 13 1.8 Meridional flow measured with time-distance helioseismology . ........ 15 1.9 Large-scale subsurface flows from ring-diagram analysis . .......... 16 2.1 Steps involved in ring-diagram helioseismology . .........