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Copyright by Shizuka Akiyama 2006 the Dissertation Committee for Shizuka Akiyama Certifies That This Is the Approved Version of the Following Dissertation Copyright by Shizuka Akiyama 2006 The Dissertation Committee for Shizuka Akiyama certi¯es that this is the approved version of the following dissertation: The Role of Rotation and Magnetic Fields in a Core Collapse Supernova Committee: John Craig Wheeler, Supervisor Peter HÄoflich David L. Meier Edward L. Robinson John M. Scalo Paul R. Shapiro The Role of Rotation and Magnetic Fields in a Core Collapse Supernova by Shizuka Akiyama, B.A.;B.S.;M.A. DISSERTATION Presented to the Faculty of the Graduate School of The University of Texas at Austin in Partial Ful¯llment of the Requirements for the Degree of DOCTOR OF PHILOSOPHY THE UNIVERSITY OF TEXAS AT AUSTIN August 2006 Dedicated to my father and mother, Sadao and Yoshiko Akiyama. Acknowledgments As I write this acknowledgments, I pondered my past six years as a graduate student. I realize that how fortunate I am to be where I am now and that this was not possible without tremendous support that I have received from many people. Firstly, I would like to express my sincere gratitude to my adviser, J. Craig Wheeler, for his guidance, support, help, patience, and encouragements. I admire his passion and dedication for science, and treasure the time we spent for discussing interesting science together in the \Center for Stu® Wheeler is Interested in." He has generously helped me with technical and editorial aspect of research including this dissertation, and I have learned innumerable lessons and insights on the workings of academic research in gen- eral. In addition, he is genuinely considerate person who is wise and fun at the same time. I enjoyed our interaction as collaborators and friends, and hope to continue as such. I would like to thank my local committee members, Peter HÄoflich, Rob Robinson, John Scalo, and Paul Shapiro for their guidance and encourage- ment for my research and this dissertation. I have appreciated independent viewpoint provided during each committee meeting that has always been im- provement on my research. I thank my outside committee member, David Meier, for being supportive, and I enjoyed our discussion of MHD jets. I wish v to extend my thank to people with whom I worked with during my undergrad- uate years. In particular, I thank Harriet Dinerstein for giving me the very ¯rst opportunity to research in astronomy when I was an undergraduate student. I understand that having undergraduate students takes time and e®ort, which she has generously provided me with. I thank Antonella Nota with whom I had summer internship at the Space Telescope Science Institute. The whole expe- rience of being at the Space Telescope Science Institute was valuable for me. I thank Gary Hill for giving me an opportunity to work on galactic research as well as observation experiences at the McDonald Observatory. I thank Peter HÄoflich with whom I worked during my last year as a undergraduate student. He was (and still is) very patient with me and generous with his time and help. I am also grateful of being at such a supportive department with ded- icated sta® members. I have spent large fraction of my waking hours at the department, and it has been very comfortable and pleasant thanks to them. I would like to express my special thanks to my dear friends from the de- partment, especially Niv Drory, Mike Endal, Claudia Knez, Martin Landriau, Jeong-Eun Lee, Eva Noyola, Robert Quimby, for having interesting conversa- tions and for keeping my non{academic life amusing; there has been count- less movies we watched, meals we shared, glasses of alcoholic substances we consumed, celebrations we partied, plus some special occasions. Those ex- periences are priceless, and I treasure them. I also thank my friends from Capoeira Angola Group, with whom I had such a delightful time practicing the art of Capoeira, and my long{time friends, especially Jodie Martin and vi Yumi Sakawa, for our continuing friendship. I am indebted to my family for all the love and support. My parents agreed to send me to United States when I was still eighteen years old. I knew they were not happy to see me get on the plane, and now I understand how dif- ¯cult it must have been for them. I think they were very brave, and appreciate their unconditional love and encouragement. My sister shares many similar interest with me including astrophysics, and it is truly amazing how close we are. I appreciate my cats, Morpheus and Persephone, for their unassuming nature that have given me comfort and relaxation. At last but certainly not least, I thank my husband, Marcelo Alvarez, who are also my colleague and best friend. I can always count for his love and support which has been tremendous help for me. Our scienti¯c discussion has been stimulating, which I sincerely enjoy. He is truely a special person for me, and I thank him for taking steps in our life together. vii The Role of Rotation and Magnetic Fields in a Core Collapse Supernova Publication No. Shizuka Akiyama, Ph.D. The University of Texas at Austin, 2006 Supervisor: John Craig Wheeler While the process that converts implosion into explosion in core col- lapse supernovae is poorly understood, their observed asphericity provides new constraints on the physics of these events. Since pulsars are rotating and mag- netized neutron stars, there is no doubt that rotation and magnetic ¯elds are inherent to the exploding engine. We have shown that magnetic ¯eld ampli¯ca- tion is an inevitable by{product of the di®erential rotation that accompanies core{collapse. We performed 1D core{collapse simulations of rotating iron cores with various rotational pro¯les and velocities. We found that di®erential rotation was a generic feature of rotating iron core collapse. As a result, the magnetorotational instability (MRI) generates magnetic ¯elds of order 1015¡17 G in a few tens of milliseconds where the negative shear is the strongest. Al- though magnetic ¯elds of order 1015¡17 G are very strong, they are not strong viii enough to modify the equation of state of degenerate electron gas near the proto{neutron star. The corresponding MHD luminosity available is 1052 » erg s¡1, which can modify the explosion dynamics if the power is sustained for a fraction of a second. When rotational e®ects are included, we found that there is a critical iron core rotation rate that gives the most rapidly rotating proto{neutron star, faster than which the rotational velocity of the proto{neutron star decreases due to centrifugal support. This non{monotonic behavior of post{collapse core rotation suggests that the progenitor of the most rapidly rotating proto{ neutron star is not the most rapidly rotating iron core, but that those iron cores with nearly the critical initial rotation rate may produce the maximum proto{neutron star rotation, the strongest magnetic ¯elds, and the most ro- bust supernova explosions. Even small rotation may induce non{axisymmetric instabilities, which drive magneto{acoustic flux in to the mantle, transporting enegy out of the proto{neutron star to the region near the stalled shock. Fur- ther implications for rotation and magnetic ¯elds, pulsars and magnetars, and jet formation mechanisms are discussed. ix Table of Contents Acknowledgments v Abstract viii List of Tables xiii List of Figures xiv Chapter 1. Introduction 1 1.1 Outline of Dissertation . 9 Chapter 2. The Magnetorotational Instability in Core Collapse Supernova Explosions 11 2.1 Introduction . 12 2.2 Method . 17 2.2.1 Angular Velocity Pro¯le . 18 2.2.2 Magnetic Field . 25 2.2.2.1 Saturation Fields . 27 2.2.2.2 Time Dependent Calculation . 34 2.2.3 MHD Power . 35 2.3 Results . 36 2.3.1 Initial Di®erential Rotation Case . 43 2.3.2 Initial Solid Body Rotation Case . 52 2.3.3 MHD Outflow Power . 55 2.4 Discussion and Conclusions . 57 x Chapter 3. E®ects of Super{Strong Magnetic Fields in a Core Collapse Supernova 71 3.1 Introduction . 71 3.2 Background . 73 3.3 Calculations . 75 3.4 Discussion . 79 Chapter 4. The Non{Monotonic Dependence of Supernova and Remnant Formation on Progenitor Rotation 80 4.1 Introduction . 81 4.2 Qualitative Non{monotonic Behavior and a Simple Model . 84 4.3 Time{Dependent Behavior with Varying Initial Angular Mo- mentum . 86 4.4 Summary and Conclusions . 98 Chapter 5. De{leptonization and Non{Axisymmetric Instabili- ties in Core Collapse Supernovae 110 5.1 Introduction . 110 5.2 Non{Axisymmetric Modes in Neutron Stars . 111 5.3 The De{leptonization Phase . 117 5.4 Conclusions . 126 Chapter 6. On Accuracy and Precision 129 6.1 Errors in Numerical Simulations { Accuracy and Precision . 130 6.2 Sources of Errors . 131 6.2.1 Rounding Error . 134 6.3 Propagation of Error . 138 6.4 Portability . 142 6.5 Veri¯cation . 144 6.5.1 Implementation of the COLLAPSE code . 145 6.5.1.1 Energy Conservation . 147 6.5.1.2 Adding Rotation and Magnetic Fields . 157 6.5.2 Convergence Tests . 163 6.5.2.1 Calibration between machines . 165 xi 6.5.2.2 Time Step Convergence . 172 6.5.2.3 Spatial Resolution Convergence . 178 6.5.2.4 Optimization and Parallelization . 187 6.5.3 Veri¯cation of Results in Earlier Work . 190 Chapter 7. Conclusion 198 Appendix 204 Appendix A. Timeline for advance of supernova knowledge 205 Bibliography 210 Vita 228 xii List of Tables 4.1 Parameters of the models calculated . 89 6.1 Speci¯cations of machines used . 166 6.2 Calibration run data . 171 6.3 Parameters for time resolution convergence .
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