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Towards Simulations of Binary Neutron Star Mergers and Core- Collapse Supernovae with Genasis

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Towards Simulations of Binary Neutron Star Mergers and Core- Collapse Supernovae with Genasis University of Tennessee, Knoxville TRACE: Tennessee Research and Creative Exchange Doctoral Dissertations Graduate School 8-2010 Towards Simulations of Binary Neutron Star Mergers and Core- Collapse Supernovae with GenASiS Reuben Donald Budiardja University of Tennessee - Knoxville, [email protected] Follow this and additional works at: https://trace.tennessee.edu/utk_graddiss Part of the Fluid Dynamics Commons, Numerical Analysis and Scientific Computing Commons, and the Stars, Interstellar Medium and the Galaxy Commons Recommended Citation Budiardja, Reuben Donald, "Towards Simulations of Binary Neutron Star Mergers and Core-Collapse Supernovae with GenASiS. " PhD diss., University of Tennessee, 2010. https://trace.tennessee.edu/utk_graddiss/781 This Dissertation is brought to you for free and open access by the Graduate School at TRACE: Tennessee Research and Creative Exchange. It has been accepted for inclusion in Doctoral Dissertations by an authorized administrator of TRACE: Tennessee Research and Creative Exchange. For more information, please contact [email protected]. To the Graduate Council: I am submitting herewith a dissertation written by Reuben Donald Budiardja entitled "Towards Simulations of Binary Neutron Star Mergers and Core-Collapse Supernovae with GenASiS." I have examined the final electronic copy of this dissertation for form and content and recommend that it be accepted in partial fulfillment of the equirr ements for the degree of Doctor of Philosophy, with a major in Physics. Michael W. Guidry, Major Professor We have read this dissertation and recommend its acceptance: Christian Y. Cardall, Soren Sorensen, George Siopsis, Jim Chambers Accepted for the Council: Carolyn R. Hodges Vice Provost and Dean of the Graduate School (Original signatures are on file with official studentecor r ds.) To the Graduate Council: I am submitting herewith a dissertation written by Reuben Donald Budiardja entitled “Towards Simulations of Binary Neutron Star Mergers and Core-Collapse Supernovae with GenASiS.” I have examined the final electronic copy of this dissertation for form and content and recommend that it be accepted in partial fulfillment of the requirements for the degree of Doctor of Philosophy, with a major in Physics. Michael Guidry, Major Professor We have read this dissertation and recommend its acceptance: Christian Y. Cardall Soren Sorensen George Siopsis Jim Chambers Accepted for the Council: Carolyn R. Hodges Vice Provost and Dean of the Graduate School (Original signatures are on file with official student records.) Towards Simulations of Binary Neutron Star Mergers and Core-Collapse Supernovae with GenASiS A Dissertation Presented for the Doctor of Philosophy Degree The University of Tennessee, Knoxville Reuben Donald Budiardja August 2010 c by Reuben Donald Budiardja, 2010 All Rights Reserved. ii Acknowledgements I would like to thank my advisor Mike Guidry, first for introducing me to the fascinating world of computational astrophysics and supernova science when I visited the departmental open house before I enrolled the graduate program. That got me hooked. I would also like to thank him for the support and guidance I received throughout the years of my graduate career. I would like to thank my scientific advisor Christian Cardall for all his support and guidance in the process of this work. I enjoyed the many long hours of our ‘pair programming’ and discussion sessions, in which he is always gracious and patient in explaining difficult concepts to me. His advises and ideas to the seemingly difficult problems are invaluable. Trying to mimic how he solves problems have in a way shape me in my development as an aspiring scientist. I learned a great deal from many insightful discussions with Eirik Endeve. Eirik has always been willing to take the time to explain things I did not understand, answer my questions thoroughly, and help me troubleshoot our code. This work would not be possible without Eirik’s many contributions, suggestions, and support. Thanks also to everyone else in our research group, especially our group leader Tony Mezzacappa, Bronson Messer, Raph Hix, and Eric Lents. They have provided a very supportive environment that makes this work a lot of fun. I am looking forward to our future collaborations. My deepest gratitude goes to my parents. I am who I am today because of their love to me and what they taught me in life. They have sacrificed a lot to make sure that I could iii get the highest education and becomes whatever I aspire to be. Thank you for sending me abroad, letting me pursue my dreams, and supporting me in whatever I do. Finally, to my wife, Maudy, the last five years have been the most wonderful time in my life. Thinking that I will spend the rest of my life with you always brings me joy. Thank you for all your support, understanding, and patience you have given me throughout these years, especially during the completion of my graduate career. I could not have done it without you. iv “The most incomprehensible thing about the world is that it is comprehensible.” – Albert Einstein “God is the unrestricted act of understanding, the eternal rapture glimpsed in every Archimedean cry of Eureka.” – Bernard Lonergan v Abstract This dissertation describes the current version of GenASiS and reports recent progress in its development. GenASiS is a new computational astrophysics code built for large-scale and multi-dimensional computer simulations of astrophysical phenomena, with primary emphasis on the simulations of neutron star mergers and core-collapse supernovae. Neutron star mergers are of high interest to the astrophysics community because they should be the prodigious source of gravitation waves and the most promising candidates for gravitational wave detection. Neutron star mergers are also thought to be associated with the production of short-duration, hard-spectral gamma-ray bursts, though the mechanism is not well understood. In contrast, core-collapse supernovae with massive progenitors are associated with long-duration, soft-spectral gamma-ray bursts, with the ‘collapsar’ hypothesis as the favored mechanism. Of equal interest is the mechanism of core-collapse supernovae themselves, which has been in the forefront of many research efforts for the better half of a century but remains a partially-solved mystery. In addition supernovae, and possibly neutron star mergers, are thought to be sites for the r-process nucleosynthesis responsible for producing many of the heavy elements. Until we have a proper understanding of these events, we will have only a limited understanding of the origin of the elements. These questions provide some of the scientific motivations and guidelines for the development of GenASiS. In this document the equations and numerical scheme for Newtonian and relativistic magnetohydrodynamics are presented. A new FFT-based parallel solver for Poisson’s equation in GenASiS are described. Adaptive mesh refinement in GenASiS, and a novel way to solve Poisson’s equation on a mesh with refinement based on a vi multigrid algorithm, are also presented. Following these descriptions, results of simulations of neutron star mergers with GenASiS such as their evolution and the gravitational wave signals and spectra that they generate are shown. In the context of core-collapse supernovae, we explore the capacity of the stationary shock instability to generate magnetic fields starting from a weak, stationary, and radial magnetic field in an initially spherically symmetric fluid configuration that models the stalled shock in the post-bounce supernova environment. Our results show that the magnetic energy can be amplified by almost 4 orders of magnitude. The amplification mechanisms for the magnetic fields are then explained. vii Contents List of Tables xii List of Figures xiii List of Attachments xxvi List of Abbreviations xxvii 1 Introduction1 1.1 Scientific Background.............................1 1.1.1 Observables..............................2 1.1.1.1 Gamma-ray Bursts.....................2 1.1.1.2 Gravitational Waves....................4 1.1.2 Phenomena..............................6 1.1.2.1 Core-collapse Supernovae.................6 1.1.2.2 Binary Neutron Star Mergers...............9 1.2 Computational Challenges.......................... 12 2 Fluid and Magnetic Field Evolution 16 2.1 Numerical Schemes.............................. 18 2.1.1 Newtonian Hydrodynamics..................... 18 2.1.2 Relativistic Hydrodynamics..................... 22 2.1.3 Newtonian Magnetohydrodynamics................. 24 viii 2.1.4 Relativistic Magnetohydrodynamics................. 28 2.2 Equation of State............................... 31 2.3 Parallel Implementation............................ 32 2.4 Numerical Test Problems........................... 35 2.4.1 Newtonian Riemann Shock Tube Problem.............. 38 2.4.1.1 Analytic Solution..................... 38 2.4.1.2 Numerical Solution.................... 42 2.4.2 Newtonian Magnetized Shock Tube Problem............ 43 2.4.3 Relativistic Riemann Shock Tube Problems............. 44 2.4.3.1 1D Relativistic Blast Waves................ 44 2.4.3.2 1D Shock Tube with Non-zero Velocity.......... 49 2.4.3.3 2D Relativistic Shock Tube................ 51 2.4.4 Relativistic Magnetized Shock Tube Problems........... 53 2.4.4.1 1D Compound Wave.................... 53 2.4.4.2 1D Magnetized Relativistic Blast Waves......... 53 2.4.5 Circularly-Polarized Alfven` Wave.................. 57 2.4.6 Relativistic Circularly Polarized Alven` Wave............ 61 3 Poisson’s
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