A COMPREHENSIVE STUDY OF SUPERNOVAE MODELING by Chengdong Li BS, University of Science and Technology of China, 2006 MS, University of Pittsburgh, 2007 Submitted to the Graduate Faculty of the Dietrich School of Arts and Sciences in partial fulfillment of the requirements for the degree of Doctor of Philosophy University of Pittsburgh 2013 UNIVERSITY OF PITTSBURGH PHYSICS AND ASTRONOMY DEPARTMENT This dissertation was presented by Chengdong Li It was defended on January 22nd 2013 and approved by John Hillier, Professor, Department of Physics and Astronomy Rupert Croft, Associate Professor, Department of Physics Steven Dytman, Professor, Department of Physics and Astronomy Michael Wood-Vasey, Assistant Professor, Department of Physics and Astronomy Andrew Zentner, Associate Professor, Department of Physics and Astronomy Dissertation Director: John Hillier, Professor, Department of Physics and Astronomy ii Copyright ⃝c by Chengdong Li 2013 iii A COMPREHENSIVE STUDY OF SUPERNOVAE MODELING Chengdong Li, PhD University of Pittsburgh, 2013 The evolution of massive stars, as well as their endpoints as supernovae (SNe), is important both in astrophysics and cosmology. While tremendous progress towards an understanding of SNe has been made, there are still many unanswered questions. The goal of this thesis is to study the evolution of massive stars, both before and after explosion. In the case of SNe, we synthesize supernova light curves and spectra by relaxing two assumptions made in previous investigations with the the radiative transfer code cmfgen, and explore the effects of these two assumptions. Previous studies with cmfgen assumed γ-rays from radioactive decay deposit all energy into heating. However, some of the energy excites and ionizes the medium. A new solver is developed to include these non-thermal excitation and ionization processes. Non-thermal excitation and ionization are crucial for forming some lines, especially Hα in the nebular phase. To investigate non-thermal effects, a comparison is made between models with, and without, the non-thermal solver. Benchmarking the solver is done by comparing the non-thermal models with observations of SN 1987A. Satisfactory agreement is achieved and possible problems are discussed. With the new solver, future studies will shed light on the mixing of material between layers of different composition in supernova explosions and put further constraints on supernova explosion models. Hubble expansion is a good approximation for most types of SNe, except Type II-P. Red supergiants are widely accepted to be the progenitors of Type II-P SNe and they have radii of hundreds to thousands of times larger than that of the Sun. Type II-P SNe \memorize" their large radii at the time of explosion for several weeks and material is still being accelerated. A time-dependent fully relativistic solver is developed to handle such cases. iv TABLE OF CONTENTS PREFACE ......................................... xxiii 1.0 INTRODUCTION ................................. 1 1.1 EVOLUTION OF MASSIVE STARS ..................... 1 1.1.1 Stellar evolution ............................. 1 1.1.2 Massive stars ............................... 3 1.2 CLASSIFICATION OF SUPERNOVAE ................... 5 1.3 THE IMPORTANCE OF CORE-COLLAPSE SUPERNOVAE ....... 11 1.4 THE PROBLEMS OF CORE-COLLAPSE SUPERNOVAE ......... 15 1.4.1 Progenitor problems ........................... 15 1.4.2 Explosion problems ............................ 19 1.4.3 Mixing problems ............................. 21 1.5 ASYMMETRY OF CORE-COLLAPSE SUPERNOVAE .......... 24 1.6 OUTLINE OF THE THESIS ......................... 25 2.0 RADIATION TRANSPORT THEORY .................... 27 2.1 THE RADIATIVE TRANSFER EQUATION ................ 27 2.1.1 The specific intensity ........................... 27 2.1.2 The radiative transfer equation ..................... 27 2.1.3 Sources of opacity and emissivity .................... 29 2.2 MOMENTS OF THE TRANSFER EQUATION ............... 29 2.2.1 Moments of the radiation field ..................... 29 2.2.2 Scattering problem ............................ 30 2.2.3 Moments of the transfer equation .................... 31 v 2.2.4 The boundary conditions ........................ 32 2.3 THE STATISTICAL AND RADIATIVE EQUILIBRIUM EQUATIONS .. 32 2.3.1 LTE VS Non-LTE ............................ 32 2.3.2 The statistical equilibrium equations .................. 33 2.3.3 The radiative equilibrium equation ................... 34 2.4 THE RADIATIVE TRANSFER CODE cmfgen .............. 34 2.4.1 Super levels ................................ 36 2.4.2 The elimination scheme ......................... 36 2.4.3 Fully Non-LTE .............................. 37 2.4.4 Time-dependence ............................. 38 2.4.5 Link to a hydrodynamical model .................... 42 3.0 PART I. NONTHERMAL EXCITATION AND IONIZATION IN SU- PERNOVAE ..................................... 43 3.1 WHY WITH NON-THERMAL EXCITATION AND IONIZATION .... 43 3.2 THE NON-THERMAL SOLVER ....................... 44 3.2.1 The Spencer-Fano Equation ....................... 44 3.2.2 Ionization cross sections ......................... 47 3.2.3 Excitation cross sections ......................... 49 3.3 The hydrodynamical input ........................... 52 3.4 The non-thermal model ............................. 53 3.4.1 The degradation spectrum ........................ 54 3.4.2 Number density of non-thermal electrons ................ 55 3.4.3 Energy fraction of the three channels .................. 56 3.4.4 Excitation and ionization ........................ 57 3.5 Non-thermal vs thermal models ........................ 59 3.5.1 Comparison of the temperature structure ............... 59 3.5.2 Controlling processes for H i and He i lines .............. 60 3.5.3 Comparison of optical and IR spectra ................. 66 3.5.4 Comparison of the spectral evolution .................. 68 3.6 The influence of Fe i .............................. 70 vi 3.7 Comparison with the observations ....................... 72 3.7.1 The synthetic and observed light curves ................ 72 3.7.2 Spectral comparison ........................... 75 3.7.3 Comparison of the spectral evolution .................. 77 3.8 UNCERTAINTIES ............................... 77 3.8.1 Impact excitation and ionization cross sections ............ 77 3.8.2 Emax for high energy electrons ...................... 81 3.8.3 The time-dependence effects on non-thermal processes ........ 81 3.9 DISCUSSION .................................. 82 3.10 CONCLUSION ................................. 84 4.0 PART II. FULLY RELATIVISTIC RADIATIVE TRANSFER ..... 87 4.1 DEVIATION FROM HUBBLE EXPANSION ................ 87 4.2 TRANSFER EQUATIONS IN THE FULLY RELATIVISTIC FORM ... 88 4.3 INITIAL SETUP ................................ 92 4.4 TESTING .................................... 93 4.4.1 Solution to homologous models ..................... 93 4.4.2 Departure coefficients .......................... 95 4.4.3 Ejecta temperature ............................ 97 4.4.4 Global energy constraint ......................... 100 4.5 MODEL EVOLUTION ............................. 101 4.6 LIGHT CURVES AND SPECTRAL EVOLUTION ............. 105 4.6.1 Bolometric and multi-band light curves ................. 105 4.6.2 Spectral evolution ............................ 106 4.7 DISCUSSION .................................. 106 4.7.1 Bias of distance measurements ..................... 106 4.8 CONCLUSIONS ................................ 108 5.0 PART III. ETA CARINAE ........................... 110 5.1 INTRODUCTION ............................... 110 5.2 OPTICAL MAPPING OF THE HOMUNCULUS .............. 113 5.3 THE POSITIONAL APPEARANCES OF HYDROGEN PROFILES ... 115 vii 5.4 THE EQUIVALENT WIDTH MAP OF Hα ................. 117 5.4.1 Calculation of EW and uncertainty ................... 118 5.4.2 Positional variation of the EW map ................... 120 5.4.3 The Equatorial disk and NW lobe ................... 121 5.4.4 SE lobe .................................. 124 5.4.5 Core region ................................ 124 5.4.6 The EW \sword" ............................. 125 5.4.7 The pixel-to-pixel variation ....................... 126 5.4.8 Interpretation of the EW map ...................... 128 5.4.8.1 The NW lobe .......................... 128 5.4.8.2 The SE lobe ........................... 131 5.4.8.3 Pixel-to-pixel variations ..................... 133 5.5 Absorption constraints on the wind structure ................. 134 5.5.1 P Cygni absorption in the SE lobe ................... 134 5.5.2 Abnormality of the P Cygni absorption ................ 136 5.6 Optical depth of the Homunculus ....................... 141 5.7 CONCLUSION ................................. 146 6.0 PART IV. FUNDAMENTAL PARAMETERS AND THE EUV FLUX OF ϵ CANIS MAJORIS ............................. 149 6.1 INTRODUCTION ............................... 149 6.2 OBSERVATIONAL DATA ........................... 151 6.3 MODELS .................................... 154 6.4 RESULTS .................................... 155 6.4.1 Balmer line wings fitting ......................... 155 6.4.2 Balmer jump ............................... 156 6.4.3 Equivalent widths of silicon lines .................... 159 6.4.4 Spectral energy distribution ....................... 161 6.5 DISCUSSION .................................. 167 6.5.1 Continuum determination of echelle spectra .............. 167 6.5.2 Microturbulence ............................. 168 viii 6.5.3 Mass loss ................................. 168 6.5.4 Reddening ...............................