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On the Launching of Optically Thick Outflows from Massive Stars By On The Launching of Optically Thick Outflows from Massive Stars by Stephen Ro A thesis submitted in conformity with the requirements for the degree of Doctor of Philosophy Graduate Department of Astronomy & Astrophysics University of Toronto Copyright c 2017 by Stephen Ro Abstract On The Launching of Optically Thick Outflows from Massive Stars Stephen Ro Doctor of Philosophy Graduate Department of Astronomy & Astrophysics University of Toronto 2017 For decades, massive stars have been seen to lose mass at every stage of evolution. In recent years, detections of outbursts and circumstellar relics uncover transient modes emerging moments before the supernova. The goal of this thesis is to bring theoretical attention into how massive stars launch outflows. In this thesis, we study two modes of mass loss seen during rare, but critical, phases of stellar evolution. The first considers dense, steady outflows from Wolf-Rayet stars. The second considers the eruptions and explosions seen from luminous blue variables (LBVs) and Type IIn supernova (SN) progenitors. Outflows from both systems are optically thick but either radiative or adiabatic in nature. Wolf-Rayet winds are driven by strong radiative pressure on metal lines. Suppressing the outflow is shown to drastically alter the stellar structure with peculiar features including an extended radiative cavity encased in a massive shell. We construct outflow models and conclude the galactic WR population does not harbour such structures. We derive a minimum mass loss rate to launch a transonic, optically thick outflow and find the iron opacity bump to be responsible for launching WR winds. LBVs and Type IIn SN progenitors are seen to abruptly expel mass. Observational inferences suggest the rates are both exceptional and unsustainable with durations exceeding the outer envelope dynamical time. Yet, these outflows are occasionally preceded by fast motions indicative of shock acceleration. In this thesis, we explain how waves can be responsible for these dynamics. We derive an analytic solution wave ii steepening and shock formation for an inhomogeneous medium. The results suggest that any super-Eddington phenomenon driven by waves must involve shocks. Shocks form deep in the star where they are initially weak. We show how weak shocks are capable of accelerating to become strong, breakout, and produce fast ejecta using a revived semi-analytical approximation. We discuss how a train of shocks can heat a large volume of the envelope and eject significant mass. iii “You know, you blow up one sun and suddenly everyone expects you to walk on water.” - Colonel Samantha Carter, Stargate SG-1 iv Acknowledgements Graduate school can often require a spontaneous degree of diligence, discipline, and direction. Where I was unready, my friends, family, and colleagues were the reliable beacons that guided me through. Each one has given me a gift; a handful to which are described below. This thesis is dedicated to them and our fond memories. When asked for compassion and perseverance, I see my mother. She has endowed me with the moral compass and fibre to face the world. I love you, mom, and I am proud to be your son. Chris is the mentor that people wish for. He has always made me feel welcome and equal. The freedom to ask any question and pursue whatever is most interesting (within reason) is an attitude I’ll keep with me. Chris, you are a phenomenal role model and friend. Thank you for everything. Virginia is my relentless force for growth. She has witnessed my life and forged each lesson into a brick in my foundation. And, over several years, we’ve built quite the house. Wherever life takes us next, Virginia, you will always be with me. To Charles, Ilana, Jamil, Mubdi, and Rob: I am a ridiculous man, and you are the best witnesses for this truth. It is rare to find people that resonate in the ways that we do. You are my favourite people and I look forward to our next adventure together. Jamil, let’s pick one with fewer border guards and dubious knee surgeries. Also, Jimmy’s sounds good. Where would I be without Chris, Joel, Krista, and Naoya? A lot less frustrated and a lot less funny. Heidi, Lauren, Liam, and Max, thank you for living it with me. I’ll miss our arguments and laughs in the library. Also, thank you, Lee, for letting us live there (with enthusiasm). Big praises to Chun, Brent, Steph, Nick, Frank, and Shakira for making me stronger. Thank you, Marten, Chris (Thompson), and Shelley for their lessons and guidance. And, thank you Mike (Reid), Yanqin, and all of the students I’ve TA’ed for helping me become a better teacher. This is slightly unconventional, but I’d also like to acknowledge Samantha Carter, an astrophysicist from Stargate SG-1. You misled me to believe this profession uses guns and alien tech to solve problems. I am both disappointed and grateful. I love my cat, Mo, and dog, Lucky. v Contents 1 Introduction 1 1.1 Treatment of Mass Loss in Stellar Evolution . .2 1.2 Physics of Mass Loss . .3 1.2.1 Radiation and Metallicity . .3 1.2.2 Rotation . 10 1.2.3 Pulsations, Eruptions, and Explosions . 12 1.3 Summary . 15 2 Launching of Optically-Thick Radiatively Driven Winds 16 2.1 Chapter Overview . 16 2.2 Background . 17 2.3 Stellar Wind Models . 20 2.3.1 Structure equations . 21 2.3.2 Sonic point criteria . 22 2.3.3 Inner boundary: matching a hydrostatic star . 25 2.3.4 Regime of validity . 25 2.3.5 Numerical Method . 26 2.4 Results . 32 2.4.1 23 M Helium Star . 32 2.4.2 Other helium stars . 36 2.5 Inflation, Inversion, and Stability . 43 2.5.1 Convective instability . 43 2.5.2 Onset of Envelope Inflation and Extended Winds . 45 vi 2.5.3 The nature of weak WR winds . 49 2.5.4 Radiation-driven acoustic instabilities . 49 2.6 Discussion . 50 2.7 Addendum 1: The Phase Space of WR Wind Structures . 51 2.8 Addendum 2: Force Multiplier Approximation . 52 3 Shock Dynamics in Stellar Outbursts: I. Shock formation 55 3.1 Chapter Overview . 55 3.2 Background . 56 3.3 Propagation of a sound pulse . 58 3.3.1 Thermal diffusion . 60 3.4 Shock Formation . 61 3.4.1 Shock formation radius: heuristic derivation . 61 3.4.2 Detailed derivation of shock formation radius . 63 3.4.3 Maturation of the shockwave . 67 3.5 Hydrodynamic Simulations . 68 3.5.1 Planar Earth Atmosphere . 69 3.5.2 Spherical Polytropes . 72 3.6 Shock dissipation or radiative damping? . 72 3.7 Conclusion . 76 4 Shock Dynamics in Stellar Outbursts: II. Shock propagation 78 4.1 Chapter Overview . 78 4.2 Brinkley & Kirkwood Theory . 79 4.2.1 The Derivation . 80 4.2.2 Equations for Shock Propagation . 87 4.3 Numerical Simulation . 88 4.4 A Modified Brinkley & Kirkwood Theory . 90 4.5 Shock Dissipation and ‘Duds’ . 95 4.6 An Approximate Shock Formula . 98 4.7 Discussion . 98 vii 5 Shock Emergence in Supernovae 101 5.1 Chapter Overview . 101 5.2 Background . 101 5.3 Problem, method, and solutions . 103 5.3.1 Shock acceleration parameter and its limits . 104 5.4 Post-Shock Flow and Asymptotic Free Expansion . 106 5.4.1 The acceleration factor and its limits . 107 5.5 Discussion . 109 6 Conclusions & Future Work 114 6.1 Optically Thick Radiatively Driven Outflows . 114 6.2 Non-Terminal Eruptions and Explosions . 115 6.2.1 Optically Thick Adiabatic Outflows . 117 6.3 Future Work . 118 Appendices 120 A Acoustic Wave-Steepening 121 B Shock Maturation 124 Bibliography 127 viii List of Tables 3.1 Wave characteristics, planar simulations. 69 5.1 Shock acceleration index β ......................... 111 5.1 – Continued . 112 5.2 Shock acceleration factor vf =vs ....................... 113 ix List of Figures 2.1 Stellar density profiles. Light blue is by Gräfener et al. (2012), and the remaining are wind solutions across a range of mass loss rates. Arrows indicate the sonic point location for each wind model. Dashed regions indicate where the Rosseland approximation is no longer valid. 33 2.2 Temperature profile for the stellar wind solutions. Arrows indicate the sonic point location. Dashed regions indicate where the diffusion approximation is no longer valid. Note the contrast in temperature scale height between weak and strong winds. Compact wind models are truncated to temperatures above the partial ionization zone of helium (104:8 K). 34 2.3 Radius and local sound speed at the sonic point location across a range of mass loss rates. The bifurcation in behaviour does not appear in the sonic point location or velocity. 35 2.4 Wind velocity showing the bifurcation between strong, compact winds and weak, extended ones. The green line indicates the sonic point location and velocity, and dashed regions are where the Rosseland approximation 1=2 −1 becomes invalid. Note that the escape speed is 2100(2R =r) km s for the 23 M .................................... 37 2.5 Profiles of stellar wind models for M = 15; 20; 25; 30M helium stars. For figures (a) and (b), arrows indicate the respective sonic point location. For all figures, dashed-lines indicate where the Rosseland approximation is invalid. 41 x 2.6 Shown is a diagram illustrating the onset of envelope inflation and extended 4 winds for a 23 M (or L∗=M∗ = 2:7 10 (L =M )) star. The density and × temperature structure of the MESA-generated model (thick red line) and stellar wind (colours) extends from the stellar interior (bottom-right) to the surface (top-left).
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