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The Evolutionary Pathways of Tidal Disruption Events: from Stars to Debris Streams, Accretion Disks, and Relativistic Jets

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The Evolutionary Pathways of Tidal Disruption Events: from Stars to Debris Streams, Accretion Disks, and Relativistic Jets The Evolutionary Pathways of Tidal Disruption Events: from Stars to Debris Streams, Accretion Disks, and Relativistic Jets by E. R. Coughlin B.S., Lehigh University, 2011 M.S., University of Colorado at Boulder, 2013 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 2016 This thesis entitled: The Evolutionary Pathways of Tidal Disruption Events: from Stars to Debris Streams, Accretion Disks, and Relativistic Jets written by E. R. Coughlin has been approved for the Department of Astrophysical and Planetary Sciences Prof. Mitchell C. Begelman Prof. Philip J. Armitage Prof. Andrew J. Hamilton Prof. Mark Rast Prof. Oliver DeWolfe 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. Coughlin, E. R. (Ph.D., Astrophysics) The Evolutionary Pathways of Tidal Disruption Events: from Stars to Debris Streams, Accretion Disks, and Relativistic Jets Thesis directed by Prof. Mitchell C. Begelman Tidal disruption events, which occur when a star is destroyed by the gravitational field of a supermassive black hole, are unique probes of the inner regions of galaxies. In this thesis we explore various stages of the tidal disruption process, in an attempt to relate the observable signatures of tidal disruption events to the properties of the disrupted star and the black hole. We use numerical techniques to study the long-term evolution of the debris streams produced from tidal disruption events, showing that they can be gravitationally unstable and, as a result of the instability, frag- ment into small-scale, localized clumps. The implications of this finding are discussed, and we investigate how the thermodynamic properties of the gas comprising the stream affect the nature of the instability. We derive an analytic model for the structure of tidally-disrupted, stellar debris streams, and we compare the predictions of our model to numerical results. We present a model for the accretion disk that forms from a tidal disruption event when the accretion rate surpasses the Eddington limit of the supermassive black hole, showing that these disks are puffed up into quasi- spherical envelopes that are threaded by bipolar, relativistic jets. We compare the predictions of this model to observations of the jetted tidal disruption event Swift J1644+57. Finally, we derive, from the relativistic Boltzmann equation, the general relativistic equations of radiation hydrody- namics in the viscous limit, which characterize the interaction between radiation and matter when changes in the fluid over the photon mean free path are small. Our results demonstrate that, in contrast to previous works, a radiation-dominated fluid does in fact possess a finite bulk viscosity and a correction to the comoving energy density. Using the general relativistic equations of radia- tion hydrodynamics in the viscous limit, we present two models to describe the interaction between a relativistic jet launched during a tidal disruption event and its surroundings. These models show iv that regions of very large shear that arise between the fast-moving outflow and the surrounding envelope possess fewer scatterers and a harder photon spectrum, meaning that observers looking \down the barrel of the jet" infer vastly different properties of the outflow than those who look off-axis. Dedication This thesis is dedicated to my wonderful wife Sarah and all of her sass. vi Acknowledgements First I would like to thank my advisor, Mitch Begelman, for taking me on as one of his students. In addition to providing crucial insights at various stages of the projects contained in this thesis, he has been thoroughly supportive of my research endeavors and, especially during my first year as a graduate student, provided me the time necessary to learn the subject matter that comprises my work. By giving me the (guided) freedom to pursue my own lines of reasoning and thought he has been fundamental to my growth as a scientist. I would also like to thank Chris Nixon and Phil Armitage, with whom I have had numerous enlightening conversations about astrophysics. They have also been invaluable to the numerical aspects of my research, and they contributed significantly to the improvement of my disc golf game through the countless rounds we played at Valmont. Without the love and support of my parents, Kathleen Harley and Robert Coughlin, none of this would have been possible, and to them both I am eternally grateful. By allowing me to pursue my dreams they have made this thesis a reality. My grandparents Richard and Joan Huber (Gingop and Ganga) have been inspirational to much of my work; they serve as two role models against whom I measure my success as a human being. My in-laws, Robert and Tina Berger, have been incredibly loving and kind to me since the day we first met (c. March 2006) and have always supported me (and haven't complained too openly about the fact that I stole their daughter and took her to Colorado). I'd also like to thank my stepdad, Glenn Harley, for making the 27-hour drive out to Colorado with me, encouraging me in my academic pursuits, and being a great role model. vii The friends I met at the University of Colorado made graduate school a fun and enjoyable experience. I had innumerable great times with my housemates, Chris Fowler, Katy Goodrich, Jen Kulow, and Eddy Barratt (and, at an earlier epoch, Matt McJunkin and Seth Jacobson). I thank Greg Salvesen and Susanna Kohler for enlivening the office, generating fruitful discussions, and adorning my wall with pictures of youthful Mitch. I am grateful to Grant Buckingham, Devin Silvia, Jordan Mirocha, and Marek Slipski for the great times we had playing ultimate. Finally, last but in no way least, I thank my wife Sarah Coughlin for not only tolerating me since we met in high school, but for being the supportive, encouraging partner I needed throughout the completion of this thesis. During my time in graduate school she never once doubted me (even if I did) and kept me sane. Without her none of this would have been possible. viii Contents Chapter 1 Introduction 1 2 Gravitationally Unstable Streams 11 2.1 Introduction . 11 2.2 Self-gravity . 13 2.3 Simulation setup . 15 2.4 Results . 16 2.5 Discussion and conclusions . 21 3 Post-periapsis Pancakes: Sustenance for Self-gravity in Tidal Disruption Events 25 3.1 Introduction . 25 3.2 The impulse approximation . 27 3.2.1 Equations . 29 3.2.2 Solutions . 32 3.3 Numerical simulations . 37 3.3.1 Simulation setup and initial conditions . 37 3.3.2 Results . 38 3.4 Discussion . 47 3.4.1 Is the pancake necessary? . 52 3.5 Implications . 55 ix 3.5.1 Fragmentation . 55 3.5.2 Fallback rate features . 57 3.5.3 Clump fates . 61 3.5.4 Entropy . 62 3.6 Summary and conclusions . 63 4 On the Structure of Tidally-disrupted Stellar Debris Streams 68 4.1 Introduction . 68 4.2 Velocity distribution . 69 4.2.1 Self-similar velocity profile . 69 4.2.2 Radial positions . 73 4.3 Stream width . 79 4.3.1 Quasi-hydrostatic width . 80 4.3.2 Shear dominated . 81 4.3.3 Approximate, full solution . 82 4.4 Density . 83 4.5 Density scalings and fragmentation conditions . 91 4.5.1 Marginally bound material . 91 4.5.2 Unbound material . 93 4.5.3 Bound material and overall scalings . 95 4.6 Discussion . 97 4.6.1 The neglect of angular momentum . 98 4.6.2 Comparison with Kochanek (1994) . 99 4.6.3 To fragment or not to fragment? . 103 4.6.4 A more realistic entropy prescription . 106 4.7 Summary and conclusions . 110 x 5 Hyperaccretion During Tidal Disruption Events: Weakly Bound Debris Disks and Jets 113 5.1 Introduction . 113 5.2 Zero-Bernoulli accretion model . 117 5.2.1 Gyrentropic flow . 119 5.2.2 Self-similar solutions . 120 5.3 ZEBRA models of TDE debris disks . 122 5.4 Jet properties and temporal evolution . 128 5.4.1 Inner regions of the accretion disk . 128 5.4.2 Accretion rate and jet power . 137 5.4.3 Time-dependent analysis . 138 5.4.4 Swift J1644+57 . 156 5.5 Discussion and conclusions . 159 6 The General Relativistic Equations of Radiation Hydrodynamics in the Viscous Limit 164 6.1 Introduction . 164 6.2 Relativistic Boltzmann equation . 168 6.3 Diffusion approach to the transport equation . 171 6.4 Relativistic, diffusive equations of radiation hydrodynamics . 177 6.5 Perturbation analysis . 182 6.6 Discussion and Conclusions . 189 7 Viscous boundary layers of radiation-dominated, relativistic jets. I. The two-stream model195 7.1 Introduction . 195 7.2 Governing equations . 198 7.3 Two-stream boundary layer . 200 7.3.1 Basic setup . 201 7.3.2 Boundary layer equations . 201 7.3.3 Self-similar approximation . 203 xi 7.3.4 Solutions . 207 7.4 Discussion . 215 7.5 Summary and conclusions . 218 8 Viscous boundary layers of radiation-dominated, relativistic jets. II. The free-streaming jet model 221 8.1 Governing equations . ..
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