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UC Santa Cruz UC Santa Cruz Electronic Theses and Dissertations UC Santa Cruz UC Santa Cruz Electronic Theses and Dissertations Title Hydrodynamical Simulations of Strong Tides in Astrophysical Systems Permalink https://escholarship.org/uc/item/241342m5 Author Guillochon, James Francis Publication Date 2013 Peer reviewed|Thesis/dissertation eScholarship.org Powered by the California Digital Library University of California UNIVERSITY OF CALIFORNIA SANTA CRUZ HYDRODYNAMICAL SIMULATIONS OF STRONG TIDES IN ASTROPHYSICAL SYSTEMS A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in ASTRONOMY & ASTROPHYSICS by James Guillochon June 2013 The Dissertation of James Guillochon is approved: Professor Enrico Ramirez-Ruiz, Chair Professor Douglas N. C. Lin Professor Daniel Kasen Dean Tyrus Miller Vice Provost and Dean of Graduate Studies Copyright c by James Guillochon 2013 Table of Contents List of Figures vi List of Tables ix Abstract x Dedication xii Acknowledgments xiii 1 Introduction1 2 Shock Breakout from Stars Compressed by Strong Tides8 2.1 Introduction....................................8 2.2 Numerical Method and Initial Model....................... 10 2.3 Hydrodynamics of Stellar Disruption....................... 12 2.3.1 Initial Approach............................. 12 2.3.2 Rebound................................. 13 2.3.3 Free Expansion.............................. 16 2.4 Shock Breakout.................................. 18 2.4.1 Self-Similar Solutions.......................... 19 2.5 Observability................................... 26 2.5.1 X-ray Transient.............................. 26 2.5.2 Gravitational Wave Signal........................ 32 2.6 Conclusion.................................... 33 3 Surface Detonations in Roche Lobe Filling Double Degenerate Systems 35 3.1 Introduction.................................... 35 3.2 Numerical Method and Initial Models...................... 37 3.3 Accretion Stream Instabilities........................... 40 3.4 Surface Detonations................................ 42 3.5 Results and Discussion.............................. 45 iii 4 Tidal Ejection and Disruption of Giant Planets 49 4.1 Introduction.................................... 49 4.2 Modeling Planetary Disruption.......................... 52 4.2.1 Previous Disruption Models....................... 52 4.2.2 Our Approach............................... 56 4.3 Simulation Results................................ 58 4.3.1 Single Passage Encounters........................ 58 4.3.2 Multiple Passage Encounters....................... 61 4.3.3 The Role of Chaos............................ 66 4.3.4 Debris Accreted by the Star....................... 70 4.4 Discussion..................................... 72 4.4.1 The Jupiter Exclusion Zone....................... 72 4.4.2 Stellar Spin-Up from Planetary Disruption................ 77 4.4.3 Observational Signatures......................... 82 4.5 Conclusions.................................... 84 4.5.1 Limitations and Future Directions.................... 84 4.5.2 The Fates of Scattered Jupiters...................... 86 5 The Importance of the Impact Parameter and Stellar Structure for the Tidal Dis- ruption of Stars 95 5.1 Introduction.................................... 95 5.2 Method...................................... 98 5.2.1 Parameter Study............................. 100 5.2.2 Calculation of ∆M and M_ ........................ 103 5.3 Hydrodynamics of the tidal disruption of MS stars................ 106 5.3.1 The Boundary Between Survival or Destruction............. 107 5.3.2 Characteristic features of M_ ....................... 112 5.3.3 The Influence of Stellar Structure.................... 122 5.3.4 Long-term evolution of M_ ........................ 125 5.4 Discussion..................................... 127 5.4.1 Can γ and β be determined a posteriori?................. 128 5.4.2 Future work................................ 131 6 PS1-10jh: The Case for the Disruption of a Solar-Type Star 135 6.1 Introduction.................................... 135 6.2 Method...................................... 138 6.2.1 Hydrodynamical Simulations...................... 138 6.2.2 Fitting TDE Observations........................ 141 6.3 Hydrodynamics of Post-Disruption Debris.................... 144 6.3.1 Debris Stream with Self-Gravity..................... 144 6.3.2 Dissipative Effects within the Nozzle.................. 149 6.3.3 Is the Debris Disk Dissipative Enough?................. 159 6.4 The Relationship Between Steadily-Accreting AGN and TDE Debris Disks.. 160 iv 6.4.1 The Conversion of Mass to Light.................... 160 6.4.2 Source of Broad Emission Lines..................... 163 6.5 A Generalized Model for the Observational Signatures of TDEs........ 168 6.5.1 Model description and free parameters.................. 169 6.5.2 Using the existence/absence of emission lines and their properties to constrain TDEs.............................. 178 6.6 Model Fitting of PS1-10jh, a Prototypical Tidal Disruption........... 181 6.6.1 Available Data.............................. 181 6.6.2 Bare Disk Model............................. 182 6.6.3 Fits to Generalized Model With Reprocessing Layer.......... 183 6.7 Discussion..................................... 188 6.7.1 Arguments against the helium star interpretation............ 188 6.7.2 Inclusion of priors............................ 189 6.7.3 How BLRs can help us understand TDEs................ 190 6.7.4 How TDEs can help us understand BLRs................ 191 6.7.5 Caveats and future directions....................... 191 6.7.6 Lessons Learned............................. 193 A Modified PPM Gravity Algorithm 228 B Fitting Parameters for Main-Sequence Star Disruptions 235 v List of Figures 1.1 Competing geometries proposed by Newton and Cassini for the tide raised by the Moon upon the Earth.............................2 2.1 Events in the life of a tidally-disrupted solar-type star..............9 2.2 The hydrodynamics of shock formation in the core of a tidally compressed star. 13 2.3 Histogram of the energies summed over all fluid elements during maximum compression.................................... 15 2.4 Snapshots from a hydrodynamical simulation of a deeply-penetrating tidal en- counter...................................... 17 2.5 Light curve produced by the breakout of shocks across the surface of the dis- rupted star..................................... 25 2.6 Peak luminosity and detectability of events as a function of Mh and β ..... 28 2.7 Detection rate of tidal shock breakouts as function of black hole mass..... 30 3.1 Setup of hydrodynamical model for rapidly mass-transferring double white dwarf systems...................................... 37 3.2 Dynamical timescale versus nuclear timescale and the stability of DWD systems 43 3.3 The convergence of helium detonations after ignition.............. 44 3.4 Temperature profile of accretor after initiation of helium detonation...... 47 4.1 Change in orbital energy and angular momentum after a single disruptive en- counter...................................... 52 4.2 Orbital trajectories of star and planet over the course of a multiple disruption event........................................ 53 4.3 Excitation of normal modes and mass loss in giant planets, shortly after pericenter 59 4.4 Excitation of normal modes and mass loss in giant planets, at apocenter.... 60 4.5 Fallback accretion stream formed as the result of the 8th encounter between a 1 M star and 1 MJ planet............................. 62 4.6 Pressure perturbations and spin excited by a grazing encounter with rp = 3rt .. 88 4.7 Change in orbital energy Eorb attributed to each passage as a function of rp and orbit number Norb ................................. 89 vi 4.8 Criteria leading to planet ejection given an initial periastron passage distance rp and eccentricity e ................................. 90 4.9 The evolution of two multiple encounter simulations with almost identical ini- tial conditions................................... 91 4.10 Mass loss history of multiple passage encounters for different initial values of rp 92 4.11 Possible apastrons ra for the known hot Jupiters with MP > 0:25MJ ....... 93 4.12 Changes to the stellar spin as a result of accreting tidally disrupted planets... 94 5.1 Snapshots of the density logρ for all γ = 4=3 simulations............ 101 5.2 Snapshots of logρ for all γ = 5=3 simulations.................. 102 5.3 Evolution of maximum density ρmax and bound mass Mbound as a function of time since disruption............................... 105 5.4 Fits to ∆M .................................... 109 6 5.5 Fallback accretion rate M_ onto a 10 M black hole from the disruption of a 1 M star as a function of γ and β ......................... 110 5.6 Average spread of matter post-disruption as compared to the change in orbital energy for binary disruptions........................... 114 5.7 Power-law index n of the fallback as a function of t and at t ! 1 for γ = 4=3 and γ = 5=3 stars................................. 115 5.8 Cartoon showing the gravitational effect of a surviving core on the dynamics of material that is removed from the star during a partially-disruptive encounter.. 119 5.9 Regions that contain the mass that contributes to M_ peak(t), and the evolution of M_ with time.................................... 120 5.10 Evolution of dM=dE and M_ for the disruption of a star with polytropic index γ = 5=3 and impact parameter β = 0:55...................... 122 5.11 Distribution of mass as a function
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