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Star and Planet Formation Through Cosmic Time

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Star and Planet Formation Through Cosmic Time Star and Planet Formation Through Cosmic Time By Aaron Thomas Lee A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in Astrophysics in the Graduate Division of the University of California, Berkeley Committee in charge: Professor Christopher F. McKee, Chair Adjunct Professor Richard I. Klein Professor Eliot Quataert Researcher Steven W. Stahler Professor Leo Blitz Professor James Demmel Summer 2017 Star and Planet Formation Through Cosmic Time Copyright 2017 by Aaron Thomas Lee 1 Abstract Star and Planet Formation Through Cosmic Time by Aaron Thomas Lee Doctor of Philosophy in Astrophysics University of California, Berkeley Professor Christopher F. McKee, Chair The computational advances of the past several decades have allowed theoretical astro- physics to proceed at a dramatic pace. Numerical simulations can now simulate the formation of individual molecules all the way up to the evolution of the entire universe. Observational astrophysics is producing data at a prodigious rate, and sophisticated analysis techniques of large data sets continue to be developed. It is now possible for terabytes of data to be effectively turned into stunning astrophysical results. This is especially true for the field of star and planet formation. Theorists are now simulating the formation of individual planets and stars, and observing facilities are finally capturing snapshots of these processes within the Milky Way galaxy and other galaxies. While a coherent theory remains incomplete, great strides have been made toward this goal. This dissertation discusses several projects that develop models of star and planet forma- tion. This work spans large spatial and temporal scales: from the AU-scale of protoplanetary disks all the way up to the parsec-scale of star-forming clouds, and taking place in both con- temporary environments like the Milky Way galaxy and primordial environments at redshifts of z ∼ 20. Particularly, I show that planet formation need not proceed in incremental stages, where planets grow from millimeter-sized dust grains all the way up to planets, but instead can proceed directly from small dust grains to large kilometer-sized boulders. The requirements for this model to operate effectively are supported by observations. Additionally, I draw suspicion toward one model for how you form high mass stars (stars with masses exceeding ∼ 8 M ), which postulates that high-mass stars are built up from the gradual accretion of mass from the cloud onto low-mass stars. I show that magnetic fields in star forming clouds thwart this transfer of mass, and instead it is likely that high mass stars are created from the gravitational collapse of large clouds. This work also provides a sub-grid model for computational codes that employ sink particles accreting from magnetized gas. Finally, I analyze the role that radiation plays in determining the final masses of the first stars to ever form in the universe. These stars formed in starkly different environments than stars 2 form in today, and the role of the direct radiation from these stars turns out to be a crucial component of primordial star formation theory. These projects use a variety of computational tools, including the use of spectral hydro- dynamics codes, magneto-hydrodynamics grid codes that employ adaptive mesh refinement techniques, and long characteristic ray tracing methods. I develop and describe a long characteristic ray tracing method for modeling hydrogen-ionizing radiation from stars. Ad- ditionally, I have developed Monte Carlo routines that convert hydrodynamic data used in smoothed particle hydrodynamics codes for use in grid-based codes. Both of these advances will find use beyond simulations of star and planet formation and benefit the astronomical community at large. i This thesis is dedicated to those whose love and never-faltering support made its completion possible: my sister, my parents, and Marta Belcher. ii Contents Acknowledgmentsv 1 Introduction1 1.1 Star and Planet Formation............................2 1.1.1 Contemporary Environments.......................2 1.1.2 Primordial Environments.........................4 1.2 Outline.......................................5 2 Forming Planetesimals by Gravitational Instability: I. The Role of the Richardson Number in Triggering the Kelvin-Helmholtz Instability7 2.1 Introduction....................................8 2.1.1 Basic Estimates..............................8 2.1.2 Our Study in Relation to Previous Numerical Simulations...... 10 2.1.3 The Perfect Coupling Approximation vs. The Streaming Instability vs. Tur- bulent Concentration Between Eddies.................. 11 2.1.4 Organization of this Chapter....................... 13 2.2 Methods...................................... 13 2.2.1 Equations................................. 13 2.2.2 Initial Conditions............................. 17 2.2.3 Code.................................... 19 2.2.4 Box Size and Numerical Resolution................... 19 2.3 Results....................................... 20 2.3.1 Criteria for Stability........................... 22 2.3.2 Stability as a Function of Ri, µ0, and Σd=Σg .............. 22 2.3.3 Tests at Higher Resolution, Higher Arms, and Higher vmax ....... 23 2.4 Summary and Discussion............................. 23 3 Forming Planetesimals by Gravitational Instability: II. How Dust Settles to its Marginally Stable State 34 3.1 Introduction.................................... 35 3.2 Method...................................... 40 3.3 Results....................................... 43 Contents iii 3.3.1 Solar Metallicity............................. 43 3.3.2 Metal-Rich Case: 4 × Solar Metallicity................. 44 3.4 Extensions..................................... 45 3.4.1 Bigger Box Runs............................. 45 3.4.2 Refining the Marginally Stable State Using a Modified Settling Procedure 55 3.5 Summary and Discussion............................. 56 3.5.1 How Spatially Constant is the Richardson Number?.......... 60 3.5.2 The Super-Linear Relation Between Maximum Dust-to-Gas Ratio µ0 and Bulk Metallicity Σd=Σg ....................... 61 3.5.3 Future Directions............................. 62 3.5.4 Connection to Observations and The Need For Supersolar Metallicity 63 4 Bondi-Hoyle Accretion in an Isothermal Magnetized Plasma 67 4.1 Introduction.................................... 68 4.2 Mass Accretion Rates............................... 69 4.2.1 Known Results.............................. 69 4.2.2 Alfvén-Bondi-Hoyle Accretion...................... 72 4.3 Numerical Methods................................ 74 4.4 Results....................................... 78 4.4.1 Morphology................................ 78 4.4.2 Mass Accretion Rate........................... 80 4.5 Validity of the Steady-State Approximation.................. 83 4.6 Summary and Discussion............................. 85 5 Radiative Feedback in the Formation of Population III Stars 101 5.1 Introduction.................................... 101 5.2 Numerical Methods................................ 104 5.2.1 Overall Methodology........................... 104 5.2.2 Chemistry................................. 106 5.2.3 Primordial Stellar Evolution Model................... 108 5.2.4 Ray Tracing................................ 111 5.2.5 Initial Conditions............................. 112 5.2.6 Grid Parameters and Refinement Criteria................ 113 5.3 Results....................................... 113 5.4 Summary and Future Work........................... 116 A Background Protoplanetary Disk Model 124 A.1 The Super-Linear Relation Between µ0 and Σd=Σg ............... 125 B Sink Particle Sub-grid Model 128 B.1 Sink Particle Creation.............................. 128 B.2 Sink Particle Accretion.............................. 129 _ B.2.1 Estimated Accretion Rate, Mfit ..................... 129 Contents iv _ B.2.2 The Adjusted Accretion Rate, Msink: Capping the Alfvén Velocity.. 133 B.2.3 Verifying the Algorithm for the Accretion Rate............ 134 C Ray Tracing and Ionization 139 C.1 Ray Tracing Method............................... 140 C.2 Ionization..................................... 142 C.2.1 Sub-Grid Model.............................. 144 C.2.2 Algorithm................................. 145 C.3 Tests........................................ 146 C.3.1 Photon conservation and R-Type Ionization Front Expansion..... 147 C.3.2 D-Type Ionization Front Expansion................... 148 D Monte Carlo Projection Code 154 D.1 Mapping Method................................. 156 D.2 Example & Conservation Test.......................... 158 Bibliography 161 v Acknowledgments Writing the acknowledgments section has proven to be one of the most challenging com- ponents of this dissertation. This thesis would never have even started without the support and love of countless individuals, and it is an incredible challenge to resist listing the names of every one of them here. First off, I acknowledge the support and facilities of the NSF, NASA, UCB, and any other source that assisted in the completion of the projects detailed in this thesis. Furthermore, I thank all of the employees at these institutions for the work they do. I thank my adviser, Christopher McKee, as well as other members of the UCB astronomy department, Richard Klein, Steven Stahler, and Eugene Chiang, for taking me on as a student and for teaching me how high-quality research in astrophysics is done. Your persistent demand for excellence has molded my
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