UC Berkeley UC Berkeley Electronic Theses and Dissertations Title Numerical Investigations of Star Formation and Interstellar Clouds Permalink https://escholarship.org/uc/item/91s6x91k Author Myers, Andrew Publication Date 2013 Peer reviewed|Thesis/dissertation eScholarship.org Powered by the California Digital Library University of California Numerical Investigations of Star Formation and Interstellar Clouds By Andrew Thomas Myers A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in Physics in the Graduate Division of the University of California, Berkeley Committee in charge: Christopher McKee, Co-chair Richard Klein, Co-chair Leo Blitz Daniel Kasen Fall 2013 Numerical Investigations of Star Formation and Interstellar Clouds Copyright 2013 by Andrew Thomas Myers 1 Abstract Numerical Investigations of Star Formation and Interstellar Clouds by Andrew Thomas Myers Doctor of Philosophy in Physics University of California, Berkeley Christopher McKee, Co-chair Richard Klein, Co-chair This thesis explores several related questions on the physics of star formation and interstellar clouds. Chapter 2 addresses the remarkable independence of the stellar initial mass function to gas metallicity across a wide a range of galactic and extra-galactic environments. I perform analytic calculations that suggest the temperature structure of a centrally heated, dusty gas cloud should be relatively insensitive to the dust-to-gas ratio over the range of variation probed by observations. I support these calculations with full radiation-hydrodynamic simulations. Chapter 3 investigates the fragmentation of magnetized, massive cores via direct numerical simulation, finding that a combination of magnetic fields and protostellar heating strongly suppresses core fragmentation. These results could explain why the stellar initial mass function so closely resembles the dense core mass function, even at very high core masses. Chapter 4 analyzes the magnetic field structure around a rotationally-dominated protostellar disk formed in the above simulations. I present a map of the column density, magnetic field vectors, and outflow lobes at various length scales and viewing angles that can be compared against observations. I find that the disk begins to influence the geometry of the magnetic field on ∼ 100 AU scales, which should begin to be probed in nearby stellar cores by the next generation of radio interferometers. Chapter 5 addresses the long-standing question of the high CH+ abundance along diffuse molecular sight lines. I compute the CH+ abundance in a turbulent, diffuse molecular cloud by post-processing numerical simulations of magnetohydrodynamic turbulence. The results agree well with observations of the column + densities of CH and of rotationally-excited H2. Finally, Chapter 6 presents the results of radiation-magnetohydrodynamic simulations of star formation at the cluster scale. The results show that the magnetic field plays a role in determining the star formation rate, the degree of fragmentation, and the characteristic stellar mass. i I dedicate this dissertation to Heather. ii Contents List of Figuresv List of Tables xi Acknowledgments xii 1 Introduction1 1.1 The Initial Mass Function............................2 1.2 The Core Mass Function.............................2 1.3 The Magnetic Braking “Catastrophe”......................3 1.4 The CH+ problem.................................4 1.5 Star Formation on the Cluster Scale.......................4 2 Metallicity and the Universality of the IMF6 2.1 Introduction....................................6 2.2 Simulation Setup.................................8 2.2.1 Numerical Techniques..........................8 2.2.2 Refinement criteria............................ 11 2.2.3 Initial conditions............................. 11 2.3 Results....................................... 13 2.3.1 Temperature and density structure................... 13 2.3.2 Fragmentation and Star Formation................... 15 2.4 Discussion..................................... 18 2.4.1 Analytic Model.............................. 18 2.4.2 Comparison to simulations........................ 22 2.4.3 Predictions for star-forming regions................... 24 2.5 Conclusions.................................... 26 3 The Fragmentation of Magnetized, Massive Star-Forming Cores with Ra- diative Feedback 29 3.1 Introduction.................................... 30 3.2 Numerical Setup................................. 31 3.2.1 Equations and Algorithms........................ 31 Contents iii 3.2.2 Refinement and Sink Creation...................... 34 3.2.3 Initial and Boundary Conditions..................... 37 3.3 Results....................................... 40 3.3.1 Density Structure............................. 40 3.3.2 Magnetic Field Structure......................... 45 3.3.3 Fragmentation and Star Formation................... 45 3.3.4 Thermal Structure............................ 50 3.4 Discussion..................................... 54 3.4.1 Why do Magnetic Fields and Radiation Suppress Fragmentation?.. 54 3.4.2 Comparison to Commerçon et. al..................... 56 3.4.3 Where is Fragmentation Suppressed?.................. 58 3.5 Conclusions.................................... 58 3.6 Appendix..................................... 59 3.6.1 The MHD Truelove Condition...................... 59 4 The (Mis-)Alignment of a Protostellar Disk with the Core Magnetic Field 64 4.1 Introduction.................................... 64 4.2 Simulation Setup................................. 65 4.3 Results....................................... 66 4.4 Discussion and Conclusion............................ 69 5 The CH+ Abundance in Turbulent, Diffuse Molecular Clouds 72 5.1 Introduction.................................... 72 5.2 Methodology................................... 74 5.2.1 Model Description............................ 74 5.2.2 Scaling to Physical Units......................... 75 5.2.3 Heating and Cooling........................... 78 5.2.4 Ion-Neutral Drift............................. 80 5.2.5 Chemistry................................. 83 5.3 Results....................................... 85 5.3.1 Temperature and CH+ abundance.................... 85 5.3.2 Sight line analysis............................. 89 5.3.3 H2 Emission................................ 91 5.4 Conclusions.................................... 94 6 Star Cluster Formation in Turbulent, Magnetized Dense Clumps with Ra- diative and Outflow Feedback 96 6.1 Introduction.................................... 97 6.2 Simulations.................................... 97 6.2.1 Numerical Methods............................ 98 6.2.2 Initial Conditions............................. 99 6.3 Results....................................... 102 Contents iv 6.3.1 Global Evolution............................. 102 6.3.2 Star Formation.............................. 108 6.3.3 The Initial Mass Function........................ 112 6.3.4 The Protostellar Mass Function..................... 114 6.3.5 Core Magnetic Field Structure...................... 116 6.3.6 Turbulent Core Accretion........................ 118 6.3.7 Mass Segregation............................. 120 6.3.8 Multiplicity................................ 124 6.4 Discussion..................................... 126 6.5 Conclusions.................................... 128 Bibliography 130 v List of Figures 2.1 Projections through the simulation volumes at tff = 0:5. The left panels show the column density of the entire core, defined as R ρdx. The middle column is also the column density, zoomed in to show the middle 5000 AU. The right column shows R R the column density-weighted temperature, ρTgasdx= ρdx, at the same scale. The rows, from top to bottom, show runs “Solar," “0.2 Solar," “0.05 Solar," and “High Σ". Stars are represented by circles drawn on the plots, with the size of the circle corresponding to the size of the star. Stars with masses between 0:05M and 1M are the smallest, intermediate mass stars with 1M < m < 5M are larger, and stars with masses greater than 5M are the largest.......... 14 2.2 Star particle statistics as a function of time for all four runs. The top panel shows the total mass in stars (the top set of lines) and the mass of the most massive star (bottom, dotted set). The middle plot shows fmax, the fraction of total stellar mass that is in the most massive star. The bottom plot is the total stellar luminosity. 16 2.3 Cumulative mass distributions from all four runs at tff = 0:5. f(> m) the fraction of the total stellar mass that is in stars with masses greater than m........ 19 2.4 Temperature scaling exponent kT as a function of δ for the two different values of Σ considered in the simulations............................ 23 2.5 Temperature profiles from the simulations (dots) and analytic theory (solid lines). To show both values of Σ on the same plot, we have normalized r by the size of the core Rc. The simulations profiles are averaged over tff = 0:2 to tff = 0:5.... 25 2.6 Contours of the mean core temperature T (ρ¯) at the early stages of collapse as a function of Σ and δ for a core with mass M = 300M . The turnover of the T = 30 K contour at high Σ and δ is due to kT becoming large; see Equation (2.24) and Figure 2.4.................................. 27 List of Figures vi 3.1 Column density through the simulation volume at 6 different times for runs BR (left), BI (middle), and HR (right). Projections are taken along the x direction, and the initial magnetic field is oriented in