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JASON D. FIEGE, B.Sc.H, M-Sc

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JASON D. FIEGE, B.Sc.H, M-Sc FILAMENTARY MOLECULAR CLOUDS AND THEIR PROLATE CORES BY JASON D. FIEGE, B.Sc.H, M-Sc. A Thesis Submitted to the School of Graduate Studies in Partial Fulfilment of the Requirements for the Degree Doctor of Philosophy McMaster University @ Copyright by Jason D. Fiege, 1999 National Library Bibliothèque nationale 1*1 of Canada du Canada Acquisitions and Acquisitions et Bibliographie Services services bibliographiques 395 WeUington Street 395, rue Wellington OttawON KIAON4 OttawaON KlAûN4 Canada Canada The author has granted a non- L'auteur a accordé une licence non exclusive licence allowing the exclusive permettant à la National Lhrary of Canada to Bibliothèque nationale du Cana& de reproduce, loan, distribute or sell reproduire, prêter, distribuer ou copies of this thesis in rnicrofom, vendre des copies de cette thèse sous paper or electronic formats. la forme de microfiche/nlm, de reproduction sur papier ou sur format électronique. The author retains ownership of the L'auteur conserve la propriété du copyright in this thesis. Neither the droit d'auteur qui protège cette thèse. thesis nor substantial extracts fiom it Ni la thèse ni des extraits substantiels may be printed or othewise de celle-ci ne doivent être imprimés reproduced without the author's ou autrement reproduits sans son permission. autorisation. FILAMENTARY MOLECULAR CLOUDS AND THEIR PROLATE CORES DOCTOR OF PHILOSOPHY McMaster University (Physics and Astronomy) Hamilton, Ontario TITLE: Filamentary Molecular Clouds and Their Prolate Cores AUTHOR: Jason D. Fiege, B.Sc., M.Sc. (Queen's University) SUPERVISOR: Dr. Mph E. Pudritz NUMBER OF PAGES: xiv, 252. Abstract We develop a mode1 of self-gravitating, pressure truncated, filarnentary molecdar clouds wi t h a rather general helical magnetic field topology. By comparing with existing observational data, Our analysis suggests that the mas per unit length of many filamentary cIouds is significantly reduced by the effects of extemal pressure, and that toroidal fields play a significant role in squeezing clouds. We show that there is an upper limit to the mass per unit Iength allowed for equilibriurn, whose value depends on the strength and character of the magnetic field threading the filament. Clouds that are below this critical mass per unit lengt h are always stable against radial gravitational collapse. Our theoretical modeis involve 3 parameters; two to describe the mass Ioading of the poloidal and toroidal fields, and a third to describe the radial concentration of the filament. We find that many of our models with heIical fields are in good agreement with the observed - r-2 radial density structure of filamentary clouds. Unmagnetized filaments and models with purely poloidal magnetic fields result in steep density gradients that are not aliowed by the observations. We consider the stability of our models against axisymrnetric modes of fragmentation. Many of Our models fragment gravitationdly, although some are subject to MHD-driven "sausage" modes of ins tabil- ity. Our main result is that the toroidal magnetic field helps to stabilize long wavelength gravitational instabilities, but short wavelength MHD "sausage" instabilities result when the toroidal field is suffi- ciently strong. Many of our models lie in a physical regime where the growth rates of gravitational and MHD instabilities are at a minimum. We then go on to develop a mode1 of the helicdy magnetized cores that rnight originate from finite segments of Our filament models. Only modest toroidal fields are required to produce proiate cores, with mean projected axis ratios in the range 0.3 - 1. Thus, many of our models are in good agreement with the observed shapes of cores (Myers et al 1991, Ryden 1996), which find axis ratios distributed about a mean value in the range 0.5 - 0.6. We show that the Bonnor-Ebert critical mass is reduced by about 2076, as a result of the helical field in our models. iii Acknowledgement s During the past four years, 1 have benefited enormously fiom working under the supervision of Ralph Pudritz. His combination of sharp physicai insight, scientific knowledge, and enthusiasm for astrophysics continue to amaze me. 1 would like to thank Brenda Matthews for many useful discussions regarding ber observational data and general aspects of sub-millimetre polarirnetry. She also provided technicd assistance in the preparation of some of my figures. 1 am also indebted to Marcel Van DaEen, who provided technical assistance with the lYW document preparation system on more thau one occasion. Th& also to Kathy Durrell, who helpeci me by proofreading several chapters. Thanks are also due to the office std, especidy graduate secretax-y Jackie Collin, for guiding me through the formalities of submitting this thesis. My wife's family, John, Elsie, and Melika Ramkissoon have been very supportive for the past three years, and especially in the Iast few weeks. Their kindness, generosity, and warmth are beyond compare. 1 also thank my own parents for a solid foundation and strong early influences. The greatest debt of dl is to my wife Annica, whose love, care, and understanding have seen me through this degree and the writing of this thesis. She also compiled and typed aii of the references, which helped enormously in my timely completion. For Annica Sic ita ad astnr... Contents 1 Introduction 1 2 Observations and Theory of Molecular Clouds in the Milky Way 5 2.1 Observations of Molecdar Clouds ................................ 5 2.1.1 Molecular Lines ...................................... 5 2.1-2 Sub-rnillimetre Observations of Molecular Clouds ................... 10 2.2 Observations of Magnetic Fields in Molecdar Clouds ..................... 10 2.2.1 Zeeman Observations of Magnetic Field Strengths in Molecular Clouds and Their HI Envelopes ....................................... 13 2.2.2 Observations of Polarization in Molecular Clouds ................... 16 2.2.3 The Polarized Light of Ba& ground Stars ....................... 17 2.2.4 The Polarized Far-Inhared and Sub-Millimetre Emission of Dust Grains ...... 18 2.2.5 Ordered Magnetic Fields in Molecular Clouds ..................... 19 2.3 The Formation of Molecular Clouds - Spiral Shocks and Supershells ............ 20 2.3.1 Spiral Shocks ....................................... 20 2.3.2 Supershells ........................................ 20 2.4 Non-Thermal Motions in Molecular Clouds .......................... 22 2.4.1 Non-thermal Pressure .................................. 22 2.5 The Origins of Non-Thermal Motions in Molecular Clouds .................. 24 2.5.1 Alfvén Waves ....................................... 24 2.5.2 Tùrbulence in Molecular Clouds and the ISM ..................... 25 2.5.3 Origins of Turbulence .................................. 25 2.5.4 Kolmogorov Turbulence ................................. 26 2.5.5 MHD Turbulence ..................................... 27 2.5.6 Global Properties of MHD Turbulence Simulations .................. 28 2.5.7 Filamentary HI Clouds as Density Fluctuations in a Turbulent ISM ........ 29 2.5.8 Lifetimes of Density Fluctuations ............................ 29 2.5.9 Commentary on Simulations of MHD Turbulence ................... 31 2.6 The Surface Pressure on Molecular Clouds ........................... 31 2.6.1 The Total Pressure of the ISM ............................. 32 2.6.2 HI Clouds and Atomic Envelopes ............................ 32 2.7 The Density Structure of Clouds and Clumps ......................... 33 2.8 The Internal Structure of Molecular Clouds .......................... 34 2.8.1 The Mass Spectrum of Clumps ............................. 34 2.9 Self-Gravity in Interstellar Gas Clouds ............................. 35 2.9.1 Gravity in Spheroidal and Filamentary Clouds .................... 35 2.9.2 Star Formation in Self-Gravitating Clumps ...................... 37 2.10 Jeans Instability and the Fragmentation of Molecular Clouds ................ 37 2.11 Ordered Magnetic Fields in Molecular Clouds - Theoretical Considerations ......... 39 2.11.1 A Virid Analysis of Magnetized Spheroidal Molecular Clouds ............ 39 2.1 1.2 Clouds Threaded by Purely Poloidal Fields ...................... 40 2.11.3 Are Spheroidal Clouds Magnetically Super-critical or Sub-Critical? ........ 43 2.11 -4 Larson's Laws for Molecular Clouds .......................... 44 2.11.5 Spheroidal Clouds Threaded by Both Poloidal and Toroidal Fields ......... 46 Helical Fields and Filamentary MoIecuIar Clouds 49 3.1 Introduction ............................................ 50 3.2 Virial Analysis of Filamentary Molecular Clouds ....................... 52 3.2.1 Unrnagnetized Filaments ................................. 56 3 .2.2 Magnetized Filaments .................................. 57 3.2.3 Surface Pressures on Molecular Filaments ....................... 57 3.2.4 Comparison With Observations ............................. 58 3.3 Magnetohydrostatic Models of Filamentary Molecular Clouds ................ 61 3.3.1 The Poloidal and Toroidal Flux to Mass Ratios .................... 61 3.3.2 An Idealized Model: Uniform Magnetized Filaments ................. 62 3.3.3 General Equations for Magnetized Filamentary Molecular Clouds .......... 63 3.3.4 Analytic Solutions .................................... 65 3.4 Numerical Solutions ....................................... 67 3.4.1 Numerical Results .................................... 67 3.4.2 "Best-Fitting" Models For Magnetized Filamentary CIouds ............. 76 vii 3.5 Diçcussion ............................................
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