This Thesis Has Been Submitted in Fulfilment of the Requirements for a Postgraduate Degree (E.G

This thesis has been submitted in fulfilment of the requirements for a postgraduate degree (e.g. PhD, MPhil, DClinPsychol) at the University of Edinburgh. Please note the following terms and conditions of use: • This work is protected by copyright and other intellectual property rights, which are retained by the thesis author, unless otherwise stated. • A copy can be downloaded for personal non-commercial research or study, without prior permission or charge. • This thesis cannot be reproduced or quoted extensively from without first obtaining permission in writing from the author. • The content must not be changed in any way or sold commercially in any format or medium without the formal permission of the author. • When referring to this work, full bibliographic details including the author, title, awarding institution and date of the thesis must be given. The Physics and Chemistry of Gas in Discs I V N E R U S E I T H Y T O H F G E R D I N B U Ian Tilling A thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy to the University of Edinburgh April 2012 Abstract Protoplanetary discs set the initial conditions for planet formation. By combining observations with detailed modelling, it is possible to constrain the physics and chemistry in such discs. I have used the detailed thermo-chemical disc model ProDiMo to explore the characteristics of the gas in protoplanetary discs, particularly in Herbig Ae objects. I have assessed the ability of various observational data to trace the disc properties. This has involved a number of different approaches. Firstly I compute a series of disc models with increasing mass, in order to test the diagnostic powers of various emission lines, in particular as gas mass tracers. This approach is then expanded to a large multi- parameter grid of 105 disc models. I have helped to develop a tool for analysing and ∼ plotting the huge quantity of data presented by such a model grid. Following this approach I move on to a detailed study of the Herbig Ae star HD 163296, attempting to fit the large wealth of available observations simultaneously. These include new Herschel observations of the far-infrared emission lines, as well as interferometric CO observations and a large number of continuum data. This study addresses the topical issues of the disc gas/dust ratio, and the treatment of the disc outer edge. It explores the effects of dust settling, UV variability and stellar X-ray emission on the disc chemistry and line emission. There is possible evidence for gas-depletion in the disc of HD 163296, with the line emission enhanced by dust settling, which would indicate a later evolutionary stage for this disc than suggested by other studies. Finally, I work to improve the treatment of the gas heating/cooling balance in ProDiMo, by introducing a non-LTE treatment of the atomic hydrogen line transitions and bound-free continuum transitions. I explore the effects of this on the disc chemical and thermal structure, and assess its impact in terms of the observable quantities. i Declaration Except where otherwise stated, the research undertaken in this thesis was the unaided work of the author. Where the work was done in collaboration with others, a significant contribution was made by the author. ii Acknowledgements Firstly I would like to thank my supervisors Peter Woitke, Ken Rice and Wing- Fai Thi, whose help and support have been invaluable throughout my PhD studies, and without whom I could never have made it to this stage. I would also like to thank Inga Kamp for her collaboration, her advice and for her patience throughout. I also appreciate the help given to me by my other collaborators, and in particular would like to thank Christophe Pinte, François Ménard, Gwendolyn Meeus, Benjamin Montesinos, Gaspard Duchêne and Bill Dent for their useful comments and advice. I would like to thank everyone at the Royal Observatory for making my time here so enjoyable, and for keeping my seat warm the rest of the time. I also acknowledge the Science and Technology Facilities Council (STFC) for giving me the opportunity to complete this PhD. Thanks to my parents Steve and Lesley, my sister Rachel, and to all the friends in Edinburgh and elsewhere who have supported and humoured me throughout, regardless of whether or not they had any idea what “The Prof” was up to. Finally I would like to thank the members of Trapped Mice and Seneka for the music, memories, and for keeping me sane. iii Contents Abstract i Declaration ii Acknowledgements iii Contents iv List of figures vi List of tables xi 1 Introduction 1 1.1 TheImportanceofProtoplanetaryDiscs . .. 1 1.2 ThesisOutline.............................. 5 2 A Review of Protoplanetary Disk Studies 6 2.1 DiscModelling ............................. 6 2.2 PDRModelling ............................. 10 2.3 Thermo-chemicalDiscModelling . 13 2.4 DiscObservations............................ 16 3 ProDiMo 20 3.1 Introduction............................... 20 3.2 HydrostaticDiscStructure . 21 3.3 ContinuumRadiativeTransfer . 21 3.4 Chemistry................................ 23 3.5 GasThermalBalance .......................... 24 3.5.1 Non-LTEtreatmentofatoms,ionsandmolecules . 25 3.6 AtomicHydrogenbound-freetransitions . ... 30 3.6.1 Rate coefficients ........................ 31 3.6.2 Hydrogenshielding. 31 3.6.3 Externalchemicalrates. 32 3.6.4 Heatingandcoolingrates. 32 iv CONTENTS 4 Line Diagnostics in Herbig Ae Discs 35 4.1 Introduction............................... 35 4.2 Methods................................. 37 4.2.1 Lineradiativetransfer . 38 4.3 Thediscmodels............................. 41 4.3.1 Physicalstructure. 42 4.3.2 Chemicalstructure . 42 4.3.3 Self-similarity ......................... 45 4.3.4 StrengthofUVfield ...................... 46 4.3.5 Dustopacities.......................... 47 4.4 Lineemission.............................. 47 4.4.1 Far-infraredfinestructurelines. 47 4.4.2 COsub-mmlines........................ 49 4.5 Discussion................................ 54 4.5.1 Far-infraredfinestructurelines. 54 4.5.2 COsub-mmlinesandlineratios . 55 4.5.3 ComparisonwithobservationsforMWC480 . 57 4.6 Conclusions............................... 58 5 The DENT Model Grid 60 5.1 Introduction............................... 60 5.2 GridComputation............................ 61 5.3 xDENT ................................. 63 5.3.1 Modelselection......................... 64 5.3.2 Plotting............................. 64 5.3.3 Modelfitting .......................... 69 5.4 Results.................................. 70 6 GasModellingintheDiscofHD163296 73 6.1 Introduction............................... 73 6.2 Herschel/PACSObservations. 76 6.3 PropertiesofHD163296 . 79 6.3.1 Stellarparameters. 79 6.3.2 TheSED:UV,opticalandnear-IRobservations . 80 6.3.3 Spectral type from the ultraviolet and near-infrared spectra . 82 6.3.4 Theextinction ......................... 83 6.3.5 Observationalconstraints. 84 6.4 Modelling................................ 86 6.4.1 Inputspectrum ......................... 87 6.4.2 Fittingprocedure . .. .. .. .. .. .. 88 6.4.3 Dustproperties ......................... 88 6.4.4 Gas/dustratio.......................... 89 6.5 Results.................................. 90 v CONTENTS 6.5.1 Continuum emission and spectral energy distribution ..... 92 6.5.2 Gasproperties ......................... 96 6.5.3 EffectofX-rays......................... 107 6.6 SummaryandConclusions . 109 7 AtomicHydrogenModellinginProDiMo 113 7.1 Introduction............................... 113 7.2 HD163296Model ........................... 114 7.3 HD45677Model ............................ 117 7.3.1 Comparisonwithobservations . 119 7.4 SummaryandConclusions . 123 8 Conclusions 124 Bibliography 131 Publications 145 vi List of Figures 1.1 HST ACS optical image of the dust disc around the star HD 141569A. This is a young, 5 million year old object which appears to be part of a triple-star system. The disc exhibits a tightly wound spiral structure, and there is evidence that this is associated with the nearby binary system(HD141569BC)[Clampinetal.,2003]. 2 1.2 Synthetic Spectral Energy Distribution (SED) from the young Herbig Ae star HD 163296, highlighting the excess emission arising from the circumstellar disc (black line) relative to the stellar spectrum (red). The gasemissionlinesfromthediscareshowninblue. 4 2.1 Schematic diagram of a circumstellar disc, showing the dominant observable gas lines in the various disc regions, and typical gas temperaturesanddensitiesateachdiscradius. ... 12 2 3 4 4.1 From top to bottom row: disc models with 10− , 10− , 10− and 5 10− M . The first column shows the total hydrogen number density ⊙ log n H with white contours indicating gas temperatures of 100, 300, and 1000 K. The second column shows the UV radiation field strength χ (91.2 205.0 nm) from full 2D radiative transfer. The third column − shows the gas temperature log Tg with white contours indicating dust temperaturesof20,40,100,300and1000K. 43 2 3 4 4.2 From top to bottom row: disc models with 10− , 10− , 10− and 5 + 10− M . The first column shows the C density with white contours indicating⊙ the critical density for the [C ii] line and densities of 106 and 8 3 10 cm− and a red contour line where the PDR parameter χ/n H = 0.01. The second column shows the O density with white contours 4 indicating the critical densities for the two oxygen lines, n H = 6 10 5 3 8 3 × and 5 10 cm− , and a density of 10 cm− . Extinctions of AV = 0.1 and 1× are denoted by the red contour lines. The

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