Imperial College London Department of Physics Accretion discs and planet formation around young stars Marija Jankovic Submitted in part fulfilment of the requirements for the degree of Doctor of Philosophy at Imperial College London, June 2020 Declaration of Originality This thesis is my own work, except where specifically indicated in the text. Some parts of this thesis are based on work completed in collaboration with others, and some have also been published as journal articles: Chapter 2 is based on work that has been completed in collaboration with S. Mohanty, J. Tan and J. E. Owen, and is published as Subhanjoy Mohanty, Marija R. Jankovic, Jonathan C. Tan, and James E. Owen, Inside- out Planet Formation. V. Structure of the Inner Disk as Implied by the MRI, Astrophys- ical Journal, 861, 144 (2018) Chapters 3 and 4 are based on work that has been completed in collaboration with J. E. Owen and S. Mohanty, and is published as Marija R. Jankovic, James E. Owen, and Subhanjoy Mohanty, Close-in Super-Earths: The first and the last stages of planet formation in an MRI-accreting disc, Monthly Notices of the Royal Astronomical Society, 484, 2296{2308 (2019) Chapters 5 and 6 are based on work that has been completed in collaboration with S. Mohanty, J. E. Owen and J. Tan. Marija Jankovic (2020) Copyright Declaration The copyright of this thesis rests with the author. Unless otherwise indicated, its con- tents are licensed under a Creative Commons Attribution-Non Commercial-No Derivatives 4.0 International Licence (CC BY-NC-ND). Under this licence, you may copy and redistribute the material in any medium or format on the condition that; you credit the author, do not use it for commercial purposes and do not distribute modified versions of the work. When reusing or sharing this work, ensure you make the licence terms clear to others by naming the licence and linking to the licence text. Please seek permission from the copyright holder for uses of this work that are not included in this licence or permitted under UK Copyright Law. 2 Abstract Among the extrasolar planets discovered so far, the most abundant are the close-in super- Earths. These are planets with sizes between that of the Earth and Neptune, and orbits typically smaller than Mercury's. In this thesis, I study the innermost regions of accretion discs surrounding young stars, and if and how close-in super-Earths can form at such short orbital periods. I start by discussing a simple model of the inner disc structure coupled to a detailed pre- scription of disc accretion due to the magneto-rotational instability (MRI). I use the inferred structure of the gas to show that the MRI leads to accumulation of dust in the inner disc, as necessary for the formation of solid planet cores. Next, assuming that solid cores do form in the inner disc, I investigate the accretion and evolution of planetary atmospheres. I show that, despite the MRI-accreting inner disc being gas-poor, the predicted planet atmospheres are at least as large as observed. Finally, I present an improved model of the inner disc that accounts for disc heating due to accretion and stellar irradiation, vertical energy transport, dust opacities, and dust effects on disc ionization. The optically-thick inner disc is weakly affected by stellar irradiation, and also convectively unstable. Dust controls the ionization state of the inner disc, and thus the onset of the MRI. I show that sustained dust accumulation can occur in the inner disc, without suppressing the MRI. If planets form in the inner disc, larger gas accretion rates (and thus earlier times in the disc lifetime) are favoured. The work in this thesis advances our knowledge of the planet-forming environment at short orbital distances and supports the hypothesis that super-Earths could form near their present orbits. This work also identifies impediments to planet formation in the inner disc which require further study. 3 Acknowledgements I gratefully acknowledge generous support from the President's PhD scholarship of the Imperial College London, the Dositeja stipend from the Fund for Young Talents of the Serbian Ministry for Youth and Sport, ERC-STG-2019 grant (PEVAP) and the Dr Francis John Warner Prize. I would like to express my deepest gratitude to my supervisor, Subhanjoy Mohanty, for sharing with me his deep knowledge and passion for astrophysics, his guidance, and the metic- ulous comments that helped improve this thesis. I am most appreciative of his patience and exceptional support. Furthermore, I am extremely grateful to James Owen, for countless in- sightful suggestions, stimulating discussions, and constructive comments. I am most thankful for his kindness and warm encouragement. I must also thank Jonathan Tan whose ideas and expertise were instrumental in developing this work. I would like to thank Thomas Haworth for his persistent help, valuable advice and moral support. I also thank Richard Booth, Steven Desch, Eve Lee, Colin McNally, Neal Turner, Lauren Weiss, and Zhaohuan Zhu for helpful discussions. I have truly enjoyed my time at Imperial. I would like to express my gratitude to the members (past and present) of the Imperial Astrophysics group, for the friendly and engaging working environment. Special thanks to my family and friends for their continued support and encouragement. Finally, and above all, thank you, Vanja, for your love and support. 4 Contents Abstract 3 Acknowledgements 4 1 Introduction 9 1.1 Extrasolar planets . .9 1.2 Protoplanetary discs . 12 1.2.1 Thin circumstellar discs . 15 1.2.2 Viscous accretion discs . 16 1.2.3 Source of viscosity . 18 1.2.4 Evolution of dust . 21 1.3 Formation of close-in super-Earths . 23 1.3.1 Migration scenario . 24 1.3.2 Formation in the inner disc . 25 1.4 Thesis outline . 27 2 MRI-accreting inner disc 28 2.1 Introduction . 28 2.2 Methods . 29 2.2.1 Standard α-disc model . 29 2.2.2 MRI-driven viscosity parameter α ...................... 30 2.2.3 Self-consistent α-disc model . 35 2.3 Results . 36 2.3.1 Fiducial model . 36 2.3.2 Varying model parameters . 47 2.4 Discussion and conclusions . 54 3 Early stages of planet formation in the inner disc 56 3.1 Introduction . 56 3.2 Methods . 57 3.2.1 Gas disc model . 57 3.2.2 Dust evolution model . 58 3.2.3 Numerical methods . 60 3.3 Results . 61 3.4 Implications for planetesimal formation . 64 3.5 Discussion and conclusions . 67 5 4 Atmospheres of planets formed in the inner disc 69 4.1 Introduction . 69 4.2 Methods . 70 4.2.1 Accretion of planetary atmospheres . 70 4.2.2 Photoevaporation of planetary atmospheres . 71 4.3 Results . 72 4.3.1 Accretion of planetary atmospheres . 72 4.3.2 Photoevaporation of planetary atmospheres . 74 4.4 Comparison to observations . 74 4.5 Discussion and conclusions . 79 5 Improved model of the MRI-accreting inner disc 81 5.1 Introduction . 81 5.2 Methods . 82 5.2.1 The disc model . 82 5.2.2 Opacities . 85 5.2.3 Viscosity . 87 5.2.4 Ionization . 88 5.2.5 Numerical methods . 92 5.3 Results . 95 5.3.1 Disc thermal structure and the MRI . 96 5.3.2 Disc chemical structure and the MRI . 102 5.4 Discussion . 109 5.4.1 Effects of dust . 109 5.4.2 Importance of stellar irradiation . 110 5.4.3 Convective instability in the inner disc . 111 5.4.4 Energy transport by turbulent elements . 112 5.4.5 Ambipolar diffusion in the strong-coupling regime . 112 5.5 Conclusions . 113 6 Dependence on dust, disc and stellar parameters 115 6.1 Introduction . 115 6.2 Methods . 116 6.3 Results . 118 6.3.1 Dust-to-gas ratio and dust size . 119 6.3.2 Gas accretion rate, stellar mass and dead-zone viscosity . 124 6.4 Location of the pressure maximum . 125 6.5 Discussion . 129 6.5.1 Dust growth . 129 6.5.2 Dust accumulation . 133 6.6 Conclusions . 135 7 Summary and Outlook 137 7.1 Summary . 137 7.2 Outlook . 140 Bibliography 142 6 List of Figures 1.1 Extrasolar planets with known mass or radius . 11 1.2 Mass-radius relationship for a set of extrasolar planets . 13 1.3 Radius distribution for short-period planets . 14 1.4 Illustration of the onset of the magneto-rotational instability . 19 1.5 Illustration of the MRI active and dead zones . 20 1.6 Illustration of a dust trap . 22 1.7 Illustration of key transitions in protoplanetary discs . 23 2.1 Fractional ionization in the inner disc . 37 2.2 Ambipolar, Ohmic and Hall resistivities . 38 2.3 Relative importance of the Ohmic, Hall and ambipolar resistivities . 39 2.4 The MRI-active, dead, zombie and Hall zones for the fiducial model . 40 2.5 Midplane fractional ionization and MRI criteria . 41 2.6 Magnetic field strength for the fiducial model . 41 2.7 Vertically-averaged viscosity parameter for the fiducial model . 42 2.8 Disc structure for the fiducial model . ..