Comet Formation in the Framework of Streaming Instability Von der Fakultät für Elektrotechnik, Informationstechnik, Physik der Technischen Universität Carolo-Wilhelmina zu Braunschweig zur Erlangung des Grades eines Doktors der Naturwissenschaften (Dr. rer. nat.) genehmigte Dissertation von Sebastian Lorek aus Neumarkt i.d.OPf. eingereicht am: 15.09.2017 Disputation am: 19.12.2017 1. Referentin oder Referent: Prof. Dr. Jürgen Blum 2. Referentin oder Referent: Prof. Dr. Cornelis P.Dullemond Druckjahr: 2018 Bibliografische Information der Deutschen Nationalbibliothek Die Deutsche Nationalbibliothek verzeichnet diese Publikation in der Deutschen Nationalbibliografie; detaillierte bibliografische Daten sind im Internet über http://dnb.d-nb.de abrufbar. Dissertation an der Technischen Universität Braunschweig, Fakultät für Elektrotechnik, Informationstechnik, Physik ISBN 978-3-944072-62-3 uni-edition GmbH 2018 http://www.uni-edition.de c Sebastian Lorek This work is distributed under a Creative Commons Attribution 3.0 License Printed in Germany Contents Zusammenfassung 11 Summary 13 1 Introduction 15 1.1 Historical overview of comet exploration . 15 1.2 Characteristics of comets . 16 1.2.1 Source regions of comets . 16 1.2.2 Properties of the nucleus . 17 1.2.3 Coma and tail of comets . 19 1.3 The formation of comets . 19 1.3.1 Dust growth in the solar nebula . 20 1.3.2 Streaming instability . 21 1.3.3 Comet formation by gravitational instability . 22 1.3.4 Alternative hypotheses for the formation of comets . 23 1.4 Motivation and structure of the thesis . 25 2 Model of the solar nebula 27 2.1 The minimum mass solar nebula . 27 2.2 Turbulence . 28 2.3 Dust in protoplanetary disks . 29 2.3.1 Aerodynamic drag on solid aggregates . 30 2.3.2 The Stokes number . 31 2.3.3 Relative velocities between dust and gas . 32 3 Collision model 35 3.1 Dust properties . 35 3.1.1 Material properties of the monomers . 35 3.1.2 Material properties of dust aggregates . 36 3.2 Collision velocities of dust aggregates . 37 3.2.1 Brownian motion . 37 3.2.2 Turbulence induced collision velocities . 38 3.2.3 Differential drift of aggregates . 38 3.2.4 Total collision velocity . 39 3.3 The outcome of dust aggregate collisions . 39 3.3.1 Sticking and bouncing . 40 3.3.2 Fragmentation, erosion, and mass transfer . 40 3 Contents 3.3.3 The change of the aggregate mass . 41 3.3.4 Material and collision properties of water ice . 42 3.4 The porosity of dust aggregates . 42 3.4.1 Porosity change in sticking collisions . 43 3.4.2 Compression in bouncing collisions . 44 3.4.3 Porosity change in fragmentation, erosion, and mass transfer . 47 3.4.4 Non-collisional compression of porous aggregates . 47 3.5 Aggregates of mixed composition . 48 3.5.1 Composition and density . 48 3.5.2 Collision model for aggregates of mixed composition . 49 3.6 Caveats of the collision model . 53 3.6.1 Homogeneously mixed aggregates . 53 3.6.2 Combining collision outcome with porosity . 53 3.6.3 Bouncing of porous aggregates . 54 4 Monte Carlo modelling of dust coagulation 55 4.1 The Smoluchowski equation for coagulation . 55 4.2 Numerically solving the Smoluchowski equation . 56 4.2.1 Direct numerical integration . 56 4.2.2 Monte Carlo methods . 56 4.3 The representative particle method . 57 4.3.1 Collision rates and time of the next collision . 57 4.3.2 Particles involved in the collision . 58 4.3.3 Change of particle properties . 58 5 Local growth of aggregates in the solar nebula 61 5.1 Initial conditions for the simulations . 62 5.1.1 Coagulation model . 62 5.1.2 Collision model . 64 5.2 Results of aggregate growth simulations . 65 5.2.1 Nominal case: aggregate growth at 30 au . 66 5.2.2 Parameter study for aggregate growth . 73 5.2.3 Caveats . 82 5.2.4 Summary of aggregate properties . 84 6 Aggregate compression during the gravitational collapse of pebble clouds 89 6.1 Gravitational collapse of a pebble cloud . 89 6.2 Initial conditions for the simulations . 91 6.2.1 Pebble cloud model and collision model . 91 6.2.2 Coefficient of restitution of aggregates . 92 6.2.3 Summary of the initial conditions . 92 6.3 Results of pebble cloud collapse simulations . 93 6.3.1 Collision types during collapse . 93 6.3.2 Compression of aggregates . 96 6.3.3 Formation of comet-like planetesimal . 98 4 Contents 7 Implications for the formation of comets 107 7.1 Local formation of comets at large heliocentric distance . 107 7.2 Implications from the comparison with observations of cometary pebbles108 7.2.1 Compression of millimetre-sized aggregates . 108 7.2.2 Post-collapse aggregate sizes in the nominal case . 114 7.2.3 Post-collapse aggregate sizes in the parameter study . 115 7.2.4 Preferred solar nebula conditions for comet formation . 118 7.3 Formation of comets from comet-like planetesimals . 119 7.3.1 Formation of substructure by clustering of aggregates . 120 7.3.2 Rotation of pebble clouds . 120 7.3.3 Presence of fractal aggregates . 121 8 Conclusion 123 Bibliography 125 Publications 143 Acknowledgements 145 Curriculum vitae 147 5 List of Figures 1.1 Inclination as function of semi-major axis of comets. 17 1.2 Image of comet 103P/Hartley 2 . 18 3.1 Compression curve of granular water ice from laboratory experiments. 45 3.2 Compression curve for dust and ice aggregates. 46 3.3 Collision outcome map for compact aggregate collisions . 51 3.4 Collision outcome map for porous aggregate collisions . 52 5.1 Sketch of the simulation domain. 63 5.2 Aggregate properties as function of time in the nominal case. 67 5.3 Mass distribution function in the nominal case; 0.1 µm sized monomers, dust-to-ice ratio of 5. 68 5.4 Mass distribution function in the nominal case; 1 µm sized monomers, dust-to-ice ratio of 5. 68 5.5 Mass distribution function and residuals in the nominal case; 0.1 µm sized monomers. 71 5.6 Mass distribution function and residuals in the nominal case; 1 µm sized monomers. 72 5.7 Aggregate properties as function of time: different heliocentric distances. 74 5.8 Aggregate properties as function of time: weaker and stronger turbulence. 75 5.9 Aggregate properties as function of time: varying gas surface density. 76 5.10 Aggregate properties as function of time: dispersing solar nebula. 77 5.11 Aggregate properties as function of time: varying the sticking properties. 78 5.12 Aggregate properties as function of time: bouncing only for compact aggregates. 79 5.13 Aggregate mass versus heliocentric distance. 81 6.1 Collision velocity as function of pebble cloud density: initial volume- 2 filling factor of 10− , dust-to-ice ratio of 5. 95 6.2 Collision types as a function of planetesimal density: initial volume- 2 filling factor of 10− , dust-to-ice ratio of 5. 96 6.3 Mass distribution function during pebble cloud collapse: initial volume- 2 filling factor of 10− , dust-to-ice ratio of 5. 97 6.4 Volume-filling factor of aggregates as a function of initial volume-filling factor. 98 6.5 Volume-filling factor of aggregates as a function of initial volume-filling 3 factor: pure dust and ice, initial volume-filling factors 10− 0.4. 99 − 7 List of Figures 6.6 Aggregate packing as function of pebble cloud density: very low-mass pebble cloud. 101 6.7 Aggregate packing as function of pebble cloud density: low-mass pebble cloud. 102 6.8 Aggregate packing as function of pebble cloud density: intermediate- mass pebble cloud. 103 6.9 Aggregate packing as function of pebble cloud density: high-mass pebble cloud. 104 7.1 Collision velocity as function of pebble cloud density: aggregate radius 2 0.45 mm, 0.1 µm monomers, initial volume-filling factor of 1.2 10− , dust-to-ice ratio of 5 at 30 au. .× . 109 7.2 Mass distribution function during pebble cloud collapse: aggregate radius 0.45 mm, 0.1 µm monomers, initial volume-filling factor of 1.2 2 × 10− , dust-to-ice ratio of 5 at 30 au. 110 7.3 Aggregate packing as function of pebble cloud density: aggregate radius 2 0.45 mm, 0.1 µm monomers, initial volume-filling factor of 1.2 10− , dust-to-ice ratio of 5 at 30 au. .× . 112 7.4 Mass distribution function during pebble cloud collapse: aggregate radius 0.36 mm, 0.1 µm monomers, initial volume-filling factor of 1.8 1 × 10− , dust-to-ice ratio of 5 at 5 au. 113 7.5 Aggregate packing as function of pebble cloud density: aggregate radius 1 0.36 mm, 0.1 µm monomers, initial volume-filling factor of 1.8 10− , and dust-to-ice ratio of 5 at 5 au. .× . 115 7.6 Post-collapse aggregate radius versus heliocentric distance. 116 7.7 Post-collapse aggregate radius for parameter study at 30 au. 117 8 List of Tables 3.1 Parameters for the dust and ice compression curves. 47 5.1 Simulation parameters used in the nominal run. 62 5.2 Overview of model designs used in parameter study. 80 5.3 Maximum mass and mass at Stmin for 0.1 µm sized monomers. 85 5.4 Maximum mass and mass at Stmin for 1 µm sized monomers. 86 5.5 Aggregate growth for different model settings. 87 6.1 Initial conditions for simulations of pebble cloud collapse. 93 6.2 Volume-weighted mean filling factor of aggregates for all simulations.