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Monte Carlo models of dust coagulation [Elektronische Ressource] / by András Zsom

166 pages
RUPERTO-CAROLA UNIVERSITY OF HEIDELBERG(GERMANY)Monte Carlo models of dust coagulationbyAndr´as ZsomSupervisor:Prof. Dr. Cornelis DullemondReferees:Prof. Dr. Cornelis DullemondProf. Dr. Ralf KlessenSeptember 2010Dissertationsubmitted to theCombined Faculties for the Natural Sciences and for Mathematicsof the Ruperto-Carola University of Heidelberg (Germany)for the degree ofDoctor of Natural Sciencespresented byAndr´as Zsomborn in Pusp¨¨ oklad´any (Hungary)Oral examination: 18, October, 2010iAbstractThe thesis deals with the first stage of planet formation, namely dust coagulation frommicron to millimeter sizes in circumstellar disks. For the first time, we collect and com-pile the recent laboratory experiments on dust aggregates into a collision model thatcan be implemented into dust coagulation models. We put this model into a MonteCarlo code that uses representative particles to simulate dust evolution. Simulations areperformed using three different disk models in a local box (0D) located at 1 AU distancefrom the central star. We find that the dust evolution does not follow the previouslyassumed growth-fragmentation cycle, but growth is halted by bouncing before the frag-mentation regime is reached. We call this the bouncing barrier which is an additionalobstacle during the already complex formation process of planetesimals. The absence ofthe growth-fragmentation cycle and the halted growth has two important consequencesfor planet formation.
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RUPERTO-CAROLA UNIVERSITY OF HEIDELBERG
(GERMANY)
Monte Carlo models of dust coagulation
by
Andr´as Zsom
Supervisor:
Prof. Dr. Cornelis Dullemond
Referees:
Prof. Dr. Cornelis Dullemond
Prof. Dr. Ralf Klessen
September 2010Dissertation
submitted to the
Combined Faculties for the Natural Sciences and for Mathematics
of the Ruperto-Carola University of Heidelberg (Germany)
for the degree of
Doctor of Natural Sciences
presented by
Andr´as Zsom
born in Pusp¨¨ oklad´any (Hungary)
Oral examination: 18, October, 2010i
Abstract
The thesis deals with the first stage of planet formation, namely dust coagulation from
micron to millimeter sizes in circumstellar disks. For the first time, we collect and com-
pile the recent laboratory experiments on dust aggregates into a collision model that
can be implemented into dust coagulation models. We put this model into a Monte
Carlo code that uses representative particles to simulate dust evolution. Simulations are
performed using three different disk models in a local box (0D) located at 1 AU distance
from the central star. We find that the dust evolution does not follow the previously
assumed growth-fragmentation cycle, but growth is halted by bouncing before the frag-
mentation regime is reached. We call this the bouncing barrier which is an additional
obstacle during the already complex formation process of planetesimals. The absence of
the growth-fragmentation cycle and the halted growth has two important consequences
for planet formation. 1) It is observed that disk atmospheres are dusty throughout their
lifetime. Previous models concluded that the small, continuously produced fragments
can keep the disk atmospheres dusty. We however show that small fragments are not
produced because bouncing prevents fragmentation. 2) As particles do not reach the
fragmentation barrier, their sizes are smaller compared to the sizes reached in previous
dust models. Forming planetesimals from such tiny aggregates is a challenging task.
We decided to investigate point 1) in more detail. A vertical column of a disk (1D) is
modeled including the sedimentation of the particles. We find that already intermediate
levels of turbulence can prevent particles settling to the midplane. We also find that,
due to bouncing, the particle size distribution is narrow and homogenous as a function
of height in the disk. This finding has important implications for observations. If it is
reasonable to assume that the turbulence is constant as a function of height, the particles
observed at the disk atmospheres have the same properties as the ones at the midplane.
iiii
Zusammenfassung
Diese Arbeit befasst sich mit der fru¨hesten Phase der Planetenentstehung, nam¨ lich der
Koagulation von mikrometer- hin zu millimetergroßen Staubpartikeln in zirkumstellaren
Scheiben. Als erste Studie dieser Art simulieren wir die Staubentwicklung in ‘representa-
tive particle’ Monte-Carlo-Simulationen unter Verwendung eines Kollisionsmodells, das
die neuesten Laborexperimente beruc¨ ksichtigt. Die Simulationen verwenden drei ver-
schiedene Scheibenmodelle in einer lokalen Box (0D) in einem Abstand von 1 AU vom
Zentralstern. Unsere Ergebnisse zeigen, dass die Staubentwicklung nicht dem bislang
angenommenen Wachstums-Fragmentations-Zyklus folgt, sondern dass das Wachstum
von abprallenden Stoßen¨ aufgehalten wird, bevor es das Fragmentationsregime erreicht.
Wir bezeichnen dies als ‘bouncing barrier’, ein weiteres Hindernis im ohnehin schon
komplexen Entstehungsprozess von Planetesimalen. Die Abwesenheit des Wachstums-
Fragmentations-Zyklus und das unterbundene Teilchenwachstum haben zwei wichtige
Konsequenzen fur¨ die Entstehung von Planeten: 1) Beobachtungen zeigen, dass die
Atmosph¨ aren von Scheiben wah¨ rend ihrer gesamten Lebenszeit staubig sind. Bish-
erige Modelle folgerten dass kontinuierliche Fragmentation diese kleinen Staubteilchen
produziert und dadurch die Scheibenatmosph¨ are “staubig” ha¨lt. Unsere Ergebnisse
zeigen jedoch, dass kleine Fragmente gar nicht erst produziert werden, weil die Frag-
mentationsgrenze nicht erreicht wird. 2) Da Teilchen die Fragmentationsbarriere nicht
erreichen, bleiben sie kleiner als in bisherigen Modellen. Die Entstehung von Plan-
etesimalen aus solch kleinen Staubaggregaten ist eine herausforderungsvolle Aufgabe.
Wir haben uns mit Punkt 1) nah¨ er befasst. Hierzu modellieren wir einen vertikalen
Schnitt (1D) durch die Scheibe unter Beruc¨ ksichtigung von Staubsedimentation. Unsere
Ergebnisse zeigen, dass schon eine moderat ausgeprgte Turbulenz die Sedimentation zur
Mittelebene unterbinden kann. Des Weiteren fanden wir heraus, dass die Verteilung
der Teilchengr¨oße schmal und eine homogene Funktion der Hoh¨ e ub¨ er der Mittelebene
ist. Dies hat wichtige Auswirkungen fur¨ Beobachtungen: Unter der Annahme, dass
die Turbulenz ho¨henunabh¨ angig ist, haben die in der Scheibenatmosph¨ are beobachteten
Teilchen dieselben Eigenschaften wie diejenigen in der Mittelebene.
iiiContents
Abstract i
Zusammenfassung iii
1 Introduction 1
1.1 Planet formation in a nutshell......................... 3
1.2 Observations of planet-forming systems....... 5
1.2.1 The solar system ............................ 5
1.2.2 Observations of protoplanetary systems ....... 8
1.3 Dust experiments in the laboratory ......................10
1.4 The importance of dust - theoretical considerations .....1
1.5 The outline of the thesis ............................13
2 A representative particle approach to the coagulation of dust particles 17
2.1 Introduction...................................17
2.2 The method ...................19
2.2.1 Fundamentals of the method .....................19
2.2.2 Computer implementation of the method ......22
2.2.3 Acceleration of the algorithm for wide size distributions ......23
2.2.4 Including additional particle properties ...........24
2.3 Discussion of the method .......................25
2.3.1 Conservation of particle number...........25
2.3.2 The number of representative particles ............26
2.3.3 Limitations of the method...................27
2.4 Standard tests and results ...................28
2.5 Applications to protoplanetary disks .................31
2.5.1 Relative velocities ...................31
2.5.2 Fragmentation model .....................32
2.5.2.1 Results ....................33
2.5.3 Porosity .............................34
2.5.3.1 Results ....................37
2.5.3.2 Model comparison with Ormel et al. (2007) ....37
2.5.4 Monomer size distribution .......................40
2.6 Conclusions and outlook ................41
vContents CONTENTS
3 Mapping the zoo of laboratory experiments 45
3.1 Introduction...................................45
3.2 Collision experiments with relevance to planetesimal formation ..47
3.2.1 A short review on collision experiments ...............48
3.2.2 New experiments ....................51
3.2.2.1 Fragmentation with mass transfer (Exp 17) ........51
3.2.2.2 Impacts of small aggregates (Exp 18) .......54
3.2.2.3 Collisions between similar sized solid and porous aggre-
gates (Exp 19) ........................57
3.3 Classification of the laboratory experiments .........57
3.4 Collision regimes ................................68
3.5 Porosity evolution of the aggregates .........73
3.6 Discussion ....................................75
3.6.1 The bottleneck for protoplanetary dust growth .......76
3.6.2 Influence of the adopted material properties .............7
4 Introducing the bouncing barrier 81
4.1 Introduction...................................81
4.2 The nebulae model ...............84
4.2.1 Disk models...............................84
The low density model: ........84
MMSN model: .........................84
The high density model: ........85
4.2.2 Relative velocities ...........................85
4.3 Collision model and implementation .....................89
4.3.1 Short overview of the collision model.........89
4.3.2 Porosity .................................91
4.3.3 The Monte Carlo method ...........92
4.3.4 Implementation of the collision types.................93
Hit & stick (S1), sticking through surface effects (S2), pen-
etration (S3): ...................93
Mass transfer (S4): ..........94
Bouncing with compaction (B1): ...............94
Bouncing with mass transfer (B2): ......94
Fragmentation (F1): ......................95
Erosion (F2): ..............95
Fragmentation with mass transfer (F3): ...........95
4.3.5 Evolving the particle properties in time ...........96
4.3.6 Numerical issues ........................96
4.4 Results..............................97
4.4.1 Initial conditions and setup of simulations ..........97
4.4.2 The low density model.....................97
4.4.2.1 Early evolution................10
4.4.2.2 Termination of growth................101
4.4.2.3 Long-term evolution .............101
4.4.3 The MMSN model .......................102
4.4.3.1 Early evolution................103
vi

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