京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第18790号 / 理博第4048号 / 新制||理||1582(附属図書館) / 31741 / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 中村 卓史, 教授 鶴 剛, 教授 田中 貴浩 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DGAM

Super Earths are a class of exoplanets with masses between 1-10 M⊕. Comprising nearly 70 % of the discovered planet population, they are largest class of exoplanets known. Super Earths exhibit an interesting variety of compositions, as their densities imply that they range from dense, rocky planets to those with substantial amounts of water. This thesis aims to understand why super Earths form so frequently, and to connect the final compositions of super Earths to the regions where they form in protoplanetary disks. To do this, we combine a model that calculates the physical and chemical conditions within a protoplanetary disk with a core accretion model of planet formation. A key feature of our planet formation model is planet traps that act as barriers to rapid type-I migration. The traps we include in our model are the dead zone, which can be caused by cosmic ray or X-ray ionization, the ice line, and the heat transition. In disks with lifetimes >􏰐 4 Myr we find that planet formation in all traps results in Jovian planets. Typically, the X-ray dead zone and heat transition traps produce hot Jupiters orbiting near 0.05 AU while the cosmic ray dead zone and ice line traps produce Jupiters near 1 AU. Super Earths are found to form in disks with short lifetimes 􏰑< 2 Myr that photoevaporate prior to planets undergoing runaway gas accretion. Additionally, we find that super Earth formation takes place in low-mass disks (<􏰑 0.05 M⊙), where planet formation timescales exceed disk lifetimes inferred through observations. The location of various traps throughout the disk play a key role in allowing super Earths to achieve a range of compositions. Super Earths forming in the ice line or heat transition accrete solids from cold regions of the disk, resulting in planets with large ice contents (up to 50 % by mass). Conversely, super Earths formed in the dead zone trap accrete solids from warm regions of the disk and are therefore composed of mostly rocky materials (less than 5 % ice by mass). / Thesis / Master of Science (MSc)

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What sets the observable chemical composition of exoplanetary atmospheres? The available chemical abundance of the planet's natal protoplanetary disk gas will have a deciding role in the bulk abundance of the atmosphere very early in the planet's life. While late accretion of ices and inter-atmosphere physical processing can change the observable chemical abundances. We have developed a theoretical model which connects the chemical and physical evolution of an accretion disk with the growth of a young planet to predict the bulk chemical abundance of the planetary atmosphere that is inherited from the disk. We assess what variation in atmospheric chemical abundances are attributed to different planet formation histories. We find differences in the relative abundances of primary nitrogen carriers NH$_3$ and N$_2$ depending on {\it when} the planet accreted its gas. Early ($t<1$ Myr) accreters predominately accreted warmer gas which tend to have its nitrogen in NH$_3$, while later protoplanets accrete colder, more N$_2$ dominated gas. Furthermore we compute the carbon-to-oxygen ratio (C/O) for each planets, which is used to infer {\it where} a planet forms in its accretion disk. We find that each of our planets accrete their gas very close to the water ice line, thereby accreting `pristine' gas with C/O$_{planet}$ exactly matching its host star. We extend our results by tuning our initial disk parameters to reproduce the properties of the HL Tau disk. We produce three models that span the range of measured gas masses, and one model which studies a UV quiet system. We generally find that planet formation is efficient enough to produce a Jupiter-massed planet within the predicted 1 Myr age of the disk. We find a correspondence between the radial locations of ice lines within our astrochemical model and the set of observed dust gaps in the HL Tau system. / Thesis / Doctor of Philosophy (PhD)

I have carried out three-dimensional numerical simulations of self-gravitating discs to determine under what circumstances they fragment to form bound clumps that may grow into giant planets. Through radiation hydrodynamical simulations using a Smoothed Particle Hydrodynamics code, I find that the disc opacity plays a vital role in determining whether a disc fragments. Specifically, opacities that are smaller than interstellar Rosseland mean values promote fragmentation (even at small radii, R &lt; 25AU) since low opacities allow a disc to cool quickly. This may occur if a disc has a low metallicity or if grain growth has occurred. Given that the standard core accretion model is less likely to form planets in a low metallicity environment, I predict that gravitational instability is the dominant planet formation mechanism in a low metallicity environment. In addition, I find that the presence of stellar irradiation generally acts to inhibit fragmentation (since the discs can only cool to the temperature defined by stellar irradiation). However, fragmentation may occur if the irradiation is sufficiently weak that it allows the disc to attain a low Toomre stability parameter. With specific reference to the HR 8799 planetary system, I find that it is only possible for fragments to form in the radial range where the HR 8799 planets are located (approximately 24-68 AU) if the disc is massive. In such a high mass regime, mass transport occurs in the disc causing the surface mass density to alter. Therefore, fragmentation is not only affected by the disc temperature and cooling, but also by any restructuring due to the gravitational torques. The high mass discs also pose a problem for the formation of this system because the protoplanets accrete from the disc and end up with masses greater than those inferred from observation and thus, the growth of planets would need to be inhibited. In addition, I find that further subsequent fragmentation at small radii also takes place. By way of analytical arguments in combination with hydrodynamical simulations using a parameterised cooling method, I explore the fragmentation criteria which in the past, has placed emphasis on the cooling timescale in units of the orbital timescale, beta. I find that at a given radius the surface mass density (i.e. disc mass and profile) and star mass also play a crucial role in determining whether a disc fragments or not as well as where in the disc fragments form. I find that for shallow surface mass density profiles (p&lt;2, where the surface mass density is proportional to R^{-p}), fragments form in the outer regions of the disc. However for steep surface mass density profiles (p is greater than or similar to 2), fragments form in the inner regions of a disc. In addition, I find that the critical value of the cooling timescale in units of the orbital timescale, beta_crit, found in previous simulations is only applicable to certain disc surface mass density profiles and for particular disc radii and is not a general rule for all discs. I obtain an empirical fragmentation criteria between the cooling timescale in units of the orbital timescale, beta, the surface mass density, the star mass and the radius. Finally, I carry out crucial resolution testing by performing the highest resolution disc simulations to date. My results cast some serious doubts on previous conclusions concerning fragmentation of self-gravitating discs.

The Planet Formation Imager (PFI) project aims to provide a strong scientific vision for ground-based optical astronomy beyond the upcoming generation of Extremely Large Telescopes. We make the case that a breakthrough in angular resolution imaging capabilities is required in order to unravel the processes involved in planet formation. PFI will be optimised to provide a complete census of the protoplanet population at all stellocentric radii and over the age range from 0.1 to similar to 100 Myr. Within this age period, planetary systems undergo dramatic changes and the final architecture of planetary systems is determined. Our goal is to study the planetary birth on the natural spatial scale where the material is assembled, which is the "Hill Sphere" of the forming planet, and to characterise the protoplanetary cores by measuring their masses and physical properties. Our science working group has investigated the observational characteristics of these young protoplanets as well as the migration mechanisms that might alter the system architecture. We simulated the imprints that the planets leave in the disk and study how PFI could revolutionise areas ranging from exoplanet to extragalactic science. In this contribution we outline the key science drivers of PFI and discuss the requirements that will guide the technology choices, the site selection, and potential science/technology tradeoffs.

L'objectif de cette thèse est d'étudier la formation de tourbillons dans la zone morte des disques protoplanétaires. Un code numérique 3D compressible a été mis au point et utilisé pour cette étude. Deux instabilités hydrodynamiques sont envisagées pour former les tourbillons: l'instabilité de Rossby et l'instabilité barocline.La première entraine la fragmentation d'une sur-densité annulaire en une chaîne de tourbillons qui se rattrapent les uns les autres et finissent par fusionner en un seul tourbillon qui reste stable sur de très longues durées lorsque son rapport d’aspect est suffisamment grand, et possède une structure quasi bidimensionnelle. En revanche, les tourbillons tridimensionnels de petits rapport d'aspect sont affectés par l’instabilité elliptique qui les détruits en quelques rotations. Seuls persistent ceux de grand rapport d'aspect.L'instabilité barocline, fondamentalement non linéaire, produit des tourbillons à partir de perturbations d'amplitude finies ; ces tourbillons sont ensuite amplifiés et fusionnent en tourbillons plus gros si le disque est stratifié de façon instable et s’il permet aussi le transfert de chaleur. Deux types de transfert thermique ont été envisagés pour étudier cette instabilité qui conduit alors à des différences significatives dans la structure des tourbillons formés. Le rapport d'aspect étant lié à la vorticité, l'amplification des tourbillons se traduit par une diminution de leur rapport d'aspect, et les rend donc sujet à l'instabilité elliptique. Cependant, ils ne sont pas détruit et gardent une structure tourbillonnaire grâce à l'amplification barocline. / The objective of this thesis is to study the formation of vortices in the dead-zone of protoplanetary disks. A 3D compressible numerical code has been performed and used for this study. Two hydrodynamical instabilities are considered for vortex formation: the Rossby wave instability and the baroclinic instability.The first one leads tp the fragmentation of an annular bump into a chain of vortices that catch one another and merge in a single vortex; this vortex remains stable on very long durations when its aspect ratio is large enough and has a quasi two-dimensional structure. In contrast, tridimensional small aspect ratios vortices are affected by the elliptical instability and are destroyed in a few rotation periods. Only vortices with large aspect ratios can survive.The baroclinic instability, a basically non-linear one, can produce vortices from small amplitude perturbations; these vortices are then amplified and merge in bigger vortices if the disk is unstably stratified and also permits heat transfer. Two types of heat transfer have been considered leading to significant differences in the structures of the resulting vortices. As aspect ratio and vorticity are strongly related, the baroclinic amplification reduces the aspect ratio and, so, make the vortex sensitive to the elliptical instability. However, such vortices are not destroyed and keep a vertical structure thanks to the baroclinic amplification.

Erosion has a long history in science and is used in many different fields today, for example in geology for coastal erosion and in the oil industry for pipe erosion. It is very difficult to study erosion both analytically. Numerically it is difficult due to moving and shape-changing boundaries. Here we develop a numerical model in 3D using the Lattice-Boltzmann method, which is good at simulating complex moving boundaries, and erosion capabilities are implemented. Both laminar and turbulent flow can be modelled with this program. Using an experimentally derived model for the mass change due to erosion in clay and mud-type objects, one can derive equations predicting that the volume of a sphere should, due to erosion, scale as V ∼ −t2. This is also observed with simulations. The shapes of a double sphere with different orientations and a cube in laminar flow we find to have similar power law exponent P, P = 2±0.1. But a cube eroding in Re = 800 had no power law behaviour, meaning that the current analytical framework is incomplete. The possibility of a more general framework is presented for future research. Different Reynolds number also affected the power law behaviour and the shape change over time for the different solids. Very little research has been made for erosion of planetesimals, but it has been argued that erosion can be relevant to their fate. Using the same erosion model, an equation of the erosion time is found for laminar flows and for a sphere. Simulation results find that the equation works within an order of magnitude for turbulent flows, a double sphere and a cube. This gives an estimate of the erosion time t∗ of planetesimals to be t∗ ∼ 1s, given a size of radius equal to 10cm and 1km, an orbital eccentricity e &gt; 10−2 and a distance at r = 1 a.u. Implying that orbits for planetesimals with low eccentricity might be favoured.

De acordo com o modelo sequencial de acreção, os planetas gigantes se formam através de um núcleo sólido a partir da captura de planetesimais. Esse núcleo, atingindo uma determinada massa, é capaz de capturar o gás residual do disco protoplanetário que constituirá o seu envelope, formando, então, um planeta gigante (Mizuno, 1980; Pollack et al., 1996). A parte crtica desse cenário está no ajuste dos tempos de formação do núcleo sólido, de captura do gás e dos processos de migração planetária com o tempo de vida do disco (Mordasini et al., 2010). Resultados numéricos mostram que o tempo necessário para a formação de um planeta gigante é muito alto em relação ao tempo de vida do disco, e, que a migração planetária pode ser muito rápida, levando os planetas a carem na estrela antes de sua completa formação. Em geral, os trabalhos sobre formação planetária tratam a migração do planeta utilizando prescrições analíticas (Fortier et al., 2013). No entanto, diversos efeitos associados à termodinâmica do disco de gás fazem com que esses modelos analíticos sejam limitados para lidar com a migração planetária (Paardekooper et al., 2010). De fato, para lidar com a migração planetária de tipo I, esses resultados analíticos se utilizam de discos de gás fisicamente simples e da linearização das equações da hidrodinâmica (Meyer-Vernet e Sicardy, 1987; Tanaka et al., 2002). Para a migração de tipo II, a situação é ainda mais complicada, já que a alta massa do planeta cria um gap em torno da órbita planetária, que impõe uma quebra da linearidade, impossibilitando a obtenção de uma prescrição analtica (Bryden e Lin, 1999). Assim, os resultados numéricos obtidos a partir de simuladores hidrodinâmicos, como o FARGO3D (Masset, 2000; Bentez-Llambay e Masset, 2016), ZEUS (Stone e Norman, 1992), PLUTO (Mignone et al., 2012), entre outros, são essenciais para uma análise mais robusta dos processos de migração planetária dentro de uma gama maior de condições fsicas para o disco de gás. No entanto, os simuladores hidrodinâmicos que tratam da interação do planeta com o disco de gás, em geral, não possuem um modelo para formação planetária. Em alguns deles, modelos para acreção de gás são construdos com base no regime de runaway dessa acreção (Kley, 1999). Todavia, a acreção de sólidos e a acreção de gás para planetas de baixa massa, na maior parte dos casos, não são levadas em consideração. Boa parte disso se deve ao fato de os modelos de formação planetária usarem simulações N-corpos, que, aliados ao código hidrodinâmico, seriam altamente custosos computacionalmente. Assim, torna-se necessário o uso de modelos alternativos para a formação planetária, que sejam capazes de reproduzir os resultados de uma simulação N-corpos de forma confiável. Construir um modelo que considera a acreção de sólidos e gás é uma tarefa árdua e ao mesmo tempo desafiadora. Assim, o presente projeto propõe a implementação de um cenário fisicamente plausível para a formação planetária dentro do código magneto hidrodinâmico FARGO3D. Para modelar a acreção de planetesimais, usamos como base os trabalhos de Guilera et al. (2010) e Fortier et al. (2013), que utilizam um modelo estatstico para determinar a taxa de acreção de planetesimais (Inaba et al., 2001). Esse modelo será implementado pela primeira vez no FARGO3D. Atualmente, sabe-se que a acreção de peebles (material sólido entre cm e mm) tem um impacto importante na formação planetária (Lambrechts e Johansen, 2014; Guilera, 2016; Johansen e Lambrechts, 2017). No entanto, núcleos de poucas massas terrestres possuem um envelope planetário que poderia destruir esses pebbles antes dele alcançar o núcleo (Venturini et al., 2015). Nesta tese, iremos nos preocupar apenas com a acreção de planetesimais, deixando o estudo do pebbles para trabalhos futuros. Para a acreção de gás, iremos modificar o modelo de Kley (1999) incorporado no FARGO antecessor. Essas modificações visam incorporar o raio de Bondi (Bondi, 1952) para determinar a zona de acreção, o efeito da altura do disco e a mudança na taxa de acreção de gás de acordo com a massa do planeta. As modificações implementadas no modelo de acreção de gás foram realizadas com base nos trabalhos de Dürmann e Kley (2015), Russell (2011) e Fortier et al. (2013). A adaptação no código de acreção de gás para levar em conta uma faixa maior de massas planetárias foi realizada utilizando a escala de tempo de Kelvin-Helmoltz. Para isso, seguimos o trabalho de Ikoma et al. (2000) e Idae Lin (2004b). Para testar o modelo de formação planetária no FARGO3D, a simulação padrão para o disco de gás utilizada nesta tese adota um disco bidimensional fino com taxa de acreção constante. A razão de aspecto do disco será de h = 0.05 com um fator de curvatura de = 0.0. Esses valores são consistentes com a teoria de discos finos e são usados nas maioria das simulações que envolvem discos de acreção (Bell et al., 1997; Frank et al., 2002). O disco é assumido localmente isotérmico e a viscosidade do disco é dirigida pela prescrição de Shakura e Sunyaev (1973), com = 0.03. O modelo de disco é simplificado e caractersticas importantes podem influenciar no processo de formação e migração planetária, como as trocas de energia. No entanto, ele é um ótimo modelo inicial para um teste consistente do modelo de formação planetária implementado, já que possui um resultado analtico conhecido. Casos mais complexos serão explorados em trabalhos futuros. Com o modelo de formação planetária implementado, foi possível estudar simultânea- mente a formação e a migração do planeta dentro do simulador hidrodinâmico. Isto é, analisamos a escala de tempo envolvida no processo de migração em conjunto com a escala de tempo da formação planetária para vários parâmetros fsicos envolvidos no modelo. A análise revelou, para nosso modelo de disco, que a escala de crescimento do planeta conseguiu se manter mais baixa que a escala de migração, mesmo quando o planeta atravessou a linha de gelo, local onde há menor quantidade de material disponvel para a acreção de sólidos. Assim, para planetesimais pequenos (raio 0.1 km), foi possvel obter planetas com massas próximas de 5 massas de Júpiter em regiões entre 0.5 e 1 ua, num tempo menor que o tempo de vida do disco. Vale ressaltar que esta tese conta com uma descrição detalhada de como implementar o modelo dentro do FARGO3D, incluindo um apêndice com o programa comentado linha a linha. O intuito é que o leitor possa usar esse modelo de formação e migração planetária para obter novos resultados e vnculos sobre a formação de sistemas exoplanetários ou do nosso Sistema Solar, assim como usar em qualquer outra aplicação que julgar necessária. / According to the sequential model of accretion, the giant planets are formed from a solid nucleus by capturing planetesimals. When this nucleus reaches a certain mass, it captures the residual gas of the protoplanetary disc that will constitute its envelope, forming a giant planet (Mizuno, 1980; Pollack et al., 1996). The critical part of this scenario is to adjust the planet formation and migration timescales with the lifetime of the disk (Mordasini et al., 2010). Numerical results show that the time required for the formation of a giant planet is very long compared to the lifetime of the disc, and that planetary migration can be very rapid, causing the planets to fall into the star before their full formation. In general, works on planetary formation use analytical models to deal with the migration of the planets (Fortier et al., 2013). However, these analytical models are limited given that they do not include several effects associated with the thermodynamics of the gas disc (Paardekooper et al., 2010). Indeed, in order to deal with planetary migration of type I, these analytical models use physically simple gas discs and rely on the linearization of the hydrodynamic equations (Meyer-Vernet e Sicardy, 1987; Tanaka et al., 2002). For the type II migration, the situation is even more complicated. This is due to the fact that the large mass of the planet creates a gap around the orbit of the planet, causing nonlinearities (Bryden e Lin, 1999). Thus, the numerical results obtained using hydrodynamic simulators, such as FARGO3D (Masset, 2000; Bentez-Llambay e Masset, 2016), ZEUS (Stone e Norman, 1992), PLUTO (Mignone et al., 2012), among others, are essential for a more robust analysis of the processes of planetary migration considering a wider range of physical conditions for the gas disc. However, in general, hydrodynamic simulators do not have a model for the planetaryformation. In some of them, models for gas accretion are built based of the runaway regime of accretion (Kley, 1999). Furthermore, the accretion of solids and the accretion of gas for low mass planets are not considered in most of the cases. This is mainly due to the fact that the models of planetary formation use N-body simulations that are computationally very expensive. Thus, it is necessary to use alternative models for the planetary formation, that are capable of reproducing the same results of an N-body simulation. Building a complete model that takes into account all these processes is a hard and challenging task. So, this project aims the implementation of a physically plausible scenario for a planetary formation inside the magneto-hydrodynamic code FARGO3D. For the accretion model we use the works by Guilera et al. (2010) and Fortier et al. (2013), which employ an statistical model to determine the accretion rate of planetesimals (Inaba et al., 2001). This model will be implemented for the first time in the FARGO3D code. It is now known that the accretion of peebles (material with size ranging from mm and cm) has a important impact on the planetary formation (Lambrechts e Johansen, 2014; Guilera, 2016; Johansen e Lambrechts, 2017), although cores with a few masses of the Earth have a planetary envelope that could destroy those pebbles, before they reach the nucleus (Venturini et al., 2015). In this thesis, we will only deal with the accretion of planetesimals, leaving the study of pebbles for future work. For the gas accretion, we use a modified model based on Kley (1999). The modifications aim to incorporate the Bondi radius (Bondi, 1952) to determine the accretion zone, the effect of the height of the disc and the frequency of accretion. The implemented modifications are based on the works by Dürmann e Kley (2015), Russell (2011) and Fortier et al. (2013). The adaptation in the gas accretion code to take into account a wider range of planetary masses was achieved using the Kelvin-Helmoltz timescale, according to the works by Ikoma et al. (2000) and Ida e Lin (2004b). To test the planetary formation model in FARGO3D, the standard simulation for the gas disc uses a bi-dimensional thin disc. The discs aspect ratio is h = 0.05 with a curvature factor of = 0.0. These values are consistent with the theory of thin dics and are used in most of the simulations for accretion discs (Bell et al., 1997; Frank et al., 2002). The disc is assumed to be locally isothermal and the viscosity of the disc is driven by the prescription from Shakura e Sunyaev (1973), with = 0.03. The disc model is simplified and important features, such as energy exchanges, may influence the process of planetary formation andmigration. However, it is a good initial model for a consistent test of the implemented model of planetary formation, which has an known analysical result. More complex cases will be explored in future work. With the newly implemented model for planetary formation, it was possible to simul- taneously study the planet formation and the planet migration using the hydrodynamic simulator. That is, we analyzed both the timescale for planetary formation and the timescale for the migration of the planet, and compared them for the parameters of the model. The analysis revealed that, for our disc model, the timescale of the growth rate of the planet remained lower than the migration timescale, even when the planet crossed the ice line, where there is less material available for solid accretion. Thus, for small planetesimals (1km radius) it was possible to obtain planets with masses of approximately 5 Jupiter masses in regions between 0.5 and 1 au, in nearly the same time as the lifetime of the disc. It is worth noting that this thesis presents a detailed description of how to implement the model for planetary formation in the FARGO3D, including an appendix with the commented code. The goal is to allow the reader to use this planet formation model to obtain new results both about the formation of exoplanetary systems and our Solar System, as well as use it in any relevant application.