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Numerical simulations of type III planetary migration
Stockholm University, Faculty of Science, Department of Astronomy.
2008 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Planets are believed to form in primordial gas-dust discs surrounding newborn stars. An important breakthrough in our understanding of planetary formation was the discovery of extra-solar planets around sun-like stars, especially the frequent occurrence of giant planets on close orbits (hot Jupiters). The mechanisms involved in the formation of these objects remain uncertain, however the difficulties associated with their formation at their observed orbital radius has awoken an interest in theories for the migration of protoplanetary cores due to gravitational interaction with the disc. There are three fundamental regimes of planet migration. The type I and II migration regimes, driven by the differential Lindblad torques, result mostly in inward migration and concern low- and high-mass planets respectively. Type III migration, driven by the co-orbital gas flow, concerns an intermediate range of planetary masses and does not have a predefined direction.

In this thesis the orbital evolution of a high-mass, rapidly (type III) migrating planet is investigated using numerical hydrodynamical simulations. For these simulations we used the state-of-the-art hydrodynamics code FLASH. We focus on the physical aspects of type III migration. However, the problem of rapid migration of such massive planets is numerically challenging, and the disc model has to be chosen carefully, using numerical convergence as a discriminator between models (Paper I). We simulate both inward and outward directed migration (Papers II and III) and provide an extensive description of the co-orbital flow responsible for driving the migration, as well as its time evolution. The migration rate due to type III migration is found to be related to the mass of the planet's co-orbital region, making inward and outward directed migration self-decelerating and self-accelerating processes respectively (for a standard disc model). Rapid migration depends strongly on the flow structure in the planet's vicinity, which makes it sensitive to the amount of mass accumulated by the planet as it moves through the disc. This quantity in turn depends on the structure of the accretion region around the planet. The results of the numerical simulations show a good agreement with the analytical formulation of type III migration (Paper IV).

Place, publisher, year, edition, pages
Stockholm: Institutionen för astronomi , 2008. , 65 p.
Keyword [en]
planetary system formation
National Category
Astronomy, Astrophysics and Cosmology
Research subject
Astronomy
Identifiers
URN: urn:nbn:se:su:diva-7461ISBN: 978-91-7155-623-3 (print)OAI: oai:DiVA.org:su-7461DiVA: diva2:198342
Public defence
2008-05-07, sal FB53, AlbaNova universitetscentrum, Roslagstullsbacken 21, Stockholm, 10:00
Opponent
Supervisors
Available from: 2008-04-16 Created: 2008-04-16Bibliographically approved
List of papers
1. Numerical simulations of type III planetary migration - I. Disc model and convergence tests
Open this publication in new window or tab >>Numerical simulations of type III planetary migration - I. Disc model and convergence tests
2008 (English)In: Monthly notices of the Royal Astronomical Society, ISSN 0035-8711, E-ISSN 1365-2966, Vol. 386, no 1, 164-178 p.Article in journal (Refereed) Published
Abstract [en]

We investigate the fast (type III) migration regime of high-mass protoplanets orbiting in protoplanetary discs. This type of migration is dominated by corotational torques. We study the details of flow structure in the planet's vicinity, the dependence of migration rate on the adopted disc model and the numerical convergence of models (independence of certain numerical parameters such as gravitational softening).

We use two-dimensional hydrodynamical simulations with adaptive mesh refinement, based on the flash code with improved time-stepping scheme. We perform global disc simulations with sufficient resolution close to the planet, which is allowed to freely move throughout the grid. We employ a new type of equation of state in which the gas temperature depends on both the distance to the star and planet, and a simplified correction for self-gravity of the circumplanetary gas.

We find that the migration rate in the type III migration regime depends strongly on the gas dynamics inside the Hill sphere (Roche lobe of the planet) which, in turn, is sensitive to the aspect ratio of the circumplanetary disc. Furthermore, corrections due to the gas self-gravity are necessary to reduce numerical artefacts that act against rapid planet migration. Reliable numerical studies of type III migration thus require consideration of both the thermal and the self-gravity corrections, as well as a sufficient spatial resolution and the calculation of disc–planet attraction both inside and outside the Hill sphere. With this proviso, we find type III migration to be a robust mode of migration, astrophysically promising because of a speed much faster than in the previously studied modes of migration.

Keyword
accretion, accretion discs, hydrodynamics, methods: numerical, planets and satellites: formation
National Category
Astronomy, Astrophysics and Cosmology
Identifiers
urn:nbn:se:su:diva-24804 (URN)10.1111/j.1365-2966.2008.13045.x (DOI)000255142500036 ()
Available from: 2008-04-16 Created: 2008-04-16 Last updated: 2012-11-20Bibliographically approved
2. Numerical simulations of type III planetary migration - II. Inward migration of massive planets
Open this publication in new window or tab >>Numerical simulations of type III planetary migration - II. Inward migration of massive planets
2008 (English)In: Monthly notices of the Royal Astronomical Society, ISSN 0035-8711, E-ISSN 1365-2966, Vol. 386, no 1, 179-198 p.Article in journal (Refereed) Published
Abstract [en]

We present a numerical study of rapid, so-called type III migration for Jupiter-sized planets embedded in a protoplanetary disc. We limit ourselves to the case of inward migration, and study in detail its evolution and physics, concentrating on the structure of the corotation and circumplanetary regions, and processes for stopping migration. We also consider the dependence of the migration behaviour on several key parameters. We perform this study using the results of global, two-dimensional hydrodynamical simulations with adaptive mesh refinement. The initial conditions are chosen to satisfy the condition for rapid inward migration. We find that type III migration can be divided into two regimes, fast and slow. The structure of the co-orbital region, mass accumulation rate and migration behaviour differ between these two regimes. All our simulations show a transition from the fast to the slow regime, ending type III migration well before reaching the star. The stopping radius is found to be larger for more massive planets and less massive discs. A sharp density drop is also found to be an efficient stopping mechanism. In the fast migration regime the migration rate and induced eccentricity are lower for less massive discs, but almost do not depend on planet mass. Eccentricity is damped on the migration time-scale.

National Category
Astronomy, Astrophysics and Cosmology
Identifiers
urn:nbn:se:su:diva-24805 (URN)10.1111/j.1365-2966.2008.13046.x (DOI)000255142500037 ()
Available from: 2008-04-16 Created: 2008-04-16 Last updated: 2013-07-08Bibliographically approved
3. Numerical simulations of type III planetary migration: III. Outward migration of massive planets
Open this publication in new window or tab >>Numerical simulations of type III planetary migration: III. Outward migration of massive planets
2008 (English)In: Monthly notices of the Royal Astronomical Society, ISSN 0035-8711, E-ISSN 1365-2966, Vol. 387, no 3, 1063-1079 p.Article in journal (Refereed) Published
Abstract [en]

We present a numerical study of rapid, so-called type III migration for Jupiter-sized planets embedded in a protoplanetary disc. We limit ourselves to the case of outward migration, and study in detail its evolution and physics, concentrating on the structure of the corotation and circumplanetary regions, and processes for stopping migration. We also consider the dependence of the migration behaviour on several key parameters. We perform this study using global, two-dimensional hydrodynamical simulations with adaptive mesh refinement. We find that the outward-directed type III migration can be started if the initial conditions support the initial average non-dimensional migration rate bigger than one. Unlike the inward-directed migration, in the outward migration the migration rate increases due to the growing of the volume of the co-orbital region. We find the migration to be strongly dependent on the rate of the mass accumulation in the circumplanetary disc, leading to two possible regimes of migration, fast and slow. The structure of the co-orbital region and the stopping mechanism differs between these two regimes.

Keyword
accretion, accretion discs;hydrodynamics;methods: numerical;planets and satellites: formation
National Category
Astronomy, Astrophysics and Cosmology
Identifiers
urn:nbn:se:su:diva-24806 (URN)10.1111/j.1365-2966.2008.13339.x (DOI)000256732700010 ()
Available from: 2008-04-16 Created: 2008-04-16 Last updated: 2011-02-24Bibliographically approved
4. Analytical theory of type III planetary migration
Open this publication in new window or tab >>Analytical theory of type III planetary migration
2008 In: The Astrophysical JournalArticle in journal (Refereed) In press
Identifiers
urn:nbn:se:su:diva-24807 (URN)
Note
Part of urn:nbn:se:su:diva-7461Available from: 2008-04-16 Created: 2008-04-16 Last updated: 2010-01-14Bibliographically approved

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