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Turbulence-Assisted Planetary Growth: Hydrodynamical Simulations of Accretion Disks and Planet Formation
Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Physics, Department of Physics and Astronomy.
2009 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The current paradigm in planet formation theory is developed around a hierarquical growth of solid bodies, from interstellar dust grains to rocky planetary cores. A particularly difficult phase in the process is the growth from meter-size boulders to planetary embryos of the size of our Moon or Mars. Objects of this size are expected to drift extremely rapid in a protoplanetary disk, so that they would generally fall into the central star well before larger bodies can form.

In this thesis, we used numerical simulations to find a physical mechanism that may retain solids in some parts of protoplanetary disks long enough to allow for the formation of planetary embryos. We found that such accumulation can happen at the borders of so-called dead zones. These dead zones would be regions where the coupling to the ambient magnetic field is weaker and the turbulence is less strong, or maybe even absent in some cases. We show by hydrodynamical simulations that material accumulating between the turbulent active and dead regions would be trapped into vortices to effectively form planetary embryos of Moon to Mars mass.

We also show that in disks that already formed a giant planet, solid matter accumulates on the edges of the gap the planet carves, as well as at the stable Lagrangian points. The concentration is strong enough for the solids to clump together and form smaller, rocky planets like Earth. Outside our solar system, some gas giant planets have been detected in the habitable zone of their stars. Their wakes may harbour rocky, Earth-size worlds.

Place, publisher, year, edition, pages
Uppsala: Universitetsbiblioteket , 2009. , p. viii, 102
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 593
Keywords [en]
accretion, accretion disks, hydrodynamics, instabilities, methods: numerical, solar system: formation, planets and satellites: formation, magnetohydrodynamics (MHD), turbulence, diffusion, stars: planetary systems: formation
National Category
Astronomy, Astrophysics and Cosmology
Identifiers
URN: urn:nbn:se:uu:diva-9537ISBN: 978-91-554-7395-2 (print)OAI: oai:DiVA.org:uu-9537DiVA, id: diva2:173154
Public defence
2009-02-26, Polhemsalem, Ångströmlaboratoriet, Lägerhyddsvägen 1, Uppsala, 14:00
Opponent
Supervisors
Available from: 2009-02-05 Created: 2009-02-05Bibliographically approved
List of papers
1. Global magnetohydrodynamical models of turbulence in protoplanetary disks: I. A cylindrical potential on a Cartesian grid and transport of solids
Open this publication in new window or tab >>Global magnetohydrodynamical models of turbulence in protoplanetary disks: I. A cylindrical potential on a Cartesian grid and transport of solids
2008 (English)In: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 479, p. 883-901Article in journal (Refereed) Published
Abstract [en]

Aims.We present global 3D MHD simulations of disks of gas and solids, aiming at developing models that can be used to study various scenarios of planet formation and planet-disk interaction in turbulent accretion disks. A second goal is to demonstrate that Cartesian codes are comparable to cylindrical and spherical ones in handling the magnetohydrodynamics of the disk simulations while offering advantages, such as the absence of a grid singularity, for certain applications, e.g., circumbinary disks and disk-jet simulations. Methods: We employ the Pencil Code, a 3D high-order finite-difference MHD code using Cartesian coordinates. We solve the equations of ideal MHD with a local isothermal equation of state. Planets and stars are treated as particles evolved with an N-body scheme. Solid boulders are treated as individual superparticles that couple to the gas through a drag force that is linear in the local relative velocity between gas and particle. Results: We find that Cartesian grids are well-suited for accretion disk problems. The disk-in-a-box models based on Cartesian grids presented here develop and sustain MHD turbulence, in good agreement with published results achieved with cylindrical codes. Models without an inner boundary do not show the spurious build-up of magnetic pressure and Reynolds stress seen in the models with boundaries, but the global stresses and alpha viscosities are similar in the two cases. We investigate the dependence of the magnetorotational instability on disk scale height, finding evidence that the turbulence generated by the magnetorotational instability grows with thermal pressure. The turbulent stresses depend on the thermal pressure obeying a power law of 0.24 ± 0.03, compatible with the value of 0.25 found in shearing box calculations. The ratio of Maxwell to Reynolds stresses decreases with increasing temperature, dropping from 5 to 1 when the sound speed was raised by a factor 4, maintaing the same field strength. We also study the dynamics of solid boulders in the hydromagnetic turbulence, by making use of 106 Lagrangian particles embedded in the Eulerian grid. The effective diffusion provided by the turbulence prevents settling of the solids in a infinitesimally thin layer, forming instead a layer of solids of finite vertical thickness. The measured scale height of this diffusion-supported layer of solids implies turbulent vertical diffusion coefficients with globally averaged Schmidt numbers of 1.0 ± 0.2 for a model with α≈10-3 and 0.78 ± 0.06 for a model with α≈10-1. That is, the vertical turbulent diffusion acting on the solids phase is comparable to the turbulent viscosity acting on the gas phase. The average bulk density of solids in the turbulent flow is quite low (ρp = 6.0×10-11 kg m-3), but in the high pressure regions, significant overdensities are observed, where the solid-to-gas ratio reached values as great as 85, corresponding to 4 orders of magnitude higher than the initial interstellar value of 0.01

Keywords
magnetohydrodynamics (MHD), accretion, accretion disks, instabilities, turbulence, solar system: formation, diffusion
National Category
Astronomy, Astrophysics and Cosmology
Identifiers
urn:nbn:se:uu:diva-97999 (URN)10.1051/0004-6361:20077948 (DOI)000253454600026 ()
Available from: 2009-02-05 Created: 2009-02-05 Last updated: 2017-12-14Bibliographically approved
2. Embryos grown in the dead zone: Assembling the first protoplanetary cores in low mass self-gravitating circumstellar disks of gas and solids
Open this publication in new window or tab >>Embryos grown in the dead zone: Assembling the first protoplanetary cores in low mass self-gravitating circumstellar disks of gas and solids
2008 (English)In: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 491, no 3, p. L41-L44Article in journal (Refereed) Published
Abstract [en]

Context: In the borders of the dead zones of protoplanetary disks, the inflow of gas produces a local density maximum that triggers the Rossby wave instability. The vortices that form are efficient in trapping solids. Aims: We aim to assess the possibility of gravitational collapse of the solids within the Rossby vortices. Methods: We perform global simulations of the dynamics of gas and solids in a low mass non-magnetized self-gravitating thin protoplanetary disk with the Pencil Code. We use multiple particle species of radius 1, 10, 30, and 100 cm. The dead zone is modelled as a region of low viscosity. Results: The Rossby vortices excited in the edges of the dead zone are efficient particle traps. Within 5 orbits after their appearance, the solids achieve critical density and undergo gravitational collapse into Mars sized objects. The velocity dispersions are of the order of 10 m s-1 for newly formed embryos, later lowering to less than 1 m s-1 by drag force cooling. After 200 orbits, over 300 gravitationally bound embryos were formed, 20 of them being more massive than Mars. Their mass spectrum follows a power law of index -2.3 ± 0.2.

Keywords
Accretion, accretion disks; Instabilites; Stars: planetary systems: formation
National Category
Physical Sciences
Identifiers
urn:nbn:se:uu:diva-98000 (URN)10.1051/0004-6361:200810626 (DOI)000261152900001 ()
Available from: 2009-02-05 Created: 2009-02-05 Last updated: 2017-12-14Bibliographically approved
3. Planet formation bursts at the borders of the dead zone in 2D numerical simulations of circumstellar disks
Open this publication in new window or tab >>Planet formation bursts at the borders of the dead zone in 2D numerical simulations of circumstellar disks
Show others...
2009 (English)In: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 497, no 3, p. 869-888Article in journal (Refereed) Published
Abstract [en]

Context: As accretion in protoplanetary disks is enabled by turbulent viscosity, the border between active and inactive (dead) zones constitutes a location where there is an abrupt change in the accretion flow. The gas accumulation that ensues triggers the Rossby wave instability, which in turn saturates into anticyclonic vortices. It has been suggested that the trapping of solids within them leads to a burst of planet formation on very short timescales. Aims: We study in the formation and evolution of the vortices in greater detail, focusing on the implications for the dynamics of embedded solid particles and planet formation. Methods: We performed two-dimensional global simulations of the dynamics of gas and solids in a non-magnetized thin protoplanetary disk with the Pencil code. We used multiple particle species of radius 1, 10, 30, and 100 cm. We computed the particles' gravitational interaction by a particle-mesh method, translating the particles' number density into surface density and computing the corresponding self-gravitational potential via fast Fourier transforms. The dead zone is modeled as a region of low viscosity. Adiabatic and locally isothermal equations of state are used. Results: The Rossby wave instability is triggered under a variety of conditions, thus making vortex formation a robust process. Inside the vortices, fast accumulation of solids occurs and the particles collapse into objects of planetary mass on timescales as short as five orbits. Because the drag force is size-dependent, aerodynamical sorting ensues within the vortical motion, and the first bound structures formed are composed primarily of similarly-sized particles. In addition to erosion due to ram pressure, we identify gas tides from the massive vortices as a disrupting agent of formed protoplanetary embryos. We find evidence that the backreaction of the drag force from the particles onto the gas modifies the evolution of the Rossby wave instability, with vortices being launched only at later times if this term is excluded from the momentum equation. Even though the gas is not initially gravitationally unstable, the vortices can grow to Q ≈ 1 in locally isothermal runs, which halts the inverse cascade of energy towards smaller wavenumbers. As a result, vortices in models without self-gravity tend to rapidly merge towards a m = 2 or m =1 mode, while models with self-gravity retain dominant higher order modes (m = 4 or m = 3) for longer times. Non-selfgravitating disks thus show fewer and stronger vortices. We also estimate the collisional velocity history of the particles that compose the most massive embryo by the end of the simulation, finding that the vast majority of them never experienced a collision with another particle at speeds faster than 1 m s-1. This result lends further support to previous studies showing that vortices provide a favorable environment for planet formation.

Keywords
accretion, accretion disks; hydrodynamics; instabilities; stars: planetary systems: formation; methods: numerical; turbulence
National Category
Physical Sciences
Identifiers
urn:nbn:se:uu:diva-98001 (URN)10.1051/0004-6361/200811265 (DOI)000265280500022 ()
Available from: 2009-02-05 Created: 2009-02-05 Last updated: 2017-12-14Bibliographically approved
4. Standing on the shoulders of giants: Trojan Earths and vortex trapping in low mass self-gravitating protoplanetary disks of gas and solids
Open this publication in new window or tab >>Standing on the shoulders of giants: Trojan Earths and vortex trapping in low mass self-gravitating protoplanetary disks of gas and solids
2009 (English)In: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 493, no 3, p. 1125-1139Article in journal (Refereed) Published
Abstract [en]

Context: Centimeter and meter-sized solid particles in protoplanetary disks are trapped within long-lived, high-pressure regions, creating opportunities for collapse into planetesimals and planetary embryos. Aims: We aim to study the effect of the high-pressure regions generated in the gaseous disks by a giant planet perturber. These regions consist of gas retained in tadpole orbits around the stable Lagrangian points as a gap is carved, and the Rossby vortices launched at the edges of the gap. Methods: We performed global simulations of the dynamics of gas and solids in a low mass non-magnetized self-gravitating thin protoplanetary disk. We employed the Pencil code to solve the Eulerian hydro equations, tracing the solids with a large number of Lagrangian particles, usually 100 000. To compute the gravitational potential of the swarm of solids, we solved the Poisson equation using particle-mesh methods with multiple fast Fourier transforms. Results: Huge particle concentrations are seen in the Lagrangian points of the giant planet, as well as in the vortices they induce at the edges of the carved gaps. For 1 cm to 10 cm radii, gravitational collapse occurs in the Lagrangian points in less than 200 orbits. For 5 cm particles, a 2M planet is formed. For 10 cm, the final maximum collapsed mass is around 3M. The collapse of the 1 cm particles is indirect, following the timescale of gas depletion from the tadpole orbits. Vortices are excited at the edges of the gap, primarily trapping particles of 30 cm radii. The rocky planet that is formed is as massive as 17M, constituting a Super-Earth. Collapse does not occur for 40 cm onwards. By using multiple particle species, we find that gas drag modifies the streamlines in the tadpole region around the classical L4 and L5 points. As a result, particles of different radii have their stable points shifted to different locations. Collapse therefore takes longer and produces planets of lower mass. Three super-Earths are formed in the vortices, the most massive having 4.5M. Conclusions: A Jupiter-mass planet can induce the formation of other planetary embryos at the outer edge of its gas gap. Trojan Earth-mass planets are readily formed; although not existing in the solar system, might be common in the exoplanetary zoo.

Keywords
accretion, accretion disks; hydrodynamics; instabilities; methods: numerical; solar system: formation; planets and satellites: formation
National Category
Physical Sciences
Identifiers
urn:nbn:se:uu:diva-98002 (URN)10.1051/0004-6361:200810797 (DOI)000262641100033 ()
Available from: 2009-02-05 Created: 2009-02-05 Last updated: 2017-12-14Bibliographically approved

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