Potential Vorticity Evolution of a Protoplanetary Disk with an Embedded Protoplanet

Li, Hui; Li, Shengtai; Koller, J.; Wendroff, Burton; Liska, R.; Orban, Chris; Liang, Edison; Lin, D. N. C.

doi:10.1086/429367

Cited by 128 publications

(188 citation statements)

References 19 publications

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“…Vortices induced by the planet occur for low-viscosity disks and have already been seen in earlier simulations (see e.g. Li et al 2005;de Val-Borro et al 2006;Li et al 2009). Here, we do not discuss this issue any further.…”

Section: Results For the Standard Casesupporting

confidence: 71%

Low-mass planets in nearly inviscid disks: numerical treatment

Kley

Mueller

Kolb

et al. 2012

A&A

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Context. Embedded planets disturb the density structure of the ambient disk, and gravitational back-reaction possibly will induce a change in the planet's orbital elements. Low-mass planets only have a weak impact on the disk, so their wake's torque can be treated in linear theory. Larger planets will begin to open up a gap in the disk through nonlinear interaction. Accurate determination of the forces acting on the planet requires careful numerical analysis. Recently, the validity of the often used fast orbital advection algorithm (FARGO) has been put into question, and special numerical resolution and stability requirements have been suggested. Aims. We study the process of planet-disk interaction for low-mass planets of a few Earth masses, and reanalyze the numerical requirements to obtain converged and stable results. One focus lies on the applicability of the FARGO-algorithm. Additionally, we study the difference of two and three-dimensional simulations, compare global with local setups, as well as isothermal and adiabatic conditions. Methods. We study the influence of the planet on the disk through two-and three-dimensional hydrodynamical simulations. To strengthen our conclusions we perform a detailed numerical comparison where several upwind and Riemann-solver based codes are used with and without the FARGO-algorithm. Results. With respect to the wake structure and the torque density acting on the planet, we demonstrate that the FARGO-algorithm yields correct a correct and stable evolution for the planet-disk problem, and that at a fraction of the regular cpu-time. We find that the resolution requirements for achieving convergent results in unshocked regions are rather modest and depend on the pressure scale height H of the disk. By comparing the torque densities of two-and three-dimensional simulations we show that a suitable vertical averaging procedure for the force gives an excellent agreement between the two. We show that isothermal and adiabatic runs can differ considerably, even for adiabatic indices very close to unity.

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Section: Results For the Standard Casesupporting

confidence: 71%

Low-mass planets in nearly inviscid disks: numerical treatment

Kley

Mueller

Kolb

et al. 2012

A&A

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“…Lyra & Mac Low 2012;Regály et al 2012;Miranda et al 2016) and gap-edges created by giant planets (e.g. Li et al 2005). E-mail: mhammer@as.arizona.edu (MH); kkratter@email.arizona.edu (KMK); mkl@asiaa.sinica.edu.tw (M-KL) † Steward Theory Fellow.…”

Section: Introductionmentioning

confidence: 99%

Slowly-growing gap-opening planets trigger weaker vortices

Hammer

Kratter

Lin

2016

Mon. Not. R. Astron. Soc.

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The presence of a giant planet in a low-viscosity disc can create a gap edge in the disc's radial density profile sharp enough to excite the Rossby wave instability. This instability may evolve into dust-trapping vortices that might explain the 'banana-shaped' features in recently observed asymmetric transition discs with inner cavities. Previous hydrodynamical simulations of planet-induced vortices have neglected the time-scale of hundreds to thousands of orbits to grow a massive planet to Jupiter size. In this work, we study the effect of a giant planet's runaway growth time-scale on the lifetime and characteristics of the resulting vortex. For two different planet masses (1 and 5 Jupiter masses) and two different disc viscosities (α = 3 × 10 −4 and 3 × 10 −5 ), we compare the vortices induced by planets with several different growth time-scales between 10 and 4000 planet orbits. In general, we find that slowly-growing planets create significantly weaker vortices with lifetimes and surface densities reduced by more than 50 per cent. For the higher disc viscosity, the longest growth time-scales in our study inhibit vortex formation altogether. Additionally, slowly-growing planets produce vortices that are up to twice as elongated, with azimuthal extents well above 180 • in some cases. These unique, elongated vortices likely create a distinct signature in the dust observations that differentiates them from the more concentrated vortices that correspond to planets with faster growth time-scales. Lastly, we find that the low viscosities necessary for vortex formation likely prevent planets from growing quickly enough to trigger the instability in self-consistent models.

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“…A massive planet, which opens a gap, can likewise produce a sufficiently steep density gradient at the gap edges and, therefore, vortices would be developed on both sides of the gap (e.g. Li et al 2005;de Val-Borro et al 2007;Ataiee et al 2013;Fu et al 2014).…”

Section: Introductionmentioning

confidence: 99%

Planet-vortex interaction: How a vortex can shepherd a planetary embryo

Ataiee

Dullemond

Kley

et al. 2014

A&A

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Context. Anti-cyclonic vortices are considered to be a favourable places for trapping dust and forming planetary embryos. On the other hand, they are massive blobs that can interact gravitationally with the planets in the disc. Aims. We aim to study how a vortex interacts gravitationally with a planet that migrates towards the vortex or with a planet that is created inside the vortex. Methods. We performed hydrodynamical simulations of a viscous locally isothermal disc using GFARGO and FARGO-ADSG. We set a stationary Gaussian pressure bump in the disc so that a large vortex is formed and maintained as a result of Rossby wave instability (RWI). After the vortex is established, we implanted a low-mass planet ([5, 1, 0.5] × 10 −6 M ) in the outer disc or inside the vortex and allowed it to migrate. We also examined the effect of vortex strength on the planet migration by doubling the height of the bump and checked the validity of the final result in the presence of self-gravity. Results. We noticed that regardless of the planet's initial position, the planet is finally locked to the RWI-created vortex in a 1:1 resonance or its migration is stopped at a larger orbital distance, in case of a stronger vortex. For the model with the weaker vortex (our standard model), we studied the effect of different parameters such as background viscosity, background surface density, mass of the planet, and different planet positions. In these models, while the trapping time and locking angle of the planet vary for different parameters, the main result, which is the planet-vortex locking, remains valid. We discovered that even a planet with a mass less than 5 × 10 −7 M comes out from the vortex and is locked to it at the same orbital distance. For a stronger vortex, both in non-selfgravitating and self-gravitating models, the planet migration is stopped far away from the radial position of the vortex. This effect can make the vortices a suitable place for continual planet formation under the condition that they save their shape during the planetary growth.

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Potential Vorticity Evolution of a Protoplanetary Disk with an Embedded Protoplanet

Cited by 128 publications

References 19 publications

Low-mass planets in nearly inviscid disks: numerical treatment

Low-mass planets in nearly inviscid disks: numerical treatment

Slowly-growing gap-opening planets trigger weaker vortices

Planet-vortex interaction: How a vortex can shepherd a planetary embryo

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