Simulations of planet-disc interactions using Smoothed Particle Hydrodynamics

Schäfer, Christoph; Speith, R.; Hipp, M.; Kley, W.

doi:10.1051/0004-6361:20034034

Cited by 31 publications

(36 citation statements)

References 49 publications

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“…While this may seem to be quite low resolution for today's SPH simulations (cf. N gas ∼ 300 000 in Rice et al 2003;and Schäfer et al 2004) BF05 showed that this level of resolution gives the same results as simulations with almost twice as many particles (in the case of a disk without a planet). It should be noted that in our two-phase code, the time step is severely limited by the drag timescale.…”

Section: Implementation and Initial Conditionsmentioning

confidence: 81%

“…However, since observations of protoplanetary disks indicate α SS ∼ 0.01, SPH can do an adequate job and indeed one of the first simulations of an embedded planet in a disk by Sekiya et al (1987) used SPH. Schäfer et al (2004) present a new treatment of the viscosity in SPH codes which includes an additional artificial bulk viscosity term in the Navier-Stokes equation and demonstrate that their results compare well with grid-based codes. This is however very computationally expensive and has not been implemented in our code.…”

Section: Viscositymentioning

confidence: 86%

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The effect of a planet on the dust distribution in a 3D protoplanetary disk

Fouchet

Maddison²,

Gonzalez³

et al. 2007

A&A

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Aims. We investigate the behaviour of dust in protoplanetary disks under the action of gas drag in the presence of a planet. Our goal is twofold: to determine the spatial distribution of dust depending on grain size and planet mass, and therefore to provide a framework for interpretation of coming observations and future studies of planetesimal growth. Methods. We numerically model the evolution of dust in a protoplanetary disk using a two-fluid (gas + dust) Smoothed Particle Hydrodynamics (SPH) code, which is non-self-gravitating and locally isothermal. The code follows the three dimensional distribution of dust in a protoplanetary disk as it interacts with the gas via aerodynamic drag. In this work, we present the evolution of a minimum mass solar nebula (MMSN) disk comprising 1% dust by mass in the presence of an embedded planet. We run a series of simulations which vary the grain size and planetary mass to see how they affect the resulting disk structure. Results. We find that gap formation is much more rapid and striking in the dust layer than in the gaseous disk and that a system with a given stellar, disk and planetary mass will have a completely different appearance depending on the grain size. For low mass planets in our MMSN disk, a gap can open in the dust disk while not in the gas disk. We also note that dust accumulates at the external edge of the planetary gap and speculate that the presence of a planet in the disk may enhance the formation of a second planet by facilitating the growth of planetesimals in this high density region.

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Section: Implementation and Initial Conditionsmentioning

confidence: 81%

Section: Viscositymentioning

confidence: 86%

The effect of a planet on the dust distribution in a 3D protoplanetary disk

Fouchet

Maddison²,

Gonzalez³

et al. 2007

A&A

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“…Apparently, high eccentricities occur without benefit of any current companions, an attribute of observed exoplanets that is not well explained. Models of disk pumping of eccentricities (Goldreich & Sari 2003) require more attention (Schäfer et al 2004). The similarity in the eccentricities of single planets and multiple planets suggests that the origin of the eccentricities may be the same.…”

Section: Discussionmentioning

confidence: 99%

Five New Multicomponent Planetary Systems

Vogt

Butler

Marcy

et al. 2005

ApJ

234

274

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We report Doppler measurements for six nearby G-and K-type main-sequence stars that show multiple low-mass companions, at least one of which has planetary mass. One system has three planets, the fourth triple-planet system known around a normal star, and another has an extremely low minimum mass of 18 M È . HD 128311 ( K0 V ) has two planets (one previously known) with minimum masses (M sin i) of 2.18M J and 3.21M J and orbital periods of 1.26 and 2.54 yr, suggesting a possible 2:1 resonance. For HD 108874 (G5 V ), the velocities reveal two planets (one previously known) having minimum masses and periods of (M sin i b ¼ 1:36M J , P b ¼ 1:08 yr) and (M sin i c ¼ 1:02M J , P c ¼ 4:4 yr). HD 50499 (G1 V ) has a planet with P ¼ 6:8 yr and M sin i ¼ 1:7M J , and the velocity residuals exhibit a trend of À4.8 m s À1 yr À1 , indicating a more distant companion with P > 10 yr and minimum mass of 2M J . HD 37124 (G4 IV-V ) has three planets, one having M sin i ¼ 0:61M J and P ¼ 154:5 days, as previously known. We find two plausible triple-planet models that fit the data, both having a second planet near P ¼ 840 days, with the more likely model having its third planet in a 6 yr orbit and the other one in a 29 day orbit. For HD 190360, we confirm the planet having P ¼ 7:9 yr and M sin i ¼ 1:5M J as found by the Geneva team, but we find a distinctly noncircular orbit with e ¼ 0:36 AE 0:03, rendering this not an analog of Jupiter as had been reported. Our velocities also reveal a second planet with P ¼ 17:1 days and M sin i ¼ 18:1 M È . HD 217107 (G8 IV) has a previously known ''hot Jupiter'' with M sin i ¼ 1:4M J and P ¼ 7:13 days, and we confirm its high eccentricity, e ¼ 0:13. The velocity residuals reveal an outer companion in an eccentric orbit, having minimum mass of M sin i > 2M J , eccentricity e $ 0:5, and a period P > 8 yr, implying a semimajor axis a > 4 AU and providing an opportunity for direct detection. We have obtained high-precision photometry of five of the six planetary host stars with three of the automated telescopes at Fairborn Observatory. We can rule out significant brightness variations in phase with the radial velocities in most cases, thus supporting planetary reflex motion as the cause of the velocity variations. Transits are ruled out to very shallow limits for HD 217107 and are also shown to be unlikely for the prospective inner planets of the HD 37124 and HD 108874 systems. HD 128311 is photometrically variable with an amplitude of 0.03 mag and a period of 11.53 days, which is much shorter than the orbital periods of its two planetary companions. This rotation period explains the origin of periodic velocity residuals to the two-planet model of this star. All of the planetary systems here would be further constrained with astrometry by the Space Interferometry Mission.

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“…SPH is now used widely to simulate the evolution of disks (Bate et al 2003;Rice et al 2003aRice et al ,b, 2004Mayer et al 2004;Schaefer et al 2004;Boffin et al 1998;Watkins et al 1998a,b;Stamatellos et al 2008Stamatellos et al , 2009). The behaviour of viscosity in real circular shear flow in fluids is understood analytically and experimentally (e.g.…”

Section: Introductionmentioning

confidence: 99%

Controlling artificial viscosity in smoothed particle hydrodynamics simulations of accretion disks

Cartwright

Stamatellos

2010

A&A

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Context. The fidelity of smoothed particle hydrodynamics (SPH) simulations of accretion disks depends on how artificial viscosity (AV) is formulated. Aims. We investigate whether standard methodology is reliable in this regard. Methods. We test the operation of two methods for selective application of AV in SPH simulations of Keplerian accretion disks, using a ring spreading test to quantify effective viscosity, and a correlation coefficient technique to measure the formation of unwanted prograde alignments of particles. Results. Neither the Balsara switch (B) nor time dependent viscosity (TDV) work effectively, as they leave AV active in areas of smooth shearing flow, and do not eliminate the accumulation of alignments of particles in the prograde direction. The effect of both switches is periodic, the periodicity dependent on radius and unaffected by the density of particles. We demonstrate that a very simple algorithm activates AV only when truly convergent flow is detected and reduces the unwanted formation of prograde alignments. The new switch works by testing whether all the neighbours of a particle are in Keplerian orbit around the same point, rather than calculating the divergence of the velocity field, which is very strongly affected by Poisson noise in the positions of the SPH particles.

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Simulations of planet-disc interactions using Smoothed Particle Hydrodynamics

Cited by 31 publications

References 49 publications

The effect of a planet on the dust distribution in a 3D protoplanetary disk

The effect of a planet on the dust distribution in a 3D protoplanetary disk

Five New Multicomponent Planetary Systems

Controlling artificial viscosity in smoothed particle hydrodynamics simulations of accretion disks

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