FARGO: A fast eulerian transport algorithm for differentially
rotating disks

Masset, F.

doi:10.1051/aas:2000116

Cited by 514 publications

(488 citation statements)

References 7 publications

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“…The most visible manifestation of the disk's eccentric state is that the outer rim of the gap opened by the giant planet has an elliptic shape. After performing a series of hydrodynamical simulations with the code FARGO (Masset 2000), we can also confirm the results of Kley & Dirksen (2006) even using α-type viscosity. Note that beside the elliptic geometry that is clearly visible in the disk surface-density distribution, the giant planet also disturbs the motion of the gas parcels near the gap.…”

Section: Introductionsupporting

confidence: 63%

Detectability of giant planets in protoplanetary disks by CO emission lines

Regály

Sándor

Dullemond

et al. 2010

A&A

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Context. Planets are thought to form in protoplanetary accretion disks around young stars. Detecting a giant planet still embedded in a protoplanetary disk would be very important and give observational constraints on the planet-formation process. However, detecting these planets with the radial velocity technique is problematic owing to the strong stellar activity of these young objects. Aims. We intend to provide an indirect method to detect Jovian planets by studying near infrared emission spectra originating in the protoplanetary disks around T Tauri stars. Our idea is to investigate whether a massive planet could induce any observable effect on the spectral lines emerging in the disks atmosphere. As a tracer molecule we propose CO, which is excited in the ro-vibrational fundamental band in the disk atmosphere to a distance of ∼2−3 AU (depending on the stellar mass) where terrestrial planets are thought to form. Methods. We developed a semi-analytical model to calculate synthetic molecular spectral line profiles in a protoplanetary disk using a double layer disk model heated on the outside by irradiation by the central star and in the midplane by viscous dissipation due to accretion. 2D gas dynamics were incorporated in the calculation of synthetic spectral lines. The motions of gas parcels were calculated by the publicly available hydrodynamical code FARGO which was developed to study planet-disk interactions. Results. We demonstrate that a massive planet embedded in a protoplanetary disk strongly influences the originally circular Keplerian gas dynamics. The perturbed motion of the gas can be detected by comparing the CO line profiles in emission, which emerge from planet-bearing to those of planet-free disk models. The planet signal has two major characteristics: a permanent line profile asymmetry, and short timescale variability correlated with the orbital phase of the giant planet. We have found that the strength of the asymmetry depends on the physical parameters of the star-planet-disk system, such as the disk inclination angle, the planetary and stellar masses, the orbital distance, and the size of the disk inner cavity. The permanent line profile asymmetry is caused by a disk in an eccentric state in the gap opened by the giant planet. However, the variable component is a consequence of the local dynamical perturbation by the orbiting giant planet. We show that a forming giant planet, still embedded in the protoplanetary disk, can be detected using contemporary or future high-resolution near-IR spectrographs like VLT/CRIRES and ELT/METIS.

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Section: Introductionsupporting

confidence: 63%

Detectability of giant planets in protoplanetary disks by CO emission lines

Regály

Sándor

Dullemond

et al. 2010

A&A

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“…We use FARGO (Masset 2000) to carry out simulations of a gas giant planet with a prescribed growth rate embedded in a low-viscosity disc. FARGO is a 2D finite-difference hydrodynamical code that solves the Navier-Stokes equations in cylindrical polar coordinates (r, φ).…”

Section: Methodsmentioning

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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“…This approximation has the advantage of providing us an analytic expression for the computation of the gap profiles. In fact, the disk equilibrium equation (12) becomes : with a ′′ and t g given in Eq. (13) and (11) respectively.…”

Section: An Explicit Equation For the Gap Profilementioning

confidence: 99%

On the width and shape of gaps in protoplanetary disks

Crida¹,

Morbidelli²,

Masset³

2006

Icarus

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589

738

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Although it is well known that a massive planet opens a gap in a proto-planetary gaseous disk, there is no analytic description of the surface density profile in and near the gap. The simplest approach, which is based upon the balance between the torques due to the viscosity and the gravity of the planet and assumes local damping, leads to gaps with overestimated width, especially at low viscosity. Here, we take into account the fraction of the gravity torque that is evacuated by pressure supported waves. With a novel approach, which consists of following the fluid elements along their trajectories, we show that the flux of angular momentum carried by the waves corresponds to a pressure torque. The equilibrium profile of the disk is then set by the balance between gravity, viscous and pressure torques. We check that this balance is satisfied in numerical simulations, with a planet on a fixed circular orbit. We then use a reference numerical simulation to get an ansatz for the pressure torque, that yields gap profiles for any value of the disk viscosity, pressure scale height and planet to primary mass ratio. Those are in good agreement with profiles obtained in numerical simulations over a wide range of parameters. Finally, we provide a gap opening criterion that simultaneously involves the planet mass, the disk viscosity and the aspect ratio.

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FARGO: A fast eulerian transport algorithm for differentially rotating disks

Cited by 514 publications

References 7 publications

Detectability of giant planets in protoplanetary disks by CO emission lines

Detectability of giant planets in protoplanetary disks by CO emission lines

Slowly-growing gap-opening planets trigger weaker vortices

On the width and shape of gaps in protoplanetary disks

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