Formation of Giant Planets by Concurrent Accretion of Solids and Gas inside an Anti-Cyclonic Vortex

We study the formation of a giant gas planet by the core--accretion gas--capture process, with numerical simulations, under the assumption that the planetary core forms in the center of an anti-cyclonic vortex. The presence of the vortex concentrates particles of centimeter to meter size from the surrounding disk, and speeds up the core formation process. Assuming that a planet of Jupiter mass is forming at 5 AU from the star, the vortex enhancement results in considerably shorter formation times than are found in standard core--accretion gas--capture simulations. Also, formation of a gas giant is possible in a disk with mass comparable to that of the minimum mass solar nebula.Comment: 27 pages, 4 figures, ApJ in pres

Tracing large-scale structures in circumstellar disks with ALMA

Planets are supposed to form in circumstellar disks. The gravitational potential of a planet perturbs the disk and leads to characteristic structures, i.e. spiral waves and gaps, in the disk's density profile. We perform a large-scale parameter study of the observability of these planet-induced structures in circumstellar disks with ALMA. On the basis of HD and MHD simulations, we calculated the disk temperature structure and (sub)mm images of these systems. These were used to derive simulated ALMA images. Because appropriate objects are frequent in Taurus, we focused on a distance of 140pc and a declination of 20{\deg}. The explored range of star-disk-planet configurations consists of 6 HD simulations (including magnetic fields and different planet masses), 9 disk sizes, 15 total disk masses, 6 different central stars, and two different grain size distributions. On almost all scales and in particular down to a scale of a few AU, ALMA is able to trace disk structures induced by planet-disk interaction or by the influence of magnetic fields on the wavelength range between 0.4 and 2.0mm. In most cases, the optimum angular resolution is limited by the sensitivity. However, within the range of typical masses of protoplanetary disks (0.1-0.001Msun) the disk mass has a minor impact on the observability. It is possible to resolve disks down to 2.67e-6Msun and trace gaps induced by a planet with M_p/M_s = 0.001 in disks with 2.67e-4Msun with a signal-to-noise ratio greater than three. The central star has a major impact on the observability of gaps, as well as the considered maximum grainsize of the dust in the disk. In general, it is more likely to trace planet-induced gaps in our MHD models, because gaps are wider in the presence of magnetic fields. We also find that zonal flows resulting from MRI create gap-like structures in the disk's re-emission radiation, which are observable with ALMA.Comment: 17 pages, 21 figure

Planet-induced disk structures: A comparison between (sub)mm and infrared radiation

Young giant planets, which are embedded in a circumstellar disk, will significantly perturb the disk density distribution. This effect can potentially be used as an indirect tracer for planets. We investigate the feasibility of observing planet-induced gaps in circumstellar disks in scattered light. We perform 3D hydrodynamical disk simulations combined with subsequent radiative transfer calculations in scattered light for different star, disk, and planet configurations. The results are compared to those of a corresponding study for the (sub)mm thermal re-emission. The feasibility of detecting planet-induced gaps in scattered light is mainly influenced by the optical depth of the disk and therefore by the disk size and mass. Planet-induced gaps are in general only detectable if the photosphere of the disks is sufficiently disturbed. Within the limitations given by the parameter space here considered, we find that gap detection is possible in the case of disks with masses below $\sim 10^{-4\dots-3} \, \rm M_\odot$. Compared to the disk mass that marks the lower Atacama Large (Sub)Millimeter Array (ALMA) detection limit for the thermal radiation re-emitted by the disk, it is possible to detect the same gap both in re-emission and scattered light only in a narrow range of disk masses around $\sim 10^{-4} \, \rm M_\odot$, corresponding to $16\%$ of cases considered in our study.Comment: 4 pages, 6 figure

Dust sedimentation and self-sustained Kelvin-Helmholtz turbulence in protoplanetary disk mid-planes. I. Radially symmetric simulations

We perform numerical simulations of the Kelvin-Helmholtz instability in the mid-plane of a protoplanetary disk. A two-dimensional corotating slice in the azimuthal--vertical plane of the disk is considered where we include the Coriolis force and the radial advection of the Keplerian rotation flow. Dust grains, treated as individual particles, move under the influence of friction with the gas, while the gas is treated as a compressible fluid. The friction force from the dust grains on the gas leads to a vertical shear in the gas rotation velocity. As the particles settle around the mid-plane due to gravity, the shear increases, and eventually the flow becomes unstable to the Kelvin-Helmholtz instability. The Kelvin-Helmholtz turbulence saturates when the vertical settling of the dust is balanced by the turbulent diffusion away from the mid-plane. The azimuthally averaged state of the self-sustained Kelvin-Helmholtz turbulence is found to have a constant Richardson number in the region around the mid-plane where the dust-to-gas ratio is significant. Nevertheless the dust density has a strong non-axisymmetric component. We identify a powerful clumping mechanism, caused by the dependence of the rotation velocity of the dust grains on the dust-to-gas ratio, as the source of the non-axisymmetry. Our simulations confirm recent findings that the critical Richardson number for Kelvin-Helmholtz instability is around unity or larger, rather than the classical value of 1/4Comment: Accepted for publication in ApJ. Some minor changes due to referee report, most notably that the clumping mechanism has been identified as the streaming instability of Youdin & Goodman (2005). Movies of the simulations are still available at http://www.mpia.de/homes/johansen/research_en.ph

Dust diffusion in protoplanetary discs by magnetorotational turbulence

We measure the turbulent diffusion coefficient of dust grains embedded in magnetorotational turbulence in a protoplanetary disc directly from numerical simulations and compare it to the turbulent viscosity of the flow. The simulations are done in a local coordinate frame comoving with the gas in Keplerian rotation. Periodic boundary conditions are used in all directions, and vertical gravity is not applied to the gas. Using a two-fluid approach, small dust grains of various sizes (with friction times up to $\varOmega_0 \tau_{\rm f}=0.02$) are allowed to move under the influence of friction with the turbulent gas. We measure the turbulent diffusion coefficient of the dust grains by applying an external sinusoidal force field acting in the vertical direction on the dust component only. This concentrates the dust around the mid-plane of the disc, and an equilibrium distribution of the dust density is achieved when the vertical settling is counteracted by the turbulent diffusion away from the mid-plane. Comparing with analytical expressions for the equilibrium concentration we deduce the vertical turbulent diffusion coefficient. The vertical diffusion coefficient is found to be lower than the turbulent viscosity and to have an associated vertical diffusion Prandtl number of about 1.5. A similar radial force field also allows us to measure the radial turbulent diffusion coefficient. We find a radial diffusion Prandtl number of about 0.85 and also find that the radial turbulent diffusion coefficient is around 70% higher than the vertical. We also find evidence for trapping of dust grains of intermediate friction time in turbulent eddies.Comment: Accepted for publication in ApJ. An additional MPEG movie can be downloaded at http://www.mpia.de/homes/johansen

Rapid planetesimal formation in turbulent circumstellar discs

The initial stages of planet formation in circumstellar gas discs proceed via dust grains that collide and build up larger and larger bodies (Safronov 1969). How this process continues from metre-sized boulders to kilometre-scale planetesimals is a major unsolved problem (Dominik et al. 2007): boulders stick together poorly (Benz 2000), and spiral into the protostar in a few hundred orbits due to a head wind from the slower rotating gas (Weidenschilling 1977). Gravitational collapse of the solid component has been suggested to overcome this barrier (Safronov 1969, Goldreich & Ward 1973, Youdin & Shu 2002). Even low levels of turbulence, however, inhibit sedimentation of solids to a sufficiently dense midplane layer (Weidenschilling & Cuzzi 1993, Dominik et al. 2007), but turbulence must be present to explain observed gas accretion in protostellar discs (Hartmann 1998). Here we report the discovery of efficient gravitational collapse of boulders in locally overdense regions in the midplane. The boulders concentrate initially in transient high pressures in the turbulent gas (Johansen, Klahr, & Henning 2006), and these concentrations are augmented a further order of magnitude by a streaming instability (Youdin & Goodman 2005, Johansen, Henning, & Klahr 2006, Johansen & Youdin 2007) driven by the relative flow of gas and solids. We find that gravitationally bound clusters form with masses comparable to dwarf planets and containing a distribution of boulder sizes. Gravitational collapse happens much faster than radial drift, offering a possible path to planetesimal formation in accreting circumstellar discs.Comment: To appear in Nature (30 August 2007 issue). 18 pages (in referee mode), 3 figures. Supplementary Information can be found at 0708.389

Tracing Planets in Circumstellar Discs

Planets are assumed to form in circumstellar discs around young stellar objects. The additional gravitational potential of a planet perturbs the disc and leads to characteristic structures, i.e. spiral waves and gaps, in the disc density profile. We perform a large-scale parameter study on the observability of these planet-induced structures in circumstellar discs in the (sub)mm wavelength range for the Atacama Large (Sub)Millimeter Array (ALMA). On the basis of hydrodynamical and magneto-hydrodynamical simulations of star-disc-planet models we calculate the disc temperature structure and (sub)mm images of these systems. These are used to derive simulated ALMA maps. Because appropriate objects are frequent in the Taurus-Auriga region, we focus on a distance of 140 pc and a declination of ≈ 20°. The explored range of star-disc-planet configurations consists of six hydrodynamical simulations (including magnetic fields and different planet masses), nine disc sizes with outer radii ranging from 9 AU to 225 AU, 15 total disc masses in the range between 2.67·10-7 M⊙ and 4.10·10-2 M⊙, six different central stars and two different grain size distributions, resulting in 10 000 disc models. At almost all scales and in particular down to a scale of a few AU, ALMA is able to trace disc structures induced by planet-disc interaction or the influence of magnetic fields in the wavelength range between 0.4...2.0 mm. In most cases, the optimum angular resolution is limited by the sensitivity of ALMA. However, within the range of typical masses of protoplane tary discs (0.1 M⊙...0.001 M⊙) the disc mass has a minor impact on the observability. At the distance of 140 pc it is possible to resolve discs down to 2.67·10-6 M⊙ and trace gaps in discs with 2.67·10-4 M⊙ with a signal-to-noise ratio greater than three. In general, it is more likely to trace planet-induced gaps in magneto-hydrodynamical disc models, because gaps are wider in the presence of magnetic fields [1]. We also find, that zonal flows resulting from magneto-rotational instability (MRI) create gap-like structures in the disc re-emission radiation which are observable with ALMA. Through the unprecedented resolution and sensitivity of ALMA in the (sub)mm wavelength range the expected detailed observations of planet-disc interaction and global disc structures will deepen our understanding of the planet formation and disc evolution process. This article presents a summary of the study published by [2]

Tracing Planets in Circumstellar Discs

Planets are assumed to form in circumstellar discs around young stellar objects. The additional gravitational potential of a planet perturbs the disc and leads to characteristic structures, i.e. spiral waves and gaps, in the disc density profile. We perform a large-scale parameter study on the observability of these planet-induced structures in circumstellar discs in the (sub)mm wavelength range for the Atacama Large (Sub)Millimeter Array (ALMA). On the basis of hydrodynamical and magneto-hydrodynamical simulations of star-disc-planet models we calculate the disc temperature structure and (sub)mm images of these systems. These are used to derive simulated ALMA maps. Because appropriate objects are frequent in the Taurus-Auriga region, we focus on a distance of 140 pc and a declination of ≈ 20°. The explored range of star-disc-planet configurations consists of six hydrodynamical simulations (including magnetic fields and different planet masses), nine disc sizes with outer radii ranging from 9 AU to 225 AU, 15 total disc masses in the range between 2.67·10-7 M⊙ and 4.10·10-2 M⊙, six different central stars and two different grain size distributions, resulting in 10 000 disc models. At almost all scales and in particular down to a scale of a few AU, ALMA is able to trace disc structures induced by planet-disc interaction or the influence of magnetic fields in the wavelength range between 0.4...2.0 mm. In most cases, the optimum angular resolution is limited by the sensitivity of ALMA. However, within the range of typical masses of protoplane tary discs (0.1 M⊙...0.001 M⊙) the disc mass has a minor impact on the observability. At the distance of 140 pc it is possible to resolve discs down to 2.67·10-6 M⊙ and trace gaps in discs with 2.67·10-4 M⊙ with a signal-to-noise ratio greater than three. In general, it is more likely to trace planet-induced gaps in magneto-hydrodynamical disc models, because gaps are wider in the presence of magnetic fields [1]. We also find, that zonal flows resulting from magneto-rotational instability (MRI) create gap-like structures in the disc re-emission radiation which are observable with ALMA. Through the unprecedented resolution and sensitivity of ALMA in the (sub)mm wavelength range the expected detailed observations of planet-disc interaction and global disc structures will deepen our understanding of the planet formation and disc evolution process. This article presents a summary of the study published by [2]