Global structure of magnetorotationally turbulent protoplanetary discs

Flaig, Markus; Ruoff, Patrick; Kley, W.; Kissmann, R.

doi:10.1111/j.1365-2966.2011.20207.x

Cited by 25 publications

(28 citation statements)

References 34 publications

(71 reference statements)

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“…(7). The simulations span a region in radius from r = 2−10 AU, this is the range where the dead zone can be expected (Armitage 2011;Flaig et al 2012). Here, we use a larger radial domain as Nelson et al (2013) did because we intend to study the global properties of the instability over a wider range of distances.…”

Section: Numerical Modelmentioning

confidence: 99%

Vertical shear instability in accretion disc models with radiation transport

Stoll

Kley

2014

A&A

136

180

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Context. The origin of turbulence in accretion discs is still not fully understood. While the magneto-rotational instability is thought to operate in sufficiently ionised discs, its role in the poorly ionised protoplanetary disc is questionable. Recently, the vertical shear instability (VSI) has been suggested as a possible alternative. Aims. Our goal is to study the characteristics of this instability and the efficiency of angular momentum transport, in extended discs, under the influence of radiative transport and irradiation from the central star. Methods. We use multi-dimensional hydrodynamic simulations to model a larger section of an accretion disc. First we study inviscid and weakly viscous discs using a fixed radial temperature profile in two and three spatial dimensions. The simulations are then extended to include radiative transport and irradiation from the central star.Results. In agreement with previous studies, for the isothermal disc we find a sustained unstable state with a weak positive angular momentum transport of the order of α ≈ 10 −4 . Under the inclusion of radiative transport the disc cools off and the turbulence terminates. For discs irradiated from the central star we again find a persistent instability with a similar α value as for the isothermal case. Conclusions. We find that the VSI can indeed generate sustained turbulence in discs, albeit at a relatively low level with α about few times 10 −4 .

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Section: Numerical Modelmentioning

confidence: 99%

Vertical shear instability in accretion disc models with radiation transport

Stoll

Kley

2014

A&A

136

180

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“…However, protoplanetary discs have only a very low temperature regime and insufficient thermal ionization. Even considering external sources of ionization there appears to be a region of insufficient ionization level such that the MRI cannot operate, as shown by resistive MHD simulations including radiative transport (Flaig et al 2012). Hence, there may exist a dead zone somewhere between 2 − 20 au (Armitage 2011), where the MRI can only produce very weak turbulence.…”

Section: Introductionmentioning

confidence: 99%

Particle dynamics in discs with turbulence generated by the vertical shear instability

Stoll

Kley

2016

A&A

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Context. Among the candidates for generating turbulence in accretion discs in situations with low intrinsic ionization the vertical shear instability (VSI) has become an interesting candidate, as it relies purely on a vertical gradient in the angular velocity. Existing numerical simulations have shown that α-values a few times 10 −4 can be generated. Aims. The particle growth in the early planet formation phase is determined by the dynamics of embedded dust particles. Here, we address in particular the efficiency of VSI-turbulence in concentrating particles in order to generate overdensities and low collision velocities. Methods. We perform three-dimensional (3D) numerical hydrodynamical simulations of accretion discs around young stars that include radiative transport and irradiation from the central star. The motion of embedded particles within a size range of a fraction of mm up to several m is followed using standard drag formula. Results. We confirm that under realistic conditions the VSI is able to generate turbulence in full 3D protoplanetary discs. The irradiated disc shows turbulence within 10 to 60 au. The mean radial motion of the gas is such that it is directed inward near the midplane and outward in the surface layers. We find that large particles drift inward with the expected speed, while small particles can experience phases of outward drift. Additionally, the particles show bunching behaviour with overdensities reaching 5 times the average value, which is strongest for dimensionless stopping times around unity. Conclusions. Particles in a VSI-turbulent discs are concentrated in large scale turbulent eddies and show low relative speeds that allow for growing collisions. The reached overdensities will also allow for the onset streaming instabilities further enhancing particle growth. The outward drift for small particles at higher disk elevations allows for the transport of processed high temperature material in the Solar System to larger distances.

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“…In case of α-viscosity we adopt a vertically constant viscosity utilizing the mid-plane values. MHD simulations indicate that the turbulent stresses do not strongly change with height (Flaig et al 2012). For discs with constant viscosity, the initial surface density profile is the equilibrium profile, which cancels viscous transport.…”

Section: Computational Parametersmentioning

confidence: 99%

Stellar irradiated discs and implications on migration of embedded planets

Bitsch

Crida

Morbidelli

et al. 2013

A&A

Self Cite

144

190

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Context. The strength and direction of migration of embedded low mass planets depends on the disc's thermodynamic state. It has been shown that, in discs where the viscous heating is balanced by radiative transport, the migration can be directed outwards, a process which extends the lifetime of growing planetary embryos. Aims. We investigate the influence of opacity and stellar irradiation on the disc thermodynamics. We focus on equilibrium discs, which have no net mass flux. Utilizing the resulting disc structure, we determine the regions of outward migration in the disc. Methods. We performed two-dimensional numerical simulations of equilibrium discs with viscous heating, radiative cooling, and stellar irradiation. We used the explicit/implicit hydrodynamical code NIRVANA that includes a full tensor viscosity and stellar irradiation, as well as a two temperature solver that includes radiation transport in the flux-limited diffusion approximation. The migration of embedded planets was studied by using torque formulae. Results. In the constant opacity case, our code reproduces the analytical results corresponding to a black-body disc: the stellar irradiation dominates in the outer regions -leading to flaring (H/r ∝ r 2/7 ) -while the viscous heating dominates close to the star. In particular, we find that the inner edge of the disc should not be significantly puffed-up by the stellar irradiation. If the opacity depends on the local density and temperature, the structure of the disc is different, and several bumps in the aspect ratio H/r appear, due to transitions between different opacity regimes. The bumps in the disc structure are very important, as they can shield the outer disc from stellar irradiation. Conclusions. Stellar irradiation is an important factor for determining the disc structure and has dramatic consequences for the migration of embedded planets. Compared to discs with only viscous heating and radiative cooling, a stellar irradiated disc features a much smaller region of outward migration for a range of planetary masses. This suggests that the region where the formation of giant planet cores takes place is smaller, which in turn might lead to a shorter growth phase.

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Global structure of magnetorotationally turbulent protoplanetary discs

Cited by 25 publications

References 34 publications

Vertical shear instability in accretion disc models with radiation transport

Vertical shear instability in accretion disc models with radiation transport

Particle dynamics in discs with turbulence generated by the vertical shear instability

Stellar irradiated discs and implications on migration of embedded planets

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