Abstract:Aims. We present the results of hydrodynamic simulations of the growth and orbital evolution of giant planets embedded in a protoplanetary disk with a dead-zone. The aim is to examine to what extent the presence of a dead-zone affects the rates of mass accretion and migration for giant planets. Methods. We performed 3D numerical simulations using a grid-based hydrodynamics code. In these simulations of laminar, nonmagnetised disks, the dead-zone is treated as a region where the vertical profile of the viscosit… Show more
“…As such, this disc model has parameters very similar to those used in numerous previous studies of disc related phenomena (e.g. Kley et al 2001;Cresswell & Nelson 2006;Fromang et al 2011b;Pierens & Nelson 2010), although we focus primarily on the inviscid non-magnetised evolution here.…”
We analyse the stability and nonlinear dynamical evolution of power-law accretion disc models. These have midplane densities that follow radial power-laws, and have either temperature or entropy distributions that are strict power-law functions of cylindrical radius, R. We employ two different hydrodynamic codes to perform high resolution 2D-axisymmetric and 3D simulations that examine the long-term evolution of the disc models as a function of the power-law indices of the temperature or entropy, the thermal relaxation time of the fluid, and the disc viscosity. We present an accompanying stability analysis of the problem, based on asymptotic methods, that we use to interpret the results of the simulations. We find that axisymmetric disc models whose temperature or entropy profiles cause the equilibrium angular velocity to vary with height are unstable to the growth of modes with wavenumber ratios |k R /k Z | 1 when the thermodynamic response of the fluid is isothermal, or the thermal evolution time is comparable to or shorter than the local dynamical time scale. These discs are subject to the Goldreich-Schubert-Fricke (GSF) or 'vertical shear' linear instability. Development of the instability involves excitation of vertical breathing and corrugation modes in the disc, with the corrugation modes in particular being a feature of the nonlinear saturated state. Instability is found to operate when the dimensionless disc kinematic viscosity ν < 10 −6 , corresponding to Reynolds numbers Re = Hc s /ν > 2500. In three dimensions the instability generates a quasiturbulent flow, and the associated Reynolds stress produces a fluctuating effective viscosity coefficient whose mean value reaches α ∼ 6 × 10 −4 by the end of the simulation. The evolution and saturation of the vertical shear instability in astrophysical disc models which include realistic treatments of the thermal physics has yet to be examined. Should it occur on either global or local scales, however, our results suggest that it will have significant consequences for their internal dynamics, transport properties, and observational appearance.
“…As such, this disc model has parameters very similar to those used in numerous previous studies of disc related phenomena (e.g. Kley et al 2001;Cresswell & Nelson 2006;Fromang et al 2011b;Pierens & Nelson 2010), although we focus primarily on the inviscid non-magnetised evolution here.…”
We analyse the stability and nonlinear dynamical evolution of power-law accretion disc models. These have midplane densities that follow radial power-laws, and have either temperature or entropy distributions that are strict power-law functions of cylindrical radius, R. We employ two different hydrodynamic codes to perform high resolution 2D-axisymmetric and 3D simulations that examine the long-term evolution of the disc models as a function of the power-law indices of the temperature or entropy, the thermal relaxation time of the fluid, and the disc viscosity. We present an accompanying stability analysis of the problem, based on asymptotic methods, that we use to interpret the results of the simulations. We find that axisymmetric disc models whose temperature or entropy profiles cause the equilibrium angular velocity to vary with height are unstable to the growth of modes with wavenumber ratios |k R /k Z | 1 when the thermodynamic response of the fluid is isothermal, or the thermal evolution time is comparable to or shorter than the local dynamical time scale. These discs are subject to the Goldreich-Schubert-Fricke (GSF) or 'vertical shear' linear instability. Development of the instability involves excitation of vertical breathing and corrugation modes in the disc, with the corrugation modes in particular being a feature of the nonlinear saturated state. Instability is found to operate when the dimensionless disc kinematic viscosity ν < 10 −6 , corresponding to Reynolds numbers Re = Hc s /ν > 2500. In three dimensions the instability generates a quasiturbulent flow, and the associated Reynolds stress produces a fluctuating effective viscosity coefficient whose mean value reaches α ∼ 6 × 10 −4 by the end of the simulation. The evolution and saturation of the vertical shear instability in astrophysical disc models which include realistic treatments of the thermal physics has yet to be examined. Should it occur on either global or local scales, however, our results suggest that it will have significant consequences for their internal dynamics, transport properties, and observational appearance.
“…According to previous 2D simulations, such a low kinematic viscosity should lead to the RWI (de Val-Borro et al 2006. However, Pierens & Nelson (2010) did not report vortex formation, nor are vortices visible from their plots. Very recent MHD simulations of giant planets in a layered disc also did not yield vortex formation ).…”
Section: Relation To Other Workmentioning
confidence: 92%
“…Here, we simulate gapopening giant planets in 3D discs where the kinematic viscosity varies with height above the disc midplane. Our numerical setup is similar to those that in Pierens & Nelson (2010), but our interest is gap stability in a layered disc.…”
Section: Vortex Formation At Planetary Gap Edges In Layered Discsmentioning
Vortex formation through the Rossby wave instability (RWI) in protoplanetary discs has been invoked to play a role in planet formation theory, and suggested to explain the observation of large dust asymmetries in several transitional discs. However, whether or not vortex formation operates in layered accretion discs, i.e. models of protoplanetary discs including dead zones near the disc midplane -regions that are magnetically inactive and the effective viscosity greatly reduced -has not been verified. As a first step toward testing the robustness of vortex formation in layered discs, we present nonlinear hydrodynamical simulations of global 3D protoplanetary discs with an imposed kinematic viscosity that increases away from the disc midplane. Two sets of numerical experiments are performed: (i) non-axisymmetric instability of artificial radial density bumps in viscous discs; (ii) vortex-formation at planetary gap edges in layered discs. Experiment (i) shows that the linear instability is largely unaffected by viscosity and remains dynamical. The disc-planet simulations also show the initial development of vortices at gap edges, but in layered discs the vortices are transient structures which disappear well into the non-linear regime. We suggest that the long term survival of columnar vortices, such as those formed via the RWI, requires low effective viscosity throughout the vertical extent of the disc, so such vortices do not persist in layered discs.We examine the PV evolution for case P0R in Fig. 10. To highlight the vortices, which are positive (negative) density (vertical vorticity) perturbations, we show the inverse PV perturbation, δη −1 z ≡ ηz(t = 0)/ηz − 1. As noted above, a single vortex still forms despite introducing a viscous layer at t = 100P0. However, it decays rapidly compared to case P0. The region with δη −1 z > 0 (i.e. the vortex) elongates and shifts outward from R ≃ 1.38r0 at t = 140P0 to R ≃ 1.5r0 at
“…We note that the region of the disc with a dead zone should ideally be modelled with a vertically varying α viscosity parameter (e.g. Pierens & Nelson 2010) based on fits to MHD simulations (e.g. Okuzumi & Hirose 2011;Gressel et al 2011;Uribe et al 2011Uribe et al , 2013.…”
We investigate whether the regular Galilean satellites could have formed in the dead zone of a circumplanetary disc. A dead zone is a region of weak turbulence in which the magnetorotational instability (MRI) is suppressed, potentially an ideal environment for satellite formation. With the grid-based hydrodynamic code, FARGO3D, we examine the evolution of a circumplanetary disc model with a dead zone. Material accumulates in the dead zone of the disc leading to a higher total mass and but a similar temperature profile compared to a fully turbulent disc model. The tidal torque increases the rate of mass transport through the dead zone leading to a steady state disc with a dead zone that does not undergo accretion outbursts. We explore a range of disc, dead zone and mass inflow parameters and find that the maximum mass of the disc is around 0.001 MJ. Since the total solid mass of such a disc is much lower, we find that there is not sufficient material in the disc for in situ formation of the Galilean satellites and that external supplement is required.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.