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Register a new userParticle dynamics in discs with turbulence generated by the vertical shear instability
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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 simulations have shown that $alpha$-values a few times $10^{-4}$ can be generated. The particle growth in the early planet formation phase is determined by the dynamics of dust particles. Here, we address in particular the efficiency of VSI-turbulence in concentrating particles in order to generate overdensities and low collision velocities. We perform 3D numerical hydrodynamical simulations of accretion discs around young stars that include radiative transport and irradiation from the central star. The motion of particles within a size range of a fraction of mm up to several m is followed using standard drag formula. 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 60au. 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. 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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(Abridged) We analyse the stability and 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 power-law functions of cylindrical radius. We employ two different hydrodynamic codes to perform 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 viscosity. We present a stability analysis of the problem that we use to interpret the simulation results. We find that 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 operates when the dimensionless disc kinematic viscosity nu < 10^{-6} (Reynolds numbers Re>H c_s/nu > 2500). In 3D the instability generates a quasi-turbulent flow, and the Reynolds stress produces a fluctuating effective viscosity coefficient whose mean value reaches alpha ~ 6 x 10^{-4} by the end of the simulation. The vertical shear instability in disc models which include realistic thermal physics has yet to be examined. Should it occur, however, our results suggest that it will have significant consequences for their internal dynamics, transport properties, and observational appearance.
We quantify the thermodynamic requirement for the Vertical Shear Instability and evaluate its relevance to realistic protoplanetary disks as a potential route to hydrodynamic turbulence.
We investigated the formation and evolution of satellite systems in a cold, extended circumplanetary disc around a 10 $M_{rm{Jupiter}}$ gas giant which was formed by gravitational instability at 50,AU from its star. The disc parameters were from a 3D global SPH simulation. We used a population synthesis approach, where we placed satellite embryos in this disc, and let them accrete mass, migrate, collide until the gaseous disc is dissipated. In each run we changed the initial dust-to-gas ratio, dispersion- and refilling time-scales within reasonable limits, as well as the number of embryos and their starting locations. We found that most satellites have mass similar to the Galilean ones, but very few can reach a maximum of 3 $M_{rm{Earth}}$ due to the massive circumplanetary disc. Large moons are often form as far as 0.5 $R_{rm{disc}}$. The migration rate of satellites are fast, hence during the disc lifetime, an average of 10 $M_{rm{Earth}}$ worth of moons will be engulfed by the planet, increasing greatly its metallicity. We also investigated the effect of the planets semi-major axis on the resulting satellite systems by re-scaling our model. This test revealed that for the discs closer to the star, the formed moons are lighter, and a larger amount of satellites are lost into the planet due to the even faster migration. Finally, we checked the probability of detecting satellites like our population, which resulted in a low number of $leq$ 3% even with upcoming powerful telescopes like E-ELT.
The vertical shear instability (VSI) is a robust phenomenon in irradiated protoplanetary disks (PPDs). While there is extensive literature on the VSI in the hydrodynamic limit, PPDs are expected to be magnetized and their extremely low ionization fractions imply that non-ideal magneto-hydrodynamic (MHD) effects should be properly considered. To this end, we present linear analyses of the VSI in magnetized disks with Ohmic resistivity. We primarily consider toroidal magnetic fields, which are likely to dominate the field geometry in PPDs. We perform vertically global and radially local analyses to capture characteristic VSI modes with extended vertical structures. To focus on the effect of magnetism, we use a locally isothermal equation of state. We find that magnetism provides a stabilizing effect to dampen the VSI, with surface modes, rather than body modes, being the first to vanish with increasing magnetization. Subdued VSI modes can be revived by Ohmic resistivity, where sufficient magnetic diffusion overcome magnetic stabilization, and hydrodynamic results are recovered. We also briefly consider poloidal fields to account for the magnetorotational instability (MRI), which may develop towards surface layers in the outer parts of PPDs. The MRI grows efficiently at small radial wavenumbers, in contrast to the VSI. When resistivity is considered, we find the VSI dominates over the MRI for Ohmic Els{a}sser numbers $lesssim 0.09$ at plasma beta parameter $beta_Z sim 10^4$.
The growth process of proto-planets can be sped-up by accreting a large number of solid, pebble-sized objects that are still present in the protoplanetary disc. It is still an open question on how efficient this process works in realistic turbulent discs. Here, we investigate the accretion of pebbles in turbulent discs that are driven by the purely hydrodynamical vertical shear instability (VSI). For this purpose, we perform global three-dimensional simulations of locally isothermal, VSI turbulent discs with embedded protoplanetary cores from 5 to 100 $M_oplus$ that are placed at 5.2 au distance from the star. In addition, we follow the evolution of a swarm of embedded pebbles of different size under the action of drag forces between gas and particles in this turbulent flow. Simultaneously, we perform a set of comparison simulations for laminar viscous discs where the particles experience stochastic kicks. For both cases, we measure the accretion rate onto the cores as a function of core mass and Stokes number ($tau_s$) of the particles and compare it to recent MRI turbulence simulations. Overall the dynamic is very similar for the particles in the VSI turbulent disc and the laminar case with stochastic kicks. For the small mass planets (i.e. 5 and 10 $M_oplus$), well-coupled particles with $tau_s = 1$, which have a size of about one meter at this location, we find an accretion efficiency (rate of particles accreted over drifting inward) of about 1.6-3%. For smaller and larger particles this efficiency is higher. However, the fast inward drift for $tau_s = 1$ particles makes them the most effective for rapid growth, leading to mass doubling times of about 20,000 yr. For masses between 10 and 30 $M_oplus$ the core reaches the pebble isolation mass and the particles are trapped at the pressure maximum just outside of the planet, shutting off further particle accretion.
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