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Register a new userHigh Resolution Parameter Study of the Vertical Shear Instability
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Theoretical models of protoplanetary disks have shown the Vertical Shear Instability (VSI) to be a prime candidate to explain turbulence in the dead zone of the disk. However, simulations of the VSI have yet to show consistent levels of key disk turbulence parameters like the stress-to-pressure ratio $alpha$. We aim to reconcile these different values by performing a parameter study on the VSI with focus on the disk density gradient $p$ and aspect ratio $h := H/R$. We use full 2$pi$ 3D simulations of the disk for chosen set of both parameters. All simulations are evolved for 1000 reference orbits, at a resolution of 18 cells per h. We find that the saturated stress-to-pressure ratio in our simulations is dependent on the disk aspect ratio with a review{strong} scaling of $alphapropto h^{2.6}$, in contrast to the traditional $alpha$ model, where viscosity scales as $ u propto alpha h^2$ with a constant $alpha$. We also observe consistent formation of large scale vortices across all investigated parameters. The vortices show uniformly aspect ratios of $chi approx 10$ and radial widths of approximately 1.5 $H$. With our findings we can reconcile the different values reported for the stress-to-pressure ratio from both isothermal and radiation hydrodynamics models, and show long-term evolution effects of the VSI that could aide in the formation of planetesimals.
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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.
In recent years hydrodynamical (HD) models have become important to describe the gas kinematics in protoplanetary disks, especially in combination with models of photoevaporation and/or magnetic-driven winds. We focus on diagnosing the the vertical extent of the VSI at 203 cells per scale height and allude at what resolution per scale height we obtain convergence. Finally, we determine the regions where EUV, FUV and X-Rays are dominant in the disk. We perform global HD simulations using the PLUTO code. We adopt a global isothermal accretion disk setup, 2.5D (2 dimensions, 3 components) which covers a radial domain from 0.5 to 5.0 and an approximately full meridional extension. We determine the 50 cells per scale height to be the lower limit to resolve the VSI. For higher resolutions, greater than 50 cells per scale height, we observe the convergence for the saturation level of the kinetic energy. We are also able to identify the growth of the `body modes, with higher growth rate for higher resolution. Full energy saturation and a turbulent steady state is reached after 70 local orbits. We determine the location of the EUV-heated region defined by the radial column density to be 10$^{19}$ cm$^{-2}$ located at $H_mathrm{R}sim9.7$, and the FUV/X-Rays-heated boundary layer defined by 10$^{22}$ cm$^{-2}$ located at $H_mathrm{R}sim6.2$, making it necessary to introduce the need of a hot atmosphere. For the first time, we report the presence of small scale vortices in the r-Z plane, between the characteristic layers of large scale vertical velocity motions. Such vortices could lead to dust concentration, promoting grain growth. Our results highlight the importance to combine photoevaporation processes in the future high-resolution studies of the turbulence and accretion processes in disks.
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 streaming instability is a leading candidate mechanism to explain the formation of planetesimals. Yet, the role of this instability in the driving of turbulence in protoplanetary disks, given its fundamental nature as a linear hydrodynamical instability, has so far not been investigated in detail. We study the turbulence that is induced by the streaming instability as well as its interaction with the vertical shear instability. For this purpose, we employ the FLASH Code to conduct two-dimensional axisymmetric global disk simulations spanning radii from $1$ au to $100$ au, including the mutual drag between gas and dust as well as the radial and vertical stellar gravity. If the streaming instability and the vertical shear instability start their growth at the same time, we find the turbulence in the dust mid-plane layer to be primarily driven by the streaming instability. It gives rise to vertical gas motions with a Mach number of up to ${sim}10^{-2}$. The dust scale height is set in a self-regulatory manner to about $1%$ of the gas scale height. In contrast, if the vertical shear instability is allowed to saturate before the dust is introduced into our simulations, then it continues to be the main source of the turbulence in the dust layer. The vertical shear instability induces turbulence with a Mach number of ${sim}10^{-1}$ and thus impedes dust sedimentation. Nonetheless, we find the vertical shear instability and the streaming instability in combination to lead to radial dust concentration in long-lived accumulations which are significantly denser than those formed by the streaming instability alone. Thus, the vertical shear instability may promote planetesimal formation by creating weak overdensities that act as seeds for the streaming instability.
Context. Dynamical and turbulent motions of gas in a protoplanetary disk are crucial for their evolution and affect planet formation. Recent observations suggest weak turbulence in the disks outer regions. However, the physical mechanism of turbulence in these outer regions remains uncertain. The vertical shear instability (VSI) is a promising mechanism to produce turbulence in disks. Aims. Our aim is to study the observability of the gas velocity structure produced by the VSI via CO kinematics with ALMA. Methods. We perform global 3D hydrodynamical simulations of a VSI-unstable disk. We post-process the simulation results with radiative transfer calculations, and produce synthetic predictions of CO rotational emission lines. Following, we compute the line of sight velocity map, and its deviations from a sub-Keplerian equilibrium solution. We explore the detectability of the VSI by identifying kinematic signatures using realistic simulated observations. Results. Our 3D simulations of the VSI show the steady state dynamics of the gas in great detail. From the velocity structure we infer a turbulent stress value of $alpha_{rphi}=1.4 times 10^{-4}$. On large scales, we observe velocity deviations of 50 m s$^{-1}$ as axisymmetric rings. We find optimal conditions at $i lesssim 20^{circ}$ to trace for the kinematic structures of the VSI. We found that current diagnostics to constrain gas turbulence from non-thermal broadening of the line emission are not applicable to anisotropic VSI turbulence. Conclusions. The detection of kinematic signatures produced by the VSI is possible with ALMA. Observations including an extended antenna configuration combined with the highest spectral resolution available are needed for robust detection. The characterization of the large-scale velocity perturbations is required to constrain the turbulence level produced by the VSI from gas observations.
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