Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userOn the Numerical Robustness of the Streaming Instability: Particle Concentration and Gas Dynamics in Protoplanetary Disks
267
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
The Streaming Instability (SI) is a mechanism to concentrate solids in protoplanetary disks. Nonlinear particle clumping from the SI can trigger gravitational collapse into planetesimals. To better understand the numerical robustness of the SI, we perform a suite of vertically-stratified 3D simulations with fixed physical parameters known to produce strong clumping. We vary the numerical implementation, namely the computational domain size and the vertical boundary conditions (vBCs), comparing newly-implemented outflow vBCs to the previously-used periodic and reflecting vBCs. We find strong particle clumping by the SI is mostly independent of the vBCs. However, peak particle densities are higher in larger simulation domains due to a larger particle mass reservoir. We report SI-triggered zonal flows, i.e., azimuthally-banded radial variations of gas pressure. These structures have low amplitudes, insufficient to halt particle radial drift, confirming that particle trapping in gas pressure maxima is not the mechanism of the SI. We find that outflow vBCs produce artificially large gas outflow rates at vertical boundaries. However, the outflow vBCs reduce artificial reflections at vertical boundaries, allowing more particle sedimentation, and showing less temporal variation and better convergence with box size. The radial spacing of dense particle filaments is $sim0.15$ gas scale heights ($H$) for all vBCs, which sets the feeding zone for planetesimal growth in self-gravitating simulations. Our results validate the use of the outflow vBCs in SI simulations, even with vertical boundaries close ($leq 0.4H$) to the disk midplane. Overall, our study demonstrates the numerical robustness of nonlinear particle clumping by the SI.
rate research
Read More
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.
The streaming instability is a popular candidate for planetesimal formation by concentrating dust particles to trigger gravitational collapse. However, its robustness against physical conditions expected in protoplanetary disks is unclear. In particular, particle stirring by turbulence may impede the instability. To quantify this effect, we develop the linear theory of the streaming instability with external turbulence modelled by gas viscosity and particle diffusion. We find the streaming instability is sensitive to turbulence, with growth rates becoming negligible for alpha-viscosity parameters $alpha gtrsim mathrm{St} ^{1.5}$, where $mathrm{St}$ is the particle Stokes number. We explore the effect of non-linear drag laws, which may be applicable to porous dust particles, and find growth rates are modestly reduced. We also find that gas compressibility increase growth rates by reducing the effect of diffusion. We then apply linear theory to global models of viscous protoplanetary disks. For minimum-mass Solar nebula disk models, we find the streaming instability only grows within disk lifetimes beyond $sim 10$s of AU, even for cm-sized particles and weak turbulence ($alphasim 10^{-4}$). Our results suggest it is rather difficult to trigger the streaming instability in non-laminar protoplanetary disks, especially for small particles.
In the recent years, sub/mm observations of protoplanetary disks have discovered an incredible diversity of substructures in the dust emission. An important result was the finding that dust grains of mm size are embedded in very thin dusty disks. This implies that the dust mass fraction in the midplane becomes comparable to the gas, increasing the importance of the interaction between the two components there. We address this problem by means of numerical 2.5D simulations in order to study the gas and dust interaction in fully global stratified disks. To this purpose, we employ the recently developed dust grain module in the PLUTO code. Our model focuses on a typical T Tauri disk model, simulating a short patch of the disk at 10 au which includes grains of constant Stokes number of $St=0.01$ and $St=0.1$, corresponding to grains with sizes of 0.9 cm and 0.9 mm, respectively, for the given disk model. By injecting a constant pebble flux at the outer domain, the system reaches a quasi steady state of turbulence and dust concentrations driven by the streaming instability. For our given setup and using resolutions up to 2500 cells per scale height we resolve the streaming instability, leading to local dust clumping and concentrations. Our results show dust density values of around 10-100 times the gas density with a steady state pebble flux between $3.5 times 10^{-4}$ and $2.5 times 10^{-3} M_{rm Earth}/mathit{year}$ for the models with $mathit{St}=0.01$ and $mathit{St}=0.1$. The grain size and pebble flux for model $mathit{St}=0.01$ compares well with dust evolution models of the first million years of disk evolution. For those grains the scatter opacity dominates the extinction coefficient at mm wavelengths. These types of global dust and gas simulations are a promising tool for studies of the gas and dust evolution at pressure bumps in protoplanetary disks.
We present simulations of the non-linear evolution of streaming instabilities in protoplanetary disks. The two components of the disk, gas treated with grid hydrodynamics and solids treated as superparticles, are mutually coupled by drag forces. We find that the initially laminar equilibrium flow spontaneously develops into turbulence in our unstratified local model. Marginally coupled solids (that couple to the gas on a Keplerian time-scale) trigger an upward cascade to large particle clumps with peak overdensities above 100. The clumps evolve dynamically by losing material downstream to the radial drift flow while receiving recycled material from upstream. Smaller, more tightly coupled solids produce weaker turbulence with more transient overdensities on smaller length scales. The net inward radial drift is decreased for marginally coupled particles, whereas the tightly coupled particles migrate faster in the saturated turbulent state. The turbulent diffusion of solid particles, measured by their random walk, depends strongly on their stopping time and on the solids-to-gas ratio of the background state, but diffusion is generally modest, particularly for tightly coupled solids. Angular momentum transport is too weak and of the wrong sign to influence stellar accretion. Self-gravity and collisions will be needed to determine the relevance of particle overdensities for planetesimal formation.
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 $beta_Z sim 10^4$.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
