Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userThe resonant drag instability of dust streaming in turbulent protoplanetary disc
64
0
0.0
(
0
)
Added by
Viacheslav Zhuravlev
Publication date
2020
fields
Physics
and research's language is
English
Authors
V.V. Zhuravlev
Ask ChatGPT about the research
No Arabic abstract
Damping of the previously discovered resonant drag instability (RDI) of dust streaming in protoplanetary disc is studied using the local approach to dynamics of gas-dust perturbations in the limit of the small dust fraction. Turbulence in a disc is represented by the effective viscosity and diffusivity in equations of motion for gas and dust, respectively. In the standard case of the Schmidt number (ratio of the effective viscosity to diffusivity) Sc = 1, the reduced description of RDI in terms of the inertial wave (IW) and the streaming dust wave (SDW) falling in resonance with each other reveals that damping solution differs from the inviscid solution simply by adding the characteristic damping frequency to its growth rate. RDI is fully suppressed at the threshold viscosity, which is estimated analytically, first, for radial drift, next, for vertical settling of dust, and at last, in the case of settling combined with radial drift of the dust. In the last case, RDI survives up to the highest threshold viscosity, with a greater excess for smaller solids. Once Sc eq 1, a new instability specific for dissipative perturbations on the dust settling background emerges. This instability of the quasi-resonant nature is referred to as settling viscous instability (SVI). The mode akin to SDW (IW) becomes growing in a region of long waves provided that Sc > 1 (Sc < 1). SVI leads to an additional increase of the threshold viscosity.
rate research
Read More
The recently discovered resonant drag instability (RDI) of dust streaming in protoplanetary disc is considered as the mode coupling of subsonic gas-dust mixture perturbations. This mode coupling is coalescence of two modes with nearly equal phase velocities: inertial wave (IW) having positive energy and a streaming dust wave (SDW) having negative energy as measured in the frame of gas environment being at rest in vertical hydrostatic equilibrium. SDW is a trivial mode produced by the bulk streaming of dust, which transports perturbations of dust density. In this way, settling combined with radial drift of the dust makes possible coupling of SDW with IW and the onset of the instability. In accordance with the concept of the mode coupling, RDI growth rate is proportional to the square root of the coupling term of the dispersion equation, which itself is proportional to mass fraction of dust, $fll 1$. This clarifies why RDI growth rate $propto f^{1/2}$. When SDW has positive energy, its resonance with IW provides an avoided crossing instead of the mode coupling. In the high wavenumber limit RDI with unbounded growth rate $propto f^{1/3}$ is explained by the triple mode coupling, which is coupling of SDW with two IW. It coexists with a new quasi-resonant instability accompanied by bonding of two oppositely propagating low-frequency IW. The mode coupling does not exist for dust streaming only radially in a disc. In this case RDI is provided by the obscured mechanism associated with the inertia of solids.
The recently discovered resonant drag instability of dust settling in protoplanetary disc is considered as the mode coupling of subsonic gas-dust mixture perturbations. This mode coupling is coalescence of two modes with nearly equal phase velocities: the first mode is inertial wave having positive energy, while the second mode is a settling dust wave (SDW) having negative energy as measured in the frame of gas environment being at rest in vertical hydrostatic equilibrium. SDW is a trivial mode produced by the bulk settling of dust, which transports perturbations of dust density. The phase velocity of SDW is equal to the bulk settling velocity times the cosine of the angle formed by the wave vector and the rotation axis. In this way, the bulk settling of dust makes possible the coupling of SDW with the inertial wave and the onset of the instability. In accordance with the concept of the mode coupling, the instability growth rate is proportional to the square root of the dispersion equation coupling term, which itself contains the small mass fraction of dust in gas-dust mixture, the squared radial wavenumber of the modes, and the squared bulk settling velocity. Thus, the higher is the bulk settling velocity, the heavier clumps of dust can be aggregated by the instability of the same rate.
Radiation-dust driven outflows, where radiation pressure on dust grains accelerates gas, occur in many astrophysical environments. Almost all previous numerical studies of these systems have assumed that the dust was perfectly-coupled to the gas. However, it has recently been shown that the dust in these systems is unstable to a large class of resonant drag instabilities (RDIs) which de-couple the dust and gas dynamics and could qualitatively change the nonlinear outcome of these outflows. We present the first simulations of radiation-dust driven outflows in stratified, inhomogeneous media, including explicit grain dynamics and a realistic spectrum of grain sizes and charge, magnetic fields and Lorentz forces on grains (which dramatically enhance the RDIs), Coulomb and Epstein drag forces, and explicit radiation transport allowing for different grain absorption and scattering properties. In this paper we consider conditions resembling giant molecular clouds (GMCs), HII regions, and distributed starbursts, where optical depths are modest ($lesssim 1$), single-scattering effects dominate radiation-dust coupling, Lorentz forces dominate over drag on grains, and the fastest-growing RDIs are similar, such as magnetosonic and fast-gyro RDIs. These RDIs generically produce strong size-dependent dust clustering, growing nonlinear on timescales that are much shorter than the characteristic times of the outflow. The instabilities produce filamentary and plume-like or horsehead nebular morphologies that are remarkably similar to observed dust structures in GMCs and HII regions. Additionally, in some cases they strongly alter the magnetic field structure and topology relative to filaments. Despite driving strong micro-scale dust clumping which leaves some gas behind, an order-unity fraction of the gas is always efficiently entrained by dust.
In this paper, we investigate whether overdensity formation via streaming instability is consistent with recent multi-wavelength ALMA observations in the Lupus star forming region. We simulate the local action of streaming instability in 2D using the code ATHENA, and examine the radiative properties at mm wavelengths of the resulting clumpy dust distribution by focusing on two observable quantities: the optically thick fraction $ff$ (in ALMA band 6) and the spectral index $alpha$ (in bands 3-7). By comparing the simulated distribution in the $ff-alpha$ plane before and after the action of streaming instability, we observe that clump formation causes $ff$ to drop, because of the suppression of emission from grains that end up in optically thick clumps. $alpha$, instead, can either increase or decline after the action of streaming instability; we use a simple toy model to demonstrate that this behaviour depends on the sizes of the grains whose emission is suppressed by being incorporated in optically thick clumps. In particular, the sign of evolution of $alpha$ depends on whether grains near the opacity maximum at a few tenths of a mm end up in clumps. By comparing the simulation distributions before/after clump formation to the data distribution, we note that the action of streaming instability drives simulations towards the area of the plane where the data are located. We furthermore demonstrate that this behaviour is replicated in integrated disc models provided that the instability is operative over a region of the disc that contributes significantly to the total mm flux.
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.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
