The Effects of Protostellar Disk Turbulence on CO Emission Lines: A Comparison Study of Disks with Constant CO Abundance vs. Chemically Evolving Disks

The Effects of Protostellar Disk Turbulence on CO Emission Lines: A Comparison Study of Disks with Constant CO Abundance vs. Chemically Evolving Disks 

Authors:

Yu et al

Abstract:
Turbulence is the leading candidate for angular momentum transport in protoplanetary disks and therefore influences disk lifetimes and planet formation timescales. However, the turbulent properties of protoplanetary disks are poorly constrained observationally. Simon et al. (2015) suggested that the ratio of the peak line flux to the flux at line center of the CO J=3-2 transition is a reasonable diagnostic of turbulence, while Flaherty et al. (2015) and Flaherty et al. (2017) found turbulent speeds in HD 163296 smaller than what fully-developed MRI would produce based on the Simon et al. (2015) simulation results. Yet Simon et al. (2015) and Flaherty et al. (2015) assumed a constant CO/H2 ratio of 0.0001 in locations where CO is not frozen-out or photodissociated. Yu et al. (2016) found that the CO abundance varies both with distance from the star and as a function of time because CO molecules are gradually dissociated, with the liberated carbon forming complex organic molecules that freeze out on grain surfaces. We simulate the emission lines of CO based on chemical evolution models presented in Yu et al. (2016), and find that the peak-to-trough ratio changes as a function of time as CO is destroyed. Specifically, a CO-depleted disk with high turbulent velocity mimics the peak-to-trough ratios of a non-CO-depleted disk with lower turbulent velocity. We suggest that disk observers and modelers take into account the possibility of CO depletion when using line peak-to-trough ratios to constrain the degree of turbulence in disks. Assuming that CO/H2 = 0.0001 at all disk radii can lead to underestimates of turbulent speeds in the disk by at least 0.2 km/s.

Turbulence, Transport and Waves in Ohmic Dead Zones

Turbulence, Transport and Waves in Ohmic Dead Zones

Authors:

Gole et al

Abstract:

We use local numerical simulations to study a vertically stratified accretion disk with a resistive mid-plane that damps magnetohydrodynamic (MHD) turbulence. This is an idealized model for the dead zones that may be present at some radii in protoplanetary and dwarf novae disks. We vary the relative thickness of the dead and active zones to quantify how forced fluid motions in the dead zone change. We find that the residual Reynolds stress near the mid-plane decreases with increasing dead zone thickness, becoming negligible in cases where the active to dead mass ratio is less than a few percent. This implies that purely Ohmic dead zones would be vulnerable to episodic accretion outbursts via the mechanism of Martin & Lubow (2011). We show that even thick dead zones support a large amount of kinetic energy, but this energy is largely in fluid motions that are inefficient at angular momentum transport. Confirming results from Oishi & Mac Low (2009), the perturbed velocity field in the dead zone is dominated by an oscillatory, vertically extended circulation pattern with a low frequency compared to the orbital frequency. This disturbance has the properties predicted for the lowest order r mode in a hydrodynamic disk. We suggest that in a global disk similar excitations would lead to propagating waves, whose properties would vary with the thickness of the dead zone and the nature of the perturbations (isothermal or adiabatic). Flows with similar amplitudes would buckle settled particle layers and could reduce the efficiency of pebble accretion.

Magnetorotational dynamo chimeras

Magnetorotational dynamo chimeras. The missing link to turbulent accretion disk dynamo models?

Authors:

Foils et al

Abstract:

In Keplerian accretion disks, turbulence and magnetic fields may be jointly excited through a subcritical dynamo process involving the magnetorotational instability (MRI). High-resolution simulations exhibit a tendency towards statistical self-organization of MRI dynamo turbulence into large-scale cyclic dynamics. Understanding the physical origin of these structures, and whether they can be sustained and transport angular momentum efficiently in astrophysical conditions, represents a significant theoretical challenge. The discovery of simple periodic nonlinear MRI dynamo solutions has recently proven useful in this respect, and has notably served to highlight the role of turbulent magnetic diffusion in the seeming decay of the dynamics at low magnetic Prandtl number Pm (magnetic diffusivity larger than viscosity), a common regime in accretion disks. The connection between these simple structures and the statistical organization reported in turbulent simulations remained elusive, though. Here, we report the numerical discovery in moderate aspect ratio Keplerian shearing boxes of new periodic, incompressible, three-dimensional nonlinear MRI dynamo solutions with a larger dynamical complexity reminiscent of such simulations. These "chimera" cycles are characterized by multiple MRI-unstable dynamical stages, but their basic physical principles of self-sustainment are nevertheless identical to those of simpler cycles found in azimuthally elongated boxes. In particular, we find that they are not sustained at low Pm either due to subcritical turbulent magnetic diffusion. These solutions offer a new perspective into the transition from laminar to turbulent instability-driven dynamos, and may prove useful to devise improved statistical models of turbulent accretion disk dynamos.

Particle dynamics in discs with turbulence generated by the vertical shear instability

Particle dynamics in discs with turbulence generated by the vertical shear instability

Authors:

Stoll et al

Abstract:

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 α-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.

Measuring Turbulence in TW Hya with ALMA

Measuring Turbulence in TW Hya with ALMA: Methods and Limitations

Authors:

Teague et al

Abstract:

We obtain high spatial and spectral resolution images of the CO J=2-1, CN N=2-1 and CS J=5-4 emission with ALMA in Cycle~2. The radial distribution of the turbulent broadening is derived with three approaches: two `direct' and one modelling. The first requires a single transition and derives \Tex{} directly from the line profile, yielding a \vturb{}. The second assumes two different molecules are co-spatial thus their relative linewidths allow for a calculation of \Tkin{} and \vturb{}. Finally we fit a parametric disk model where physical properties of the disk are described by power laws, to compare our `direct' methods with previous values. The two direct methods were limited to the outer r>40~au disk due to beam smear. The direct method found \vturb{} ranging from ≈~\vel{130} at 40~au, dropping to ≈~\vel{50} in the outer disk, qualitatively recovered with the parametric model fitting. This corresponds to roughly 0.2−0.4 cs. CN was found to exhibit strong non-LTE effects outside r≈140~au, so \vturb{} was limited to within this radius. The assumption that CN and CS are co-spatial is consistent with observed linewidths only within r≲100~au, within which \vturb{} was found to drop from \vel{100} (≈ 0.4 cs) to nothing at 100~au. The parametric model yielded a near constant \vel{50} for CS (0.2−0.4 cs). We demonstrate that absolute flux calibration is and will be the limiting factor in all studies of turbulence using a single molecule. The magnitude of the dispersion is comparable with or below that predicted by the magneto-rotational instability theory. A more precise comparison would require to reach an absolute calibration precision of order 3\%, or to find a suitable combination of light and heavy molecules which are co-located in the disk.

Constraining turbulence mixing strength in transitional discs with planets using SPHERE and ALMA

Constraining turbulence mixing strength in transitional discs with planets using SPHERE and ALMA

Authors:

de Juan Ovelar et al

Abstract:

We investigate the effect that the turbulent mixing strength parameter αturb plays on near-infrared polarimetric and sub-millimetre interferometric imaging observations of transitional discs (TDs) with a gap carved by a planet. We generate synthetic observations of these objects with ALMA and VLT/SPHERE-ZIMPOL by combining hydrodynamical, dust evolution, radiative transfer and instrument models for values of αturb=[10−4,10−3,10−2]. We find that, through a combination of effects on the viscosity of the gas, the turbulent mixing and dust evolution processes, αturb strongly affects the morphology of the dust distribution that can be traced with these observations. We constrain the value of αturb to be within an order of magnitude of 10−3 in TD sources that show cavities in sub-mm continuum images while featuring continuous distribution of dust or smaller cavities in NIR-polarimetric images.

Dust dynamics in 2D gravito-turbulent disks

Dust dynamics in 2D gravito-turbulent disks

Authors:

Shi et al

Abstract:

The dynamics of solid bodies in protoplanetary disks are subject to the properties of any underlying gas turbulence. Turbulence driven by disk self-gravity shows features distinct from those driven by the magnetorotational instability (MRI). We study the dynamics of solids in gravito-turbulent disks with two-dimensional (in the disk plane), hybrid (particle and gas) simulations. Gravito-turbulent disks can exhibit stronger gravitational stirring than MRI-active disks, resulting in greater radial diffusion and larger eccentricities and relative speeds for large particles (those with dimensionless stopping times tstopΩ > 1, where Ω is the orbital frequency). The agglomeration of large particles into planetesimals by pairwise collisions is therefore disfavored in gravito-turbulent disks. However, the relative speeds of intermediate-size particles (tstopΩ ∼ 1) are significantly reduced as such particles are collected by gas drag and gas gravity into coherent filament-like structures with densities high enough to trigger gravitational collapse. First-generation planetesimals may form via gravitational instability of dust in marginally gravitationally unstable gas disks.

Dust dynamics in 2D gravito-turbulent disks

Dust dynamics in 2D gravito-turbulent disks

Authors:

Shi et al

Abstract:

The dynamics of solid bodies in protoplanetary disks are subject to the properties of any underlying gas turbulence. Turbulence driven by disk self-gravity shows features distinct from those driven by the magnetorotational instability (MRI). We study the dynamics of solids in gravito-turbulent disks with two-dimensional (in the disk plane), hybrid (particle and gas) simulations. Gravito-turbulent disks can exhibit stronger gravitational stirring than MRI-active disks, resulting in greater radial diffusion and larger eccentricities and relative speeds for large particles (those with dimensionless stopping times tstopΩ>1, where Ω is the orbital frequency). The agglomeration of large particles into planetesimals by pairwise collisions is therefore disfavored in gravito-turbulent disks. However, the relative speeds of intermediate-size particles tstopΩ∼1 are significantly reduced as such particles are collected by gas drag and gas gravity into coherent filament-like structures with densities high enough to trigger gravitational collapse. First-generation planetesimals may form via gravitational instability of dust in marginally gravitationally unstable gas disks.

A viscous-convective instability in laminar Keplerian thin disks

A viscous-convective instability in laminar Keplerian thin discs

Authors:

Malanchev et al

Abstract:

Using the anelastic approximation of linearized hydrodynamic equations, we investigate the development of axially symmetric small perturbations in thin Keplerian discs. Dispersion relation is found as a solution of general Sturm-Liouville eigenvalue problem for different values of relevant physical parameters (viscosity, heat conductivity, disc semithickness). The analysis reveals the appearance of overstable mode for Prandtl parameter higher than some critical value. These modes have a viscous-convective nature and can serve as a seed for turbulence in astrophysical discs even in the absence of magnetic fields.

On the gravitational stability of gravito-turbulent accretion disks

On the gravitational stability of gravito-turbulent accretion disks

Authors:

Lin et al

Abstract:

Low mass, self-gravitating accretion disks admit quasi-steady, `gravito-turbulent' states in which cooling balances turbulent viscous heating. However, numerical simulations show that gravito-turbulence cannot be sustained beyond dynamical timescales when the cooling rate or corresponding turbulent viscosity is too large. The result is disk fragmentation. We motivate and quantify an interpretation of disk fragmentation as the inability to maintain gravito-turbulence due to formal secondary instabilities driven by: 1) cooling, which reduces pressure support; and/or 2) viscosity, which reduces rotational support. We analyze the gravitational stability of viscous, non-adiabatic accretion disks with internal heating, external irradiation, and cooling. We consider parameterized cooling functions in 2D and 3D disks, as well as radiative diffusion in 3D. We show that generally there is no critical cooling rate/viscosity below which the disk is formally stable, although interesting limits appear for unstable modes with lengthscales on the order of the disk thickness. We apply this new linear theory to models of protoplanetary disks subject to gravito-turbulence modeled as an effective viscosity, and cooling regulated by dust opacity. We find that viscosity renders the disk beyond ∼60AU dynamically unstable on radial lengthscales a few times the local disk thickness. This is coincident with the empirical condition for disk fragmentation based on a maximum sustainable stress. We suggest turbulent stresses can play an active role in realistic disk fragmentation by removing rotational stabilization against self-gravity, and that the observed transition in behavior from gravito-turbulent to fragmenting may derive from instability of the gravito-turbulent state itself.

Effect of turbulence on collisions of dust particles with planetesimals in protoplanetary disks

Effect of turbulence on collisions of dust particles with planetesimals in protoplanetary disks

Authors:

Homann et al

Abstract:

Planetesimals in gaseous protoplanetary disks may grow by collecting dust particles. Hydrodynamical studies show that small particles generally avoid collisions with the planetesimals because they are entrained by the flow around them. This occurs when St, the Stokes number, defined as the ratio of the dust stopping time to the planetesimal crossing time, becomes much smaller than unity. However, these studies have been limited to the laminar case, whereas these disks are believed to be turbulent. We want to estimate the influence of gas turbulence on the dust-planetesimal collision rate and on the impact speeds. We used three-dimensional direct numerical simulations of a fixed sphere (planetesimal) facing a laminar and turbulent flow seeded with small inertial particles (dust) subject to a Stokes drag. A no-slip boundary condition on the planetesimal surface is modeled via a penalty method. We find that turbulence can significantly increase the collision rate of dust particles with planetesimals. For a high turbulence case (when the amplitude of turbulent fluctuations is similar to the headwind velocity), we find that the collision probability remains equal to the geometrical rate or even higher for St≥0.1, i.e., for dust sizes an order of magnitude smaller than in the laminar case. We derive expressions to calculate impact probabilities as a function of dust and planetesimal size and turbulent intensity.

Implications of Magnetorotational Instability for Turbulence in Outer Protoplanetary Disks

ELECTRON HEATING IN MAGNETOROTATIONAL INSTABILITY: IMPLICATIONS FOR TURBULENCE STRENGTH IN THE OUTER REGIONS OF PROTOPLANETARY DISKS

Authors:

Mori et al

Abstract:

The magnetorotational instability (MRI) drives vigorous turbulence in a region of protoplanetary disks where the ionization fraction is sufficiently high. It has recently been shown that the electric field induced by the MRI can heat up electrons and thereby affect the ionization balance in the gas. In particular, in a disk where abundant dust grains are present, the electron heating causes a reduction of the electron abundance, thereby preventing further growth of the MRI. By using the nonlinear Ohm's law that takes into account electron heating, we investigate where in protoplanetary disks this negative feedback between the MRI and ionization chemistry becomes important. We find that the "e-heating zone," the region where the electron heating limits the saturation of the MRI, extends out up to 80 AU in the minimum-mass solar nebula with abundant submicron-sized grains. This region is considerably larger than the conventional dead zone whose radial extent is ~20 AU in the same disk model. Scaling arguments show that the MRI turbulence in the e-heating zone should have a significantly lower saturation level. Submicron-sized grains in the e-heating zone are so negatively charged that their collisional growth is unlikely to occur. Our present model neglects ambipolar and Hall diffusion, but our estimate shows that ambipolar diffusion would also affect the MRI in the e-heating zone.

Critical Layers and Protoplanetary Disk Turbulence

Critical layers and protoplanetary disk turbulence

Authors:

Umurhan et al

Abstract:

A linear analysis of the zombie vortex instability is performed in a stratified shearing sheet setting for three model barotropic shear flows: the vorticity step, the shear layer and the asymmetric jet. The examination assumes that both disk-normal gravity and stratification is constant. The aim is to better understand the instability of so-called Z-modes and the subsequent nonlinear self-reproduction process discussed in the literature. We report several results: The instability is the result of a resonant interaction between a Rossby wave and a gravity wave. The associated critical layer is the location where the Doppler shifted frequency of a distant Rossby wave equals the local Brunt-Vaisala frequency. For the shear flow model we confirm the minimum required Rossby number (Ro) for instability to be 0.2. It is also found that the shear layer supports the instability in the limit where stratification vanishes. The zombie vortex instability as well as the Rossby wave instability are examined for the first time in a jet model, finding that the instability can occur for Ro= 0.05. For all model flows considered, nonlinear vorticity forcing due to unstable Z-modes is shown to result in the creation of a jet flow at the critical layer. The jet-flow emerges as the result of the competition between the vertical lifting of perturbation radial vorticity and the radial transport of vertical perturbation vorticity wherein the former mechanism usually dominates the latter. We confirm that nonlinear forcing results in a self-replicating/self-reproducing pattern of creation and destruction: parent jets spawn and grow child jets at associated critical layers and once the child jet grows strong enough it subsequently creates a next generation of jets associated with its critical layer while simultaneously destroying itself due to the Rossby wave instability.