Abstract
The trans-Neptunian object 2014 MU69, named Arrokoth, is the most recent evidence that planetesimals did not form by successive collisions of smaller objects, but by the direct gravitational ...collapse of a pebble cloud. But what process sets the physical scales on which this collapse may occur? Star formation has the Jeans mass, that is, when gravity is stronger than thermal pressure, helping us to understand the mass of our Sun. But what controls mass and size in the case of planetesimal formation? Both asteroids and Kuiper Belt objects show a kink in their size distribution at 100 km. Here we derive a gravitational collapse criterion for a pebble cloud to fragment to planetesimals, showing that a critical mass is needed for the clump to overcome turbulent diffusion. We successfully tested the validity of this criterion in direct numerical simulations of planetesimal formation triggered by the streaming instability. Our result can therefore explain the sizes for planetesimals found forming in streaming instability simulations in the literature, while not addressing the detailed size distribution. We find that the observed characteristic diameter of ∼100 km corresponds to the critical mass of a pebble cloud set by the strength of turbulent diffusion stemming from streaming instability for a wide region of a solar nebula model from 2 to 60 au, with a tendency to allow for smaller objects at distances beyond and at late times, when the nebula gas gets depleted.
Hydrodynamic instabilities in disks around young stars depend on the thermodynamic stratification of the disk and on the local rate of thermal relaxation. Here, we map the spatial extent of unstable ...regions for the Vertical Shear Instability (VSI), the Convective Overstability (COS), and the amplification of vortices via the Subcritical Baroclinic Instability (SBI). We use steady-state accretion disk models, including stellar irradiation, accretion heating, and radiative transfer. We determine the local radial and vertical stratification and thermal relaxation rate in the disk, which depends on the stellar mass, disk mass, and mass accretion rate. We find that passive regions of disks-that is, the midplane temperature dominated by irradiation-are COS unstable about one pressure scale height above the midplane and VSI unstable at radii >10 au. Vortex amplification via SBI should operate in most parts of active and passive disks. For active parts of disks (midplane temperature determined by accretion power), COS can become active down to the midplane. The same is true for the VSI because of the vertically adiabatic stratification of an internally heated disk. If hydrodynamic instabilities or other nonideal MHD processes are able to create -stresses (>10−5) and released accretion energy leads to internal heating of the disk, hydrodynamic instabilities are likely to operate in significant parts of the planet-forming zones in disks around young stars, driving gas accretion and flow structure formation. Thus, hydrodynamic instabilities are viable candidates to explain the rings and vortices observed with the Atacama Large Millimeter/submillimeter Array and Very Large Telescope.
Abstract
We perform streaming-instability simulations at Hill density and beyond to demonstrate that planetesimal formation is not completed when pebble accumulations exceed the local Hill density. ...We find that Hill density is not a sufficient criterion for further gravitational collapse of a pebble cloud into a planetesimal, but that additionally the accumulated mass has to be large enough to overcome turbulent diffusion. A Toomre analysis of the system indicates that linear self-gravity modes play no role on the scale of our numerical simulation. We nevertheless find that self-gravity, by vertically contracting the pebble layer, increases the strength of turbulence, which is either an indication of Kelvin–Helmholtz instability or a boost of the streaming instability. We furthermore determine the Bonnor–Ebert central density to which a pebble cloud of a given mass has to be compressed before it would be able to continue contraction against internal diffusion. As the equivalent “solid body” size of the pebble cloud scales with the central density to the power of −1/6, it is much easier to have a pebble cloud of 100 km equivalent size to collapse than one of 10 km for the same level of turbulent diffusion. This can explain the lack of small bodies in the solar system and predicts small objects will form at large pebble-to-gas ratios, so either in the outskirts of the solar nebula or at late times of generally reduced gas mass.
Abstract
Turbulence has a profound impact on the evolution of gas and dust in protoplanetary disks (PPDs), from driving the collisions and the diffusion of dust grains, to the concentration of ...pebbles in giant vortices, thus, facilitating planetesimal formation. The vertical shear instability (VSI) is a hydrodynamic mechanism, operating in PPDs if the local rate of thermal relaxation is high enough. Previous studies of the VSI have, however, relied on the assumption of constant cooling rates, or neglected the finite coupling time between the gas particles and the dust grains. Here, we present the results of hydrodynamic simulations of PPDs with the PLUTO code that include a more realistic thermal relaxation prescription, which enables us to study the VSI in the optically thick and optically thin parts of the disk under consideration of the thermal dust-gas coupling. We show the VSI to cause turbulence even in the optically thick inner regions of PPDs in our two- and three-dimensional simulations. The collisional decoupling of dust and gas particles in the upper atmosphere and the correspondingly inefficient thermal relaxation rates lead to the damping of the VSI turbulence. Long-lived anticyclonic vortices form in our three-dimensional simulation. These structures emerge from the turbulence in the VSI-active layer, persist over hundreds of orbits and extend vertically over the whole extent of the turbulent region. We conclude that the VSI leads to turbulence and the formation of long-lived dust traps within ±3 pressure scale heights distance from the disk midplane.
The collapse of dust particle clouds directly to kilometer-sized planetesimals is a promising way to explain the formation of planetesimals, asteroids, and comets. In the past, this collapse has been ...studied in stratified shearing box simulations with super-solar dust-to-gas ratio ϵ, allowing for streaming instability (SI) and gravitational collapse. This paper studies the non-stratified SI under dust-to-gas ratios from up to without self-gravity. The study covers domain sizes of , , and in terms of the gas-disk scale height using the PencilCode. They are performed in radial-azimuthal (2D) and radial-vertical (2.5D) extents. The used particles of and 0.1 mark the upper end of the expected dust growth. SI activity is found up to very high dust-to-gas ratios, providing fluctuations in the local dust-to-gas ratios and turbulent particle diffusion δ. We find an SI-like instability that operates in r- , even when vertical modes are suppressed. This new azimuthal streaming instability (aSI) shows similar properties and appearance as the SI. Both, SI and aSI show diffusivity at only to be two orders of magnitude lower than at , suggesting a relation that is shallow around . The (a)SI ability to concentrate particles is found to be uncorrelated with its strength in particle turbulence. Finally, we performed a resolution study to test our findings of the aSI. This paper stresses the importance of properly resolving the (a)SI at high dust-to-gas ratios and planetesimal collapse simulations, leading otherwise to potentially incomplete results.
We propose an expression for a local planetesimal formation rate proportional to the instantaneous radial pebble flux. The result-a radial planetesimal distribution-can be used as an initial ...condition to study the formation of planetary embryos. We follow the idea that one needs particle traps to locally enhance the dust-to-gas ratios sufficiently, such that particle gas interactions can no longer prevent planetesimal formation on small scales. The locations of these traps can emerge everywhere in the disk. Their occurrence and lifetime is subject to ongoing research; thus, here they are implemented via free parameters. This enables us to study the influence of the disk properties on the formation of planetesimals, predicting their time-dependent formation rates and the location of primary pebble accretion. We show that large -values of 0.01 (strong turbulence) prevent the formation of planetesimals in the inner part of the disk, arguing for lower values of around 0.001 (moderate turbulence), at which planetesimals form quickly at all places where they are needed for proto-planets. Planetesimals form as soon as dust has grown to pebbles (mm to dm) and the pebble flux reaches a critical value, which is after a few thousand years at 2-3 au and after a few hundred thousand years at 20-30 au. Planetesimal formation lasts until the pebble supply has decreased below a critical value. The final spatial planetesimal distribution is steeper compared to the initial dust and gas distribution, which helps explain the discrepancy between the minimum mass solar nebula and viscous accretion disks.
ABSTRACT
Theoretical models of protoplanetary discs have shown the vertical shear instability (VSI) to be a prime candidate to explain turbulence in the dead zone of the disc. However, simulations of ...the VSI have yet to show consistent levels of key disc turbulence parameters like the stress-to-pressure ratio α. We aim to reconcile these different values by performing a parameter study on the VSI with focus on the disc density gradient p and aspect ratio h = H/R. We use full 2π 3D simulations of the disc 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 disc aspect ratio with a strong scaling of α∝h2.6, in contrast to the traditional α model, where viscosity scales as ν∝αh2 with a constant α. We also observe consistent formation of large scale vortices across all investigated parameters. The vortices show uniformly aspect ratios of χ ≈ 10 and radial widths of approximately 1.5H. With our findings we can reconcile the different values reported for the stress-to-pressure ratio from both isothermal and full radiation hydrodynamics models, and show long-term evolution effects of the VSI that could aide in the formation of planetesimals.
Abstract
Planetary embryos are built through the collisional growth of 10–100 km-sized objects called planetesimals, a formerly large population of objects, of which asteroids, comets, and Kuiper ...Belt objects represent the leftovers from planet formation in our solar system. Here, we follow the paradigm that turbulence created overdense pebble clouds, which then collapse under their own self-gravity. We use the multiphysics code GIZMO to model the pebble cloud density as a continuum, with a polytropic equation of state to account for collisional interactions and capturing the phase transition to a quasi-incompressible “solid” object, i.e., a planetesimal in hydrostatic equilibrium. Thus, we study cloud collapse effectively at the resolution of the forming planetesimals, allowing us to derive an initial mass function for planetesimals in relation to the total pebble mass of the collapsing cloud. The redistribution of angular momentum in the collapsing pebble cloud is the main mechanism leading to multiple fragmentation. The angular momentum of the pebble cloud and thus the centrifugal radius increases with distance to the Sun, but the solid size of the forming planetesimals is constant. Therefore we find that with increasing distance to the Sun, the number of forming planetesimals per pebble cloud increases. For all distances, the formation of binaries occurs within higher hierarchical systems. The size distribution is top-heavy and can be described with a Gaussian distribution of planetesimal mass. For the asteroid belt, we can infer a most likely size of 125 km, all stemming from pebble clouds of equivalent size 152 km.
ABSTRACT
A certain appeal to the alpha model for turbulence and related viscosity in accretion discs was that one scales the Reynolds stresses simply on the thermal pressure, assuming that turbulence ...driven by a certain mechanism will attain a characteristic Mach number in its velocity fluctuations. Besides the notion that there are different mechanism driving turbulence and angular momentum transport in a disc, we also find that within a single instability mechanism, here the vertical shear instability, stresses do not linearly scale with thermal pressure. Here, we demonstrate in numerical simulations the effect of the gas temperature gradient and the thermal relaxation time on the average stresses generated in the non-linear stage of the instability. We find that the stresses scale with the square of the exponent of the radial temperature profile at least for a range of dlog T/dlog R = −0.5, −1, beyond which the pressure scale height varies too much over the simulation domain, to provide clear results. Stresses are also dependent on thermal relaxation times, provided they are longer than 10−3 orbital periods. The strong dependence of viscous transport of angular momentum on the local conditions in the disc (especially temperature, temperature gradient, and surface density/optical depth) challenges the ideas of viscosity leading to smooth density distributions, opening a route for structure (ring) formation and time variable mass accretion.
Abstract
Disk vortices have been heralded as promising routes for planet formation due to their ability to trap significant amounts of pebbles. While the gas motions and trapping properties of ...two-dimensional vortices have been studied in enough detail in the literature, pebble trapping in three dimensions has received less attention, due to the higher computational demand. Here we use the
Pencil Code
to study 3D vortices generated by convective overstability and the trapping of solids within them. The gas is unstratified whereas the pebbles settle to the midplane due to vertical gravity. We find that for pebbles of normalized friction times of
St
=
0.05
and
St
=
1
, and dust-to-gas ratio
ε
=
0.01
, the vortex column in the midplane is strongly perturbed. Yet when the initial dust-to-gas ratio is decreased the vortices remain stable and function as efficient pebble traps. Streaming instability is triggered even for the lowest dust-to-gas ratio (
ε
0
=
10
−
4
) and smallest pebble sizes (
St
=
0.05
) we assumed, showing a path for planetesimal formation in vortex cores from even extremely subsolar metallicity. To estimate if the reached overdensities can be held together solely by their own gravity we estimate the Roche density at different radii. Depending on disk model and radial location of the pebble clump we do reach concentrations higher than the Roche density. We infer that if self-gravity was included for the pebbles then gravitational collapse would likely occur.
PDF
