Turbulence effects in planetesimal formation (original) (raw)
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Turbulent Clustering of Protoplanetary Dust and Planetesimal Formation
The Astrophysical Journal, 2011
We study the clustering of inertial particles in turbulent flows and discuss its applications to dust particles in protoplanetary disks. Using numerical simulations, we compute the radial distribution function (RDF), which measures the probability of finding particle pairs at given distances, and the probability density function of the particle concentration. The clustering statistics depend on the Stokes number, St, defined as the ratio of the particle friction timescale, τ p , to the Kolmogorov timescale in the flow. In agreement with previous studies, we find that, in the dissipation range, the clustering intensity strongly peaks at St 1, and the RDF for St ∼ 1 shows a fast power-law increase toward small scales, suggesting that turbulent clustering may considerably enhance the particle collision rate. Clustering at inertial-range scales is of particular interest to the problem of planetesimal formation. At these large scales, the strongest clustering is from particles with τ p in the inertial range. Clustering of these particles occurs primarily around a scale where the eddy turnover time is ∼τ p. We find that particles of different sizes tend to cluster at different locations, leading to flat RDFs between different particles at small scales. In the presence of multiple particle sizes, the overall clustering strength decreases as the particle size distribution broadens. We discuss particle clustering in two recent models for planetesimal formation. We argue that, in the model based on turbulent clustering of chondrule-size particles, the probability of finding strong clusters that can seed planetesimals may have been significantly overestimated. We discuss various clustering mechanisms in simulations of planetesimal formation by gravitational collapse of dense clumps of meter-size particles, in particular the contribution from turbulent clustering due to the limited numerical resolution.
Monthly Notices of the Royal Astronomical Society, 2001
We investigate the response of dust particles in the mid-plane of a protoplanetary disc to the turbulent velocity field of long-lived, large-scale vortical circulation. The dynamical problem is studied through numerical integrations of the equations of motion for individual particles (the sizes of which range from centimetres to metres) subject to the solar gravity and the friction drag of the nebular gas. It is found, neglecting the thickness of the disc, that the particles do not drift inwards to the central star as occurs in a standard symmetrical nebula. Vortices tend to capture a large number of the particles. The effectiveness of this size-selective concentration mechanism depends not only on the value of the drag and the distance from the Sun, but also on the elongation of the vortex and its characteristic lifetime. Typical anticyclonic vortices with exponential decay times of 30 orbital periods and semiaxis ratios of 4 can increase the local surface density by a factor of 4 in a lifetime and accumulate 0:03±0:3 Earth masses. If the elongation is significant (.7), the vortex cannot concentrate any significant amount of solid material. Vortices with an elongation of about 2 are the most effective as regards trapping of dust. We have also found analytical expressions for the capture time as well as capture constraints as a function of the friction parameter, the elongation of the vortex and the impact parameter. By increasing the lifetime and the surface density of the solid particles, this confining mechanism can make the agglomeration of the solid material of the nebula (through collisional aggregation or gravitational instabilities) much more efficient than previously believed. This offers new possibilities for the formation of the planetesimals and the giant planet cores, and may explain the rapid formation of extrasolar giant planets.
2010
We investigate the formation process of planetesimals from the dust layer by the gravitational instability in the gas disk using local N-body simulations. The gas is modeled as a background laminar flow. We study the formation process of planetesimals and its dependence on the strength of the gas drag. Our simulation results show that the formation process is divided into three stages qualitatively: the formation of wake-like density structures, the creation of planetesimal seeds, and their collisional growth. The linear analysis of the dissipative gravitational instability shows that the dust layer is secularly unstable although Toomre's Q value is larger than unity. However, in the initial stage, the growth time of the gravitational instability is longer than that of the dust sedimentation and the decrease in the velocity dispersion. Thus, the velocity dispersion decreases and the disk shrinks vertically. As the velocity dispersion becomes sufficiently small, the gravitational...
Gravoturbulent Formation of Planetesimals
The Astrophysical Journal, 2006
We explore the effect of magnetorotational turbulence on the dynamics and concentrations of boulders in local box simulations of a sub-Keplerian protoplanetary disc. The solids are treated as particles each with an independent space coordinate and velocity. We find that the turbulence has two effects on the solids. 1) Meter and decameter bodies are strongly concentrated, locally up to a factor 100 times the average dust density, whereas decimeter bodies only experience a moderate density increase. The concentrations are located in large scale radial gas density enhancements that arise from a combination of turbulence and shear. 2) For meter-sized boulders, the concentrations cause the average radial drift speed to be reduced by 40%. We find that the densest clumps of solids are gravitationally unstable under physically reasonable values for the gas column density and for the dust-to-gas ratio due to sedimentation. We speculate that planetesimals can form in a dust layer that is not in itself dense enough to undergo gravitational fragmentation, and that fragmentation happens in turbulent density fluctuations in this sublayer. Subject headings: instabilities -MHD -planetary systems: formation -planetary systems: protoplanetary disks -turbulence 1 The code is available at
Dusty Vortices in Protoplanetary Disks
The Astrophysical Journal, 2006
Global two-dimensional simulations are used to study the coupled evolution of gas and solid particles in a Rossby unstable protoplanetary disk. The initial radial bump in density is unstable to the formation of Rossby waves, which roll up and break into anticyclonic vortices that gradually merge into a large-scale vortical structure persisting for more than 100 rotations. Conditions for the growth of such vortices may naturally appear at the outer edge of the ''dead zone'' of a protoplanetary disk where gas tends to pile up. We find that solid particles are captured by the vortices and change the evolution: (1) large particles rapidly sink toward the center of the vortices and increase the solid-togas ratio by an order of magnitude, (2) solid particles tend to reduce the lifetime of the vortices, and (3) solid particles are effectively confined in the vortices before they are dispersed by the Keplerian shear flow. These results confirm that in a minimum mass solar nebula, persistent vortices could be good places for the formation of the planetesimals or the rocky cores of gas giant planets as soon as particles reach boulder size.
Particle aggregation in a turbulent Keplerian flow
Physics of Fluids, 1999
For the problem of planetary formation one seeks a mechanism to gather small dust particles together into larger solid objects. Here we describe a scenario in which turbulence mediates this process by aggregating particles into anticyclonic regions. If, as our simulations suggest, anticyclonic vortices form as long-lived coherent structures, the process becomes more powerful because such vortices trap particles effectively. Even if the turbulence is decaying, following the upheaval that formed the disk, there is enough time to make the dust distribution quite lumpy.
Rapid planetesimal formation in turbulent circumstellar disks
Nature, 2007
The initial stages of planet formation in circumstellar gas discs proceed via dust grains that collide and build up larger and larger bodies 1 . How this process continues from metre-sized boulders to kilometre-scale planetesimals is a major unsolved problem 2 : boulders stick together poorly 3 , and spiral into the protostar in a few hundred orbits due to a head wind from the slower rotating gas 4 . Gravitational collapse of the solid component has been suggested to overcome this barrier 1, 5, 6 . Even low levels of turbulence, however, inhibit sedimentation of solids to a sufficiently dense midplane layer 2, 7 , but turbulence must be present to explain observed gas accretion in protostellar discs 8 . Here we report the discovery of efficient gravitational collapse of boulders in locally overdense regions in the midplane. The boulders concentrate initially in transient high pressures in the turbulent gas 9 , and these concentra-1 arXiv:0708.3890v1 [astro-ph]
Simulations of dust-trapping vortices in protoplanetary discs
Astronomy and Astrophysics, 2004
Local three-dimensional shearing box simulations of the compressible coupled dust-gas equations are used in the fluid approximation to study the evolution of different initial vortex configurations in a protoplanetary disc and their dust-trapping capabilities. The initial conditions for the gas are derived from an analytic solution to the compressible Euler equation and the continuity equation. The solution is valid if there is a vacuum outside the vortex. In the simulations the vortex is either embedded in a hot corona, or it is extended in a cylindrical fashion in the vertical direction. Both configurations are found to survive for at least one orbit and lead to accumulation of dust inside the vortex. This confirms earlier findings that dust accumulates in anticyclonic vortices, indicating that this is a viable mechanism for planetesimal formation.
N ‐Body Simulation of Planetesimal Formation through Gravitational Instability of a Dust Layer
The Astrophysical Journal, 2007
We performed N-body simulations of a dust layer without a gas component and examined the formation process of planetesimals. We found that the formation process of planetesimals can be divided into three stages: the formation of non-axisymmetric wake-like structures, the creation of aggregates, and the collisional growth of the aggregates. Finally, a few large aggregates and many small aggregates are formed. The mass of the largest aggregate is larger than the mass predicted by the linear perturbation theory. We examined the dependence of system parameters on the planetesimal formation. We found that the mass of the largest aggregates increase as the size of the computational domain increases. However the ratio of the aggregate mass to the total mass M aggr /M total is almost constant 0.8 − 0.9. The mass of the largest aggregate increases with the optical depth and the Hill radius of particles.