Gravoturbulent Formation of Planetesimals (original) (raw)

Supplementary Information for``Rapid planetesimal formation in turbulent circumstellar discs

2007

This document contains refereed supplementary information for the paper "Rapid planetesimal formation in turbulent circumstellar discs". It contains 15 sections ( §1.1 - §1.15) that address a number of subjects related to the main paper. Some of the subjects are highlighted here in the abstract. We describe in detail the Poisson solver used to find the self-potential of the solid particles, including a linear and a non-linear test problem ( §1.3). Dissipative collisions remove energy from the motion of the particles by collisional cooling ( §1.4), an effect that allows gravitational collapse to occur in somewhat less massive discs ( §1.7). A resolution study of the gravitational collapse of the boulders is presented in §1.6. We find that gravitational collapse can occur in progressively less massive discs as the grid resolution is increased, likely due to the decreased smoothing of the particle-mesh self-gravity solver with increasing resolution. In §1.10 we show that it is in good agreement with the Goldreich & Ward (1973) stability analysis to form several-hundred-km-sized bodies, when the analysis is applied to 5 AU and to regions of increased boulder column density. §11 is devoted to the measurement of random speeds and collision speeds between boulders. We find good agreement between our measurements and analytical theory for the random speeds, but the measured collision speeds are 3 times lower than expected from analytical theory. Higher resolution studies, and an improved analytical theory of collision speeds that takes into account epicyclic motion, will be needed to determine whether collision speeds have converged. In §1.12 we present models with no magnetic fields. The boulder layer still exhibits strong clumping, due to the streaming instability, if the global solids-to-gas ratio is increased by a factor 3. Gravitational collapse occurs as readily as in magnetised discs.

PLANETESIMAL AND PROTOPLANET DYNAMICS IN A TURBULENT PROTOPLANETARY DISK: IDEAL UNSTRATIFIED DISKS

The Astrophysical Journal, 2009

The dynamics of planetesimals and planetary cores may be strongly influenced by density perturbations driven by magneto-rotational turbulence in their natal protoplanetary gas disks. Using the local shearing box approximation, we perform numerical simulations of planetesimals moving as massless particles in a turbulent, magnetized, unstratified gas disk. Our fiducial disk model shows turbulent accretion characterized by a Shakura-Sunyaev viscosity parameter of α ∼ 10 −2 , with root-mean-square density perturbations of ∼10%. We measure the statistical evolution of particle orbital properties in our simulations including mean radius, eccentricity, and velocity dispersion. We confirm random walk growth in time of all three properties, the first time that this has been done with direct orbital integration in a local model. We find that the growth rate increases with the box size used at least up to boxes of eight scale heights in horizontal size. However, even our largest boxes show velocity dispersions sufficiently low that collisional destruction of planetesimals should be unimportant in the inner disk throughout its lifetime. Our direct integrations agree with earlier torque measurements showing that type I migration dominates over diffusive migration by stochastic torques for most objects in the planetary core and terrestrial planet mass range. Diffusive migration remains important for objects in the mass range of kilometer-sized -2planetesimals. Discrepancies in the derived magnitude of turbulence between local and global simulations of magneto-rotationally unstable disks remains an open issue, with important consequences for planet formation scenarios.

Global structure of magnetorotationally turbulent protoplanetary discs

Monthly Notices of the Royal Astronomical Society, 2012

The aim of the present paper is to investigate the spatial structure of a protoplanetary disc whose dynamics is governed by magnetorotational turbulence. We perform a series of local 3D chemo-radiative MHD simulations located at different radii of a disc which is twice as massive as the standard minimum mass solar nebula of Hayashi (1981). The ionisation state of the disc is calculated by including collisional ionisation, stellar X-rays, cosmic rays and the decay of radionuclides as ionisation sources, and by solving a simplified chemical network which includes the effect of the absorption of free charges by µm-sized dust grains. In the region where the ionisation is too low to assure good coupling between matter and magnetic fields, a non-turbulent central "dead zone" forms, which ranges approximately from a distance of 2 AU to 4 AU from the central star. The approach taken in the present work allows for the first time to derive the global spatial structure of a protoplanetary disc from a set of physically realistic numerical simulations.

Global magnetohydrodynamical models of turbulence in protoplanetary disks

Astronomy and Astrophysics, 2008

Aims. We present global 3D MHD simulations of disks of gas and solids, aiming at developing models that can be used to study various scenarios of planet formation and planet-disk interaction in turbulent accretion disks. Methods. We employ the PENCIL CODE, a 3D high-order finite-difference MHD code using Cartesian coordinates. We solve the equations of ideal MHD with a local isothermal equation of state. Planets and stars are treated as particles evolved with an N-body scheme. Solid boulders are treated as individual superparticles that couple to the gas through a drag force that is linear in the local relative velocity between gas and particle. Results. We find that Cartesian grids are well-suited for accretion disk problems. The disk-in-a-box models based on Cartesian grids presented here develop and sustain MHD turbulence, in good agreement with published results achieved with cylindrical codes.We investigate the dependence of the magnetorotational instability on disk scale height, finding evidence that the turbulence generated by the magnetorotational instability grows with thermal pressure. The turbulent stresses depend on the thermal pressure obeying a power law of 0.24 ± 0.03, compatible with the value of 0.25 found in shearing box calculations. The ratio of Maxwell to Reynolds stresses decreases with increasing temperature, dropping from 5 to 1 when the sound speed was raised by a factor 4, maintaing the same field strength. We also study the dynamics of solid boulders in the hydromagnetic turbulence, by making use of 10 6 Lagrangian particles embedded in the Eulerian grid. The effective diffusion provided by the turbulence prevents settling of the solids in a infinitesimally thin layer, forming instead a layer of solids of finite vertical thickness. The measured scale height of this diffusion-supported layer of solids implies turbulent vertical diffusion coefficients with globally averaged Schmidt numbers of 1.0±0.2 for a model with α ≈ 10 −3 and 0.78±0.06 for a model with α ≈ 10 −1 . That is, the vertical turbulent diffusion acting on the solids phase is comparable to the turbulent viscosity acting on the gas phase. The average bulk density of solids in the turbulent flow is quite low (ρ p =6.0 × 10 −11 kg m −3 ), but in the high pressure regions, significant overdensities are observed, where the solid-to-gas ratio reached values as great as 85, corresponding to 4 orders of magnitude higher than the initial interstellar value of 0.01

Turbulence effects in planetesimal formation

1998

The formation of planetesimals is investigated by studying the transport of dust particles in a local three- dimensionalsimulationofaccretiondiscturbulence.Heavypar- ticlesfallrapidlytowardsthemidplane,whereaslighterparticles are strongly advected by the flow. For light particles the turbu- lence leads to a rapid redistribution of particles such that their density per unit mass is approximately constant with height. There is no pronounced concentration of particles in vortices or anticyclones, as was suggested previously. This is partly be- cause of the adverse effect of keplerian shear and also because in our simulation vortices are only short lived. However, if we assume the gas velocity to be frozen in time, there is a concen- tration of dust in ring-like structures after a few orbits. This is caused mainly by a convergence of the gas flow in those loca- tions, rather than the presence of vortices or anticyclones.

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]

Evolution of protoplanetary discs driven by the MRI, self-gravity and hydrodynamical turbulence

Monthly Notices of the Royal Astronomical Society, 2007

We study the viscous evolution of protoplanetary discs driven by the combined action of magnetohydrodynamic turbulence, resulting from the magneto-rotational instability (MRI), self-gravity torques, parametrized in terms of an effective viscosity and an additional viscous agent of unspecified origin. The distribution of torques driving the evolution of the disc is calculated by analysing where in the disc the MRI develops and, to incorporate the effect of self-gravity, calculating the Toomre parameter. We find that, generally, discs rapidly evolve towards a configuration where the intermediate regions, from a fraction of an au to a few au, are stable against the MRI due to their low-ionization degree. As an additional source of viscosity is assumed to operate in those regions, subsequent evolution of the disc is eruptive. Brief episodes of high mass accretion ensue as the criterion for the development of the MRI is met in the low-ionization region. The radial distribution of mass and temperature in the disc differs considerably from disc models with constant α parameter or layered accretion models, with potentially important consequences on the process of planet formation.

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.

Evolution of protoplanetary discs driven by MHD turbulence and other agents

2004

Después de revisar el estado de nuestro conocimiento de cómo opera la inestabilidad magnetorotacional (MRI) en discos protoplanetarios, presentamos resultados preliminares sobre la evolución de tales sistemas, basándonos en la predicción de distribución espacial de torcas viscosas. Se construyen modelos unidimensionales de discos α para los discos protoplanetarios incorporando diferentes valores del parámetro α para reflejar los diferentes agentes que participan en la evolución de los discos. Tomamos en cuenta los efectos de viscosidad turbulenta debido a la MRI, de torcas de autogravedad (prescritas en términos de una viscosidad efectiva) y de otros agentes viscosos caracterizados por una eficiencia reducida. La estructura y evolución resultante para los discos es drásticamente diferente a la predicha por modelos de discos con α uniforme o por modelos de acreción en capas.