arXiv subjects

Anders Johansen

Publications and source records attributed to Anders Johansen.

At least 145 records · Page 8Linked to original sources

arXiv2012

Rapid growth of gas-giant cores by pebble accretion

The observed lifetimes of gaseous protoplanetary discs place strong constraints on gas and ice giant formation in the core accretion scenario. The approximately 10-Earth-mass solid core responsible for the attraction of the gaseous envelope has to form before gas dissipation in the protoplanetary disc is completed within 1-10 million years. Building up the core by collisions between km-sized planetesimals fails to meet this time-scale constraint, especially at wide stellar separations. Nonetheless, gas-giant planets are detected by direct imaging at wide orbital distances. In this paper, we numerically study the growth of cores by the accretion of cm-sized pebbles loosely coupled to the gas. We measure the accretion rate onto seed masses ranging from a large planetesimal to a fully grown 10-Earth-mass core and test different particle sizes. The numerical results are in good agreement with our analytic expressions, indicating the existence of two accretion regimes, one set by the azimuthal and radial particle drift for the lower seed masses and the other, for higher masses, by the velocity at the edge of the Hill sphere. In the former, the optimally accreted particle size increases with core mass, while in the latter the optimal size is centimeters, independent of core mass. We discuss the implications for rapid core growth of gas-giant and ice-giant cores. We conclude that pebble accretion can resolve the long-standing core accretion time-scale conflict. This requires a near-unity dust-to-gas ratio in the midplane, particle growth to mm and cm and the formation of massive planetesimals or low radial pressure support. The core growth time-scale is shortened by a factor 30-1,000 at 5 AU and by a factor 100-10,000 at 50 AU, compared to the gravitationally focused accretion of, respectively, low-scale-height planetesimal fragments or standard km-sized planetesimals.

astro-ph.EP↗

arXiv2011

Adding particle collisions to the formation of asteroids and Kuiper belt objects via streaming instabilities

Modelling the formation of super-km-sized planetesimals by gravitational collapse of regions overdense in small particles requires numerical algorithms capable of handling simultaneously hydrodynamics, particle dynamics and particle collisions. While the initial phases of radial contraction are dictated by drag forces and gravity, particle collisions become gradually more significant as filaments contract beyond Roche density. Here we present a new numerical algorithm for treating momentum and energy exchange in collisions between numerical superparticles representing a high number of physical particles. We adopt a Monte Carlo approach where superparticle pairs in a grid cell collide statistically on the physical collision time-scale. Collisions occur by enlarging particles until they touch and solving for the collision outcome, accounting for energy dissipation in inelastic collisions. We demonstrate that superparticle collisions can be consistently implemented at a modest computational cost. In protoplanetary disc turbulence driven by the streaming instability, we argue that the relative Keplerian shear velocity should be subtracted during the collision calculation. If it is not subtracted, density inhomogeneities are too rapidly diffused away, as bloated particles exaggerate collision speeds. Local particle densities reach several thousand times the mid-plane gas density. We find efficient formation of gravitationally bound clumps, with a range of masses corresponding to contracted radii from 100 to 400 km when applied to the asteroid belt and 150 to 730 km when applied to the Kuiper belt, extrapolated using a constant self-gravity parameter. The smaller planetesimals are not observed at low resolution, but the masses of the largest planetesimals are relatively independent of resolution and treatment of collisions.

astro-ph.EP↗

arXiv2011

High-resolution simulations of planetesimal formation in turbulent protoplanetary discs

We present high-resolution computer simulations of dust dynamics and planetesimal formation in turbulence generated by the magnetorotational instability. We show that the turbulent viscosity associated with magnetorotational turbulence in a non-stratified shearing box increases when going from 256^3 to 512^3 grid points in the presence of a weak imposed magnetic field, yielding a turbulent viscosity of $α\approx0.003$ at high resolution. Particles representing approximately meter-sized boulders concentrate in large-scale high-pressure regions in the simulation box. The appearance of zonal flows and particle concentration in pressure bumps is relatively similar at moderate (256^3) and high (512^3) resolution. In the moderate-resolution simulation we activate particle self-gravity at a time when there is little particle concentration, in contrast with previous simulations where particle self-gravity was activated during a concentration event. We observe that bound clumps form over the next ten orbits, with initial birth masses of a few times the dwarf planet Ceres. At high resolution we activate self-gravity during a particle concentration event, leading to a burst of planetesimal formation, with clump masses ranging from a significant fraction of to several times the mass of Ceres. We present a new domain decomposition algorithm for particle-mesh schemes. Particles are spread evenly among the processors and the local gas velocity field and assigned drag forces are exchanged between a domain-decomposed mesh and discrete blocks of particles. We obtain good load balancing on up to 4096 cores even in simulations where particles sediment to the mid-plane and concentrate in pressure bumps.

astro-ph.EP↗

arXiv2010

Prograde rotation of protoplanets by accretion of pebbles in a gaseous environment

We perform hydrodynamical simulations of the accretion of pebbles and rocks onto protoplanets of a few hundred kilometres in radius, including two-way drag force coupling between particles and the protoplanetary disc gas. Particle streams interacting with the gas far out within the Hill sphere of the protoplanet spiral into a prograde circumplanetary disc. Material is accreted onto the protoplanet due to stirring by the turbulent surroundings. We speculate that the trend for prograde rotation among the largest asteroids is primordial and that protoplanets accreted 10%-50% of their mass from pebbles and rocks during the gaseous solar nebula phase. Our model also offers a possible explanation for the narrow range of spin periods observed among the largest bodies in the asteroid and trans-Neptunian belts, and predicts that 1000 km-scale Kuiper belt objects that have not experienced giant impacts should preferentially spin in the prograde direction.

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arXiv2009

Particle Clumping and Planetesimal Formation Depend Strongly on Metallicity

We present three-dimensional numerical simulations of particle clumping and planetesimal formation in protoplanetary disks with varying amounts of solid material. As centimeter-size pebbles settle to the mid-plane, turbulence develops through vertical shearing and streaming instabilities. We find that when the pebble-to-gas column density ratio is 0.01, corresponding roughly to solar metallicity, clumping is weak, so the pebble density rarely exceeds the gas density. Doubling the column density ratio leads to a dramatic increase in clumping, with characteristic particle densities more than ten times the gas density and maximum densities reaching several thousand times the gas density. This is consistent with unstratified simulations of the streaming instability that show strong clumping in particle dominated flows. The clumps readily contract gravitationally into interacting planetesimals of order 100 km in radius. Our results suggest that the correlation between host star metallicity and exoplanets may reflect the early stages of planet formation. We further speculate that initially low metallicity disks can be particle enriched during the gas dispersal phase, leading to a late burst of planetesimal formation.

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arXiv2009

The role of magnetic fields for planetary formation

The role of magnetic fields for the formation of planets is reviewed. Protoplanetary disc turbulence driven by the magnetorotational instability has a huge influence on the early stages of planet formation. Small dust grains are transported both vertically and radially in the disc by turbulent diffusion, counteracting sedimentation to the mid-plane and transporting crystalline material from the hot inner disc to the outer parts. The conclusion from recent efforts to measure the turbulent diffusion coefficient of magnetorotational turbulence is that turbulent diffusion of small particles is much stronger than naively thought. Larger particles -- pebbles, rocks and boulders -- get trapped in long-lived high pressure regions that arise spontaneously at large scales in the turbulent flow. These gas high pressures, in geostrophic balance with a sub-Keplerian/super-Keplerian zonal flow envelope, are excited by radial fluctuations in the Maxwell stress. The coherence time of the Maxwell stress is only a few orbits, where as the correlation time of the pressure bumps is comparable to the turbulent mixing time-scale, many tens or orbits on scales much greater than one scale height. The particle overdensities contract under the combined gravity of all the particles and condense into gravitationally bound clusters of rocks and boulders. These planetesimals have masses comparable to the dwarf planet Ceres. I conclude with thoughts on future priorities in the field of planet formation in turbulent discs.

astro-ph.EP↗

arXiv2009

Zonal Flows and Long-Lived Axisymmetric Pressure Bumps in Magnetorotational Turbulence

We study the behavior of magnetorotational turbulence in shearing box simulations with a radial and azimuthal extent up to ten scale heights. Maxwell and Reynolds stresses are found to increase by more than a factor two when increasing the box size beyond two scale heights in the radial direction. Further increase of the box size has little or no effect on the statistical properties of the turbulence. An inverse cascade excites magnetic field structures at the largest scales of the box. The corresponding 10% variation in the Maxwell stress launches a zonal flow of alternating sub- and super-Keplerian velocity. This in turn generates a banded density structure in geostrophic balance between pressure and Coriolis forces. We present a simplified model for the appearance of zonal flows, in which stochastic forcing by the magnetic tension on short time-scales creates zonal flow structures with life-times of several tens of orbits. We experiment with various improved shearing box algorithms to reduce the numerical diffusivity introduced by the supersonic shear flow. While a standard finite difference advection scheme shows signs of a suppression of turbulent activity near the edges of the box, this problem is eliminated by a new method where the Keplerian shear advection is advanced in time by interpolation in Fourier space.

astro-ph↗

arXiv2008

High accretion rates in magnetised Keplerian discs mediated by a Parker instability driven dynamo

Hydromagnetic stresses in accretion discs have been the subject of intense theoretical research over the past one and a half decades. Most of the disc simulations have assumed a small initial magnetic field and studied the turbulence that arises from the magnetorotational instability. However, gaseous discs in galactic nuclei and in some binary systems are likely to have significant initial magnetisation. Motivated by this, we performed ideal magnetohydrodynamic simulations of strongly magnetised, vertically stratified discs in a Keplerian potential. Our initial equilibrium configuration, which has an azimuthal magnetic field in equipartion with thermal pressure, is unstable to the Parker instability. This leads to the expelling of magnetic field arcs, anchored in the midplane of the disc, to around five scale heights from the midplane. Transition to turbulence happens primarily through magnetorotational instability in the resulting vertical fields, although magnetorotational shear instability in the unperturbed azimuthal field plays a significant role as well, especially in the midplane where buoyancy is weak. High magnetic and hydrodynamical stresses arise, yielding an effective $α$-value of around 0.1 in our highest resolution run. Azimuthal magnetic field expelled by magnetic buoyancy from the disc is continuously replenished by the stretching of a radial field created as gas parcels slide in the linear gravity field along inclined magnetic field lines. This dynamo process, where the bending of field lines by the Parker instability leads to re-creation of the azimuthal field, implies that highly magnetised discs are astrophysically viable and that they have high accretion rates.

astro-ph↗

arXiv2008

A coagulation-fragmentation model for the turbulent growth and destruction of preplanetesimals

To treat the problem of growing protoplanetary disc solids across the meter barrier, we consider a very simplified two-component coagulation-fragmentation model that consists of macroscopic boulders and smaller dust grains, the latter being the result of catastrophic collisions between the boulders. Boulders in turn increase their radii by sweeping up the dust fragments. An analytical solution to the dynamical equations predicts that growth by coagulation-fragmentation can be efficient and allow agglomeration of 10-meter-sized objects within the time-scale of the radial drift. These results are supported by computer simulations of the motion of boulders and fragments in 3-D time-dependent magnetorotational turbulence. Allowing however the fragments to diffuse freely out of the sedimentary layer of boulders reduces the density of both boulders and fragments in the mid-plane, and thus also the growth of the boulder radius, drastically. The reason is that the turbulent diffusion time-scale is so much shorter than the collisional time-scale that dust fragments leak out of the mid-plane layer before they can be swept up by the boulders there. Our conclusion that coagulation-fragmentation is not an efficient way to grow across the meter barrier in fully turbulent protoplanetary discs confirms recent results by Brauer, Dullemond, & Henning who solved the coagulation equation in a parameterised turbulence model with collisional fragmentation, cratering, radial drift, and a range of particle sizes. We find that a relatively small population of boulders in a sedimentary mid-plane layer can populate the entire vertical extent of the disc with small grains and that these grains are not first generation dust, but have been through several agglomeration-destruction cycles during the simulations.

astro-ph↗

arXiv2007

Planetesimal Formation with Particle Feedback

Proposed mechanisms for the formation of km-sized solid planetesimals face long-standing difficulties. Robust sticking mechanisms that would produce planetesimals by coagulation alone remain elusive. The gravitational collapse of smaller solids into planetesimals is opposed by stirring from turbulent gas. This proceeding describes recent works showing that "particle feedback," the back-reaction of drag forces on the gas in protoplanetary disks, promotes particle clumping as seeds for gravitational collapse. The idealized streaming instability demonstrates the basic ability of feedback to generate particle overdensities. More detailed numerical simulations show that the particle overdensities produced in turbulent flows trigger gravitational collapse to planetesimals. We discuss surprising aspects of this work, including the large (super-Ceres) mass of the collapsing bound cluster, and the finding that MHD turbulence aids gravitational collapse.

astro-ph↗

arXiv2007

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

This document contains refereed supplementary information for the paper ``Rapid planetesimal formation in turbulent circumstellar discs''. It contains 15 sections (\S1.1 -- \S1.15) that address a number of subjects related to the main paper. 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 (\S1.3). Dissipative collisions remove energy from the motion of the particles by collisional cooling (\S1.4), an effect that allows gravitational collapse to occur in somewhat less massive discs (\S1.7). A resolution study of the gravitational collapse of the boulders is presented in \S1.6. 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 \S1.10 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. \S11 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 \S1.12 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.

astro-ph↗

arXiv2007

Rapid planetesimal formation in turbulent circumstellar discs

The initial stages of planet formation in circumstellar gas discs proceed via dust grains that collide and build up larger and larger bodies (Safronov 1969). How this process continues from metre-sized boulders to kilometre-scale planetesimals is a major unsolved problem (Dominik et al. 2007): boulders stick together poorly (Benz 2000), and spiral into the protostar in a few hundred orbits due to a head wind from the slower rotating gas (Weidenschilling 1977). Gravitational collapse of the solid component has been suggested to overcome this barrier (Safronov 1969, Goldreich & Ward 1973, Youdin & Shu 2002). Even low levels of turbulence, however, inhibit sedimentation of solids to a sufficiently dense midplane layer (Weidenschilling & Cuzzi 1993, Dominik et al. 2007), but turbulence must be present to explain observed gas accretion in protostellar discs (Hartmann 1998). 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 (Johansen, Klahr, & Henning 2006), and these concentrations are augmented a further order of magnitude by a streaming instability (Youdin & Goodman 2005, Johansen, Henning, & Klahr 2006, Johansen & Youdin 2007) driven by the relative flow of gas and solids. We find that gravitationally bound clusters form with masses comparable to dwarf planets and containing a distribution of boulder sizes. Gravitational collapse happens much faster than radial drift, offering a possible path to planetesimal formation in accreting circumstellar discs.

astro-ph↗

arXiv2007

Protoplanetary Disk Turbulence Driven by the Streaming Instability: Linear Evolution and Numerical Methods

We present local simulations that verify the linear streaming instability that arises from aerodynamic coupling between solids and gas in protoplanetary disks. This robust instability creates enhancements in the particle density in order to tap the free energy of the relative drift between solids and gas, generated by the radial pressure gradient of the disk. We confirm the analytic growth rates found by Youdin & Goodman (2005) using grid hydrodynamics to simulate the gas and, alternatively, particle and grid representations of the solids. Since the analytic derivation approximates particles as a fluid, this work corroborates the streaming instability when solids are treated as particles. The idealized physical conditions -- axisymmetry, uniform particle size, and the neglect of vertical stratification and collisions -- provide a rigorous, well-defined test of any numerical algorithm for coupled particle-gas dynamics in protoplanetary disks. We describe a numerical particle-mesh implementation of the drag force, which is crucial for resolving the coupled oscillations. Finally we comment on the balance of energy and angular momentum in two-component disks with frictional coupling. A companion paper details the non-linear evolution of the streaming instability into saturated turbulence with dense particle clumps.

astro-ph↗

arXiv2007

Protoplanetary Disk Turbulence Driven by the Streaming Instability: Non-Linear Saturation and Particle Concentration

We present simulations of the non-linear evolution of streaming instabilities in protoplanetary disks. The two components of the disk, gas treated with grid hydrodynamics and solids treated as superparticles, are mutually coupled by drag forces. We find that the initially laminar equilibrium flow spontaneously develops into turbulence in our unstratified local model. Marginally coupled solids (that couple to the gas on a Keplerian time-scale) trigger an upward cascade to large particle clumps with peak overdensities above 100. The clumps evolve dynamically by losing material downstream to the radial drift flow while receiving recycled material from upstream. Smaller, more tightly coupled solids produce weaker turbulence with more transient overdensities on smaller length scales. The net inward radial drift is decreased for marginally coupled particles, whereas the tightly coupled particles migrate faster in the saturated turbulent state. The turbulent diffusion of solid particles, measured by their random walk, depends strongly on their stopping time and on the solids-to-gas ratio of the background state, but diffusion is generally modest, particularly for tightly coupled solids. Angular momentum transport is too weak and of the wrong sign to influence stellar accretion. Self-gravity and collisions will be needed to determine the relevance of particle overdensities for planetesimal formation.

astro-ph↗

arXiv2006

Turbulent diffusion in protoplanetary discs: the effect of an imposed magnetic field

We study the effect of an imposed vertical magnetic field on the turbulent mass diffusion properties of magnetorotational turbulence in protoplanetary discs. It is well-known that the effective viscosity generated by the turbulence depends strongly on the magnitude of such an external field. In this letter we show that the turbulent diffusion of the flow also grows, but that the diffusion coefficient does not rise with increasing vertical field as fast as the viscosity does. The vertical Schmidt number, i.e. the ratio between viscosity and vertical diffusion, can be close to 20 for high field magnitudes, whereas the radial Schmidt number is increased from below unity to around 3.5. Our results may have consequences for the interpretation of observations of dust in protoplanetary discs and for chemical evolution modelling of these discs.

astro-ph↗

arXiv2006

Comment on A.-L. Barabasi, Nature 435 207-211 (2005)

The purpose of this communication is twofold. First, it clarifies the origin of the power law obtained in the computer simulations presented in A.-L. Barabasi, Nature 435 207-211 (2005) as well as presenting a statistically more sound analysis of the experimental email data used in that paper and in [4]. The second purpose is to clarify the origin of the the suggestion of power law probability distribution for the response times of humans presented with a piece of new information either as a news event or through the reception of an email.

physics.soc-ph↗

arXiv2006

Dust sedimentation and self-sustained Kelvin-Helmholtz turbulence in protoplanetary disk mid-planes. I. Radially symmetric simulations

We perform numerical simulations of the Kelvin-Helmholtz instability in the mid-plane of a protoplanetary disk. A two-dimensional corotating slice in the azimuthal--vertical plane of the disk is considered where we include the Coriolis force and the radial advection of the Keplerian rotation flow. Dust grains, treated as individual particles, move under the influence of friction with the gas, while the gas is treated as a compressible fluid. The friction force from the dust grains on the gas leads to a vertical shear in the gas rotation velocity. As the particles settle around the mid-plane due to gravity, the shear increases, and eventually the flow becomes unstable to the Kelvin-Helmholtz instability. The Kelvin-Helmholtz turbulence saturates when the vertical settling of the dust is balanced by the turbulent diffusion away from the mid-plane. The azimuthally averaged state of the self-sustained Kelvin-Helmholtz turbulence is found to have a constant Richardson number in the region around the mid-plane where the dust-to-gas ratio is significant. Nevertheless the dust density has a strong non-axisymmetric component. We identify a powerful clumping mechanism, caused by the dependence of the rotation velocity of the dust grains on the dust-to-gas ratio, as the source of the non-axisymmetry. Our simulations confirm recent findings that the critical Richardson number for Kelvin-Helmholtz instability is around unity or larger, rather than the classical value of 1/4

astro-ph↗

arXiv2005

Gravoturbulent formation of planetesimals

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.

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