Anders Johansen

Lund University, Lund, Skåne, Sweden

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Publications (46)207.24 Total impact

  • Michiel Lambrechts, Anders Johansen
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    ABSTRACT: The formation of planetary cores must proceed rapidly in order for the giant planets to accrete their gaseous envelopes before the dissipation of the protoplanetary gas disc (<3 Myr). In orbits beyond 10 AU, direct accumulation of planetesimals by the cores is too slow. Fragments of planetesimals could be accreted faster, but planetesimals are likely too large for fragmentation to be efficient, and resonant trapping poses a further hurdle. Here we instead investigate the accretion of small pebbles (mm-cm sizes) that are the natural outcome of an equilibrium between the growth and radial drift of particles. We construct a simplified analytical model of dust coagulation and pebble drift in the outer disc, between 5 AU and 100 AU, which gives the temporal evolution of the solid surface density and the dominant particle size. These two key quantities determine how core growth proceeds at various orbital distances. We find that pebble surface densities are sufficiently high to achieve the inside-out formation of planetary cores within the disc lifetime. The overall efficiency by which dust gets converted to planets can be high, close to 50 % for planetary architectures similar to the Solar System. Growth by pebble accretion in the outer disc is sufficiently fast to overcome catastrophic Type I migration of the cores. These results require protoplanetary discs with large radial extent (~100 AU) and assume a low number of initial seed embryos. Our findings imply that protoplanetary discs with low disc masses, as expected around low-mass stars (<1 M_sun), or with sub-solar dust-to-gas ratios, do not easily form gas-giant planets (M > 100 M_E), but preferentially form Neptune-mass planets or smaller (< 10 M_E). This is consistent with exoplanet surveys which show that gas giants are relatively uncommon around stars of low mass or low metallicity.
    08/2014;
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    ABSTRACT: In the Solar System giant planets come in two flavours: 'gas giants' (Jupiter and Saturn) with massive gas envelopes and 'ice giants' (Uranus and Neptune) with much thinner envelopes around their cores. It is poorly understood how these two classes of planets formed. High solid accretion rates, necessary to form the cores of giant planets within the life-time of protoplanetary discs, heat the envelope and prevent rapid gas contraction onto the core, unless accretion is halted. We find that, in fact, accretion of pebbles (~ cm-sized particles) is self-limiting: when a core becomes massive enough it carves a gap in the pebble disc. This halt in pebble accretion subsequently triggers the rapid collapse of the super-critical gas envelope. As opposed to gas giants, ice giants do not reach this threshold mass and can only bind low-mass envelopes that are highly enriched by water vapour from sublimated icy pebbles. This offers an explanation for the compositional difference between gas giants and ice giants in the Solar System. Furthermore, as opposed to planetesimal-driven accretion scenarios, our model allows core formation and envelope attraction within disc life-times, provided that solids in protoplanetary discs are predominantly in pebbles. Our results imply that the outer regions of planetary systems, where the mass required to halt pebble accretion is large, are dominated by ice giants and that gas-giant exoplanets in wide orbits are enriched by more than 50 Earth masses of solids.
    08/2014;
  • Karsten Dittrich, Hubert Klahr, Anders Johansen
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    ABSTRACT: Recent simulations show long -lived sub- and super-Keplerian flows in protoplanetary disks. These so-called zonal flows are found in local as well as global simulations of magneto-rotationally unstable disks. We investigate the strength and life-time of the resulting long-lived gas over- and under-densities as well as particle concentrations function of the azimuthal and radial size of the local shearing box. Changes in the azimuthal extent do not affect the zonal flow features. However, strength and life-time of zonal flows increase with increasing radial box sizes. Our simulations show indications, and support earlier results, that zonal flows have a natural length scale of approximately 5 pressure scale heights. For the first time, the reaction of dust particles in boxes with zonal flows are studied. We show that particles of some centimeters in size reach a hundred-fold higher density than initially, without any self-gravitating forces acting on the point masses. We further investigate collision velocities of dust grains in a turbulent medium.
    03/2014;
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    ABSTRACT: Accumulation of dust and ice particles into planetesimals is an important step in the planet formation process. Planetesimals are the seeds of both terrestrial planets and the solid cores of gas and ice giants forming by core accretion. Left-over planetesimals in the form of asteroids, trans-Neptunian objects and comets provide a unique record of the physical conditions in the solar nebula. Debris from planetesimal collisions around other stars signposts that the planetesimal formation process, and hence planet formation, is ubiquitous in the Galaxy. The planetesimal formation stage extends from micrometer-sized dust and ice to bodies which can undergo run-away accretion. The latter ranges in size from 1 km to 1000 km, dependent on the planetesimal eccentricity excited by turbulent gas density fluctuations. Particles face many barriers during this growth, arising mainly from inefficient sticking, fragmentation and radial drift. Two promising growth pathways are mass transfer, where small aggregates transfer up to 50% of their mass in high-speed collisions with much larger targets, and fluffy growth, where aggregate cross sections and sticking probabilities are enhanced by a low internal density. A wide range of particle sizes, from mm to 10 m, concentrate in the turbulent gas flow. Overdense filaments fragment gravitationally into bound particle clumps, with most mass entering planetesimals of contracted radii from 100 to 500 km, depending on local disc properties. We propose a hybrid model for planetesimal formation where particle growth starts unaided by self-gravity but later proceeds inside gravitationally collapsing pebble clumps to form planetesimals with a wide range of sizes.
    02/2014;
  • Katrin Ros, A. Johansen
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    ABSTRACT: Particle growth to pebble-sizes is an important first step towards the formation of planets, but dust coagulation models and experiments show that growth by collisions of rocky particles becomes inefficient at millimeter-sizes. However, close to ice lines growth can proceed both by condensation and via collisions involving sticky ice particles. We have developed a dynamical model of condensation and sublimation at the water ice line and find rapid growth from millimeters to several centimeters on a time scale of 10 000 years in turbulent protoplanetary discs. Small ice grains are coupled to the gas via drag forces and move in a turbulent diffusion, modelled as a random walk. Some of these particles diffuse either inwards or upwards from the outer, cold midplane region and sublimate. The resulting vapour recondenses onto already existing particles, leading to growing pebbles that decouple from the turbulent eddies and sediment towards the cold midplane. We model condensation and sublimation in a Monte Carlo scheme, and ignore collisions. We find resulting particles that are large enough to grow further into planetesimals and planets through dynamical instabilities, such as the streaming instability, and through pebble accretion.
    10/2013;
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    ABSTRACT: In the core accretion scenario a giant planet forms by the accretion of a gaseous envelope onto a solid core. The accumulation of solid material needs to be completed before dissipation of the protoplanetary disc within approximately 3 Myr. Forming these cores with planetesimal collisions within the available time is challenging at wide orbital distances beyond 10 AU. However, recently we found that core growth by the accretion of pebbles, particles of approximately cm sizes, is sufficiently rapid to explain the in situ formation of wide orbit giant planets. In this talk, we show how fast pebble accretion and the associated high luminosity influences the composition of giant planets. We find that gas giants naturally form in regions behind the ice line, while at even wider orbital distances we naturally form planets with an ice giant composition.
    10/2013;
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    Katrin Ros, Anders Johansen
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    ABSTRACT: We show that condensation is an efficient particle growth mechanism, leading to growth beyond decimeter-sized pebbles close to an ice line in protoplanetary discs. As coagulation of dust particles is frustrated by bouncing and fragmentation, condensation could be a complementary, or even dominant, growth mode in the early stages of planet formation. Ice particles diffuse across the ice line and sublimate, and vapour diffusing back across the ice line recondenses onto already existing particles, causing them to grow. We develop a numerical model of the dynamical behaviour of ice particles close to the water ice line, approximately 3 AU from the host star. Particles move with the turbulent gas, modelled as a random walk. They also sediment towards the midplane and drift radially towards the central star. Condensation and sublimation are calculated using a Monte Carlo approach. Our results indicate that, with a turbulent alpha-value of 0.01, growth from millimeter to at least decimeter-sized pebbles is possible on a time scale of 1000 years. We find that particle growth is dominated by ice and vapour transport across the radial ice line, with growth due to transport across the atmospheric ice line being negligible. Ice particles mix outwards by turbulent diffusion, leading to net growth across the entire cold region. The resulting particles are large enough to be sensitive to concentration by streaming instabilities, and in pressure bumps and vortices, which can cause further growth into planetesimals. In our model, particles are considered to be homogeneous ice particles. Taking into account the more realistic composition of ice condensed onto rocky ice nuclei might affect the growth time scales, by release of refractory ice nuclei after sublimation. We also ignore sticking and fragmentation in particle collisions. These effects will be the subject of future investigations.
    Astronomy and Astrophysics 02/2013; · 5.08 Impact Factor
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    Karsten Dittrich, Hubert Klahr, Anders Johansen
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    ABSTRACT: Recent numerical simulations have shown long-lived axisymmetric sub- and super-Keplerian flows in protoplanetary disks. These zonal flows are found in local as well as global simulations of disks unstable to the magnetorotational instability. This paper covers our study of the strength and lifetime of zonal flows and the resulting long-lived gas over- and underdensities as functions of the azimuthal and radial size of the local shearing box. We further investigate dust particle concentrations without feedback on the gas and without self-gravity. Strength and lifetime of zonal flows increase with the radial extent of the simulation box, but decrease with the azimuthal box size. Our simulations support earlier results that zonal flows have a natural radial length scale of 5-7 gas pressure scale heights. This is the first study that combines three-dimensional MHD simulations of zonal flows and dust particles feeling the gas pressure. The pressure bumps trap particles with $\textrm{St} = 1$ very efficiently. We show that $\textrm{St} = 0.1$ particles (of some centimeters in size if at $5\textrm{AU}$ in an MMSN) reach a hundred-fold higher density than initially. This opens the path for particles of $\textrm{St} = 0.1$ and dust-to-gas ratio of 0.01 or for particles of $\textrm{St} \geq 0.5$ and dust-to-gas ratio $10^{-4}$ to still reach densities that potentially trigger the streaming instability and thus gravoturbulent formation of planetesimals.
    The Astrophysical Journal 11/2012; 763(2). · 6.73 Impact Factor
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    ABSTRACT: In February 2011, the Kepler mission announced its discovery of 1,235 planet candidates, of which more than half have radii smaller than that of Neptune: RP<4R{earth}, where R{earth} plus is the Earth radius. We used reconnaissance spectra obtained by the Kepler Follow-up Observing Program (FOP) to derive metallicities for several hundred of the brighter planet candidates, and used the results to explore the relationship between planet size and host-star metallicity. (1 data file).
    VizieR Online Data Catalog. 07/2012;
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    ABSTRACT: The planet candidates discovered by the Kepler mission provide a rich sample to constrain the architectures and relative inclinations of planetary systems within approximately 0.5 AU of their host stars. We use the triple-transit systems from the Kepler 16-months data as templates for physical triple-planet systems and perform synthetic transit observations. We find that all the Kepler triple-transit and double-transit systems can be produced from the triple-planet templates, given a low mutual inclination of around five degrees. Our analysis shows that the Kepler data contains a population of planets larger than four Earth radii in single-transit systems that can not arise from the triple-planet templates. We explore the hypothesis that high-mass counterparts of the triple-transit systems underwent dynamical instability to produce a population of massive double-planet systems of moderately high mutual inclination. We perform N-body simulations of mass-boosted triple-planet systems and observe how the systems heat up and lose planets, most frequently by planet-planet collisions, yielding transits in agreement with the large planets in the Kepler single-transit systems. The resulting population of massive double-planet systems can nevertheless not explain the additional excess of low-mass planets among the observed single-transit systems and the lack of gas-giant planets in double-transit and triple-transit systems. Planetary instability of systems of triple gas-giant planets can be behind part of the dichotomy between systems hosting one or more small planets and those hosting a single giant planet. The main part of the dichotomy, however, is more likely to have arisen already during planet formation when the formation, migration or scattering of a massive planet, triggered above a threshold metallicity, suppressed the formation of other planets in sub-AU orbits.
    The Astrophysical Journal 06/2012; 758(1). · 6.73 Impact Factor
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    ABSTRACT: The abundance of heavy elements (metallicity) in the photospheres of stars similar to the Sun provides a 'fossil' record of the chemical composition of the initial protoplanetary disk. Metal-rich stars are much more likely to harbour gas giant planets, supporting the model that planets form by accumulation of dust and ice particles. Recent ground-based surveys suggest that this correlation is weakened for Neptunian-sized planets. However, how the relationship between size and metallicity extends into the regime of terrestrial-sized exoplanets is unknown. Here we report spectroscopic metallicities of the host stars of 226 small exoplanet candidates discovered by NASA's Kepler mission, including objects that are comparable in size to the terrestrial planets in the Solar System. We find that planets with radii less than four Earth radii form around host stars with a wide range of metallicities (but on average a metallicity close to that of the Sun), whereas large planets preferentially form around stars with higher metallicities. This observation suggests that terrestrial planets may be widespread in the disk of the Galaxy, with no special requirement of enhanced metallicity for their formation.
    Nature 06/2012; 486(7403):375-7. · 38.60 Impact Factor
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    Michiel Lambrechts, Anders Johansen
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    ABSTRACT: 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.
    Astronomy and Astrophysics 05/2012; · 5.08 Impact Factor
  • A. Johansen, A. N. Youdin, Y. Lithwick
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    ABSTRACT: The formation of km-sized planetesimals from smaller cm-dm sized pebbles faces major difficulties in the traditional coagulation scenario. Such particles do not stick well and very quickly drift towards the star to sublimate in the inner nebula. I will present an alternative scenario where overdense regions of particles collapse under their own gravity to form massive 1000-km-scale planetesimals. The overdensities are seeded by hydrodynamical streaming instabilities arising in the coupled motion of gas and particles. New computer simulations that include particle collisions show the perseverance of planetesimal formation by this route. Planetesimal masses are relatively independent of the computational resolution and the simulations reveal a characteristic planetesimal size that increases with distance from the sun. The resulting planetesimal sizes agree well with the observed largest bodies residing in the asteroid and Kuiper belts.
    03/2012;
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    Evghenii Gaburov, Anders Johansen, Yuri Levin
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    ABSTRACT: In this paper we report on the formation of magnetically-levitating accretion disks around supermassive black holes. The structure of these disks is calculated by numerically modelling tidal disruption of magnetized interstellar gas clouds. We find that the resulting disks are entirely supported by the pressure of the magnetic fields against the component of gravitational force directed perpendicular to the disks. The magnetic field shows ordered large-scale geometry that remains stable for the duration of our numerical experiments extending over 10% of the disk lifetime. Strong magnetic pressure allows high accretion rate and inhibits disk fragmentation. This in combination with the repeated feeding of manetized molecular clouds to a supermassive black hole yields a possible solution to the long-standing puzzle of black hole growth in the centres of galaxies.
    The Astrophysical Journal 01/2012; 758(2). · 6.73 Impact Factor
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    Anders Johansen, Andrew Youdin, Yoram Lithwick
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    ABSTRACT: 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.
    Astronomy and Astrophysics 11/2011; · 5.08 Impact Factor
  • A. Johansen, A. N. Youdin, Y. Lithwick
    LPI Contributions. 11/2011;
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    Anders Johansen, Mariko Kato, Takayoshi Sano
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    ABSTRACT: Large regions of protoplanetary discs are believed to be too weakly ionised to support magnetorotational instabilities, because abundant tiny dust grains soak up free electrons and reduce the conductivity of the gas. At the outer edge of this ``dead zone'', the ionisation fraction increases gradually and the resistivity drops until the magnetorotational instability can develop turbulence. We identify a new viscous instability which operates in the semi-turbulent transition region between ``dead'' and ``alive'' zones. The strength of the saturated turbulence depends strongly on the local resistivity in this transition region. A slight increase (decrease) in dust density leads to a slight increase (decrease) in resistivity and a slight decrease (increase) in turbulent viscosity. Such spatial variation in the turbulence strength causes a mass pile-up where the turbulence is weak, leading to a run-away process where turbulence is weakened and mass continues to pile up. The final result is the appearance of high-amplitude pressure bumps and deep pressure valleys. Here we present a local linear stability analysis of weakly ionised accretion discs and identify the linear instability responsible for the pressure bumps. A paper in preparation concerns numerical results which confirm and expand the existence of the linear instability.
    Proceedings of the International Astronomical Union 01/2011; 274:50-55.
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    Anders Johansen, Hubert Klahr
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    ABSTRACT: Planets form in circumstellar discs as dust grains collide together and form ever larger bodies. However a major bottleneck occurs for bodies with sizes around a few centimetres or larger. These rocks and boulders have very poor sticking properties and spiral into the star in a few hundred years due to friction with the slower rotating gas. A possible way to overcome this “meter-barrier” is to have local concentrations of rocks and boulders that become gravitationally unstable and contract to form planetesimals of several kilometers in size. We present the results of numerical simulations of the coupled motion of gas and rocks in protoplanetary disc mid-planes. The gas rotates slightly sub-Keplerian due to the global, radial pressure gradient of the disc, causing a net velocity difference between the gas and the solids. This relative motion is in turn unstable to streaming instabilities, and the saturated state of the turbulence is characterised by dense particle clumps that are fed by the radial drift of isolated rocks. For realistic protoplanetary disc parameters the clumps are gravitationally unstable and contract on the time-scale of a few orbits to form bodies of several hundred kilometers in size. Magnetic fields may further augment the particle concentrations due to relatively long-lived high pressure bumps that form in magnetorotational turbulence. However, magnetic fields are not crucial to the gravoturbulent formation of planetesimals, rather magnetised turbulence allows collapse to occur for flows that are on the average less affected by the particles, i.e. for lower particle column densities. KeywordsDiffusion–Hydrodynamics–Instabilities–Planetary systems: protoplanetary disks–Solar system: formation–Turbulence
    Earth Moon and Planets 01/2011; 108(1):39-43. · 0.83 Impact Factor
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    Anders Johansen, Hubert Klahr, Thomas Henning
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    ABSTRACT: 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 $\alpha\approx0.003$ 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.
    Astronomy and Astrophysics 10/2010; 276. · 5.08 Impact Factor
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    Anders Johansen, Pedro Lacerda
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    ABSTRACT: 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. Comment: Accepted for publication in MNRAS. Minor changes in response to referee report, general language changes throughout the paper
    Monthly Notices of the Royal Astronomical Society 10/2009; · 5.52 Impact Factor

Publication Stats

972 Citations
207.24 Total Impact Points

Institutions

  • 2010–2012
    • Lund University
      • Department of Astronomy and Theoretical Physics
      Lund, Skåne, Sweden
  • 2008–2011
    • Leiden University
      • Leiden Observartory
      Leiden, South Holland, Netherlands
  • 2007
    • American Museum of Natural History
      New York City, New York, United States
    • Universität Heidelberg
      Heidelburg, Baden-Württemberg, Germany
  • 2005–2007
    • Max Planck Institute for Astronomy
      Heidelburg, Baden-Württemberg, Germany