Concentrating small particles in protoplanetary disks through the streaming instability
TL;DR: In this article, a numerical algorithm for stiff mutual drag force was used to simulate small particles with significantly higher resolutions and longer simulation times than in previous investigations, and it was shown that particles of dimensionless stopping time τs = 10-2 and 10-3 -representing cm and mm-sized particles interior of the water ice line - concentrate themselves via the streaming instability at a solid abundance of a few percent.
Abstract: Laboratory experiments indicate that direct growth of silicate grains via mutual collisions can only produce particles up to roughly millimeters in size. On the other hand, recent simulations of the streaming instability have shown that mm/cm-sized particles require an excessively high metallicity for dense filaments to emerge. Using a numerical algorithm for stiff mutual drag force, we perform simulations of small particles with significantly higher resolutions and longer simulation times than in previous investigations. We find that particles of dimensionless stopping time τs = 10-2 and 10-3 - representing cm- and mm-sized particles interior of the water ice line - concentrate themselves via the streaming instability at a solid abundance of a few percent. We thus revise a previously published critical solid abundance curve for the regime of τs ≪ 1. The solid density in the concentrated regions reaches values higher than the Roche density, indicating that direct collapse of particles down to mm sizes into planetesimals is possible. Our results hence bridge the gap in particle size between direct dust growth limited by bouncing and the streaming instability. (Less)
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TL;DR: In this paper, the authors test the importance of the water snow line in triggering the formation of the first planetesimals during the gas-rich phase of a protoplanetary disk, when cores of giant planets have to form.
Abstract: Context. The formation stage of planetesimals represents a major gap in our understanding of the planet formation process. Late-stage planet accretion models typically make arbitrary assumptions about planetesimal and pebble distribution, while dust evolution models predict that planetesimal formation is only possible at some orbital distances.
Aims. We wish to test the importance of the water snow line in triggering the formation of the first planetesimals during the gas-rich phase of a protoplanetary disk, when cores of giant planets have to form.
Methods. We connected prescriptions for gas disk evolution, dust growth and fragmentation, water ice evaporation and recondensation, the transport of both solids and water vapor, and planetesimal formation via streaming instability into a single one-dimensional model for protoplanetary disk evolution.
Results. We find that processes taking place around the snow line facilitate planetesimal formation in two ways. First, because the sticking properties between wet and dry aggregates change, a “traffic jam” inside of the snow line slows the fall of solids onto the star. Second, ice evaporation and outward diffusion of water followed by its recondensation increases the abundance of icy pebbles that trigger planetesimal formation via streaming instability just outside of the snow line.
Conclusions. Planetesimal formation is hindered by growth barriers and radial drift and thus requires particular conditions to take place. The snow line is a favorable location where planetesimal formation is possible for a wide range of conditions, but not in every protoplanetary disk model, however. This process is particularly promoted in large cool disks with low intrinsic turbulence and an increased initial dust-to-gas ratio.
249 citations
TL;DR: The importance of the water snow line for the formation of the first planetesimals during the gas-rich phase of the protoplanetary disk has been investigated in this article, where the authors connect prescriptions for gas disk evolution, dust growth and fragmentation, water ice evaporation and recondensation, as well as transport of both solids and water vapor, and planetesimal formation via streaming instability into a single, one-dimensional model.
Abstract: Planetesimal formation stage represents a major gap in our understanding of the planet formation process. The late-stage planet accretion models typically make arbitrary assumptions about planetesimals and pebbles distribution while the dust evolution models predict that planetesimal formation is only possible at some orbital distances. We want to test the importance of water snow line for triggering formation of the first planetesimals during the gas-rich phase of protoplanetary disk, when cores of giant planets have to form. We connect prescriptions for gas disk evolution, dust growth and fragmentation, water ice evaporation and recondensation, as well as transport of both solids and water vapor, and planetesimal formation via streaming instability into a single, one-dimensional model for protoplanetary disk evolution. We find that processes taking place around the snow line facilitate planetesimal formation in two ways. First, due to the change of sticking properties between wet and dry aggregates, there is a "traffic jam" inside of the snow line that slows down the fall of solids onto the star. Second, ice evaporation and outward diffusion of water followed by its recondensation increases the abundance of icy pebbles that trigger planetesimal formation via streaming instability just outside of the snow line. Planetesimal formation is hindered by growth barriers and radial drift and thus requires particular conditions to take place. Snow line is a favorable location where planetesimal formation is possible for a wide range of conditions, but still not in every protoplanetary disk model. This process is particularly promoted in large, cool disks with low intrinsic turbulence and increased initial dust-to-gas ratio.
210 citations
TL;DR: In this article, a model for the formation and orbital architecture of the TRAPPIST-1 system is presented, where pebble-sized particles whose origin is the outer disk accumulate to trigger streaming instabilities.
Abstract: TRAPPIST-1 is a nearby 0.08 M ⊙ M-star that was recently found to harbor a planetary system of at least seven Earth-sized planets, all within 0.1 au. The configuration confounds theorists as the planets are not easily explained by either in situ or migration models. In this paper we present a scenario for the formation and orbital architecture of the TRAPPIST-1 system. In our model, planet formation starts at the H2 O iceline, where pebble-sized particles whose origin is the outer disk accumulate to trigger streaming instabilities. After their formation, planetary embryos quickly mature by pebble accretion. Planet growth stalls at Earth masses, where the planet’s gravitational feedback on the disk keeps pebbles at bay. Planets are transported by type I migration to the inner disk, where they stall at the magnetospheric cavity and end up in mean motion resonances. During disk dispersal, the cavity radius expands and the innermost planets escape resonance. We argue that the model outlined here can also be applied to other compact systems and that the many close-in super-Earth systems are a scaled-up version of TRAPPIST-1. We also hypothesize that few close-in compact systems harbor giant planets at large distances, since they would have stopped the pebble flux from the outer disk.
155 citations
TL;DR: In this article, a model for gas-assisted pebble accretion and disk-planet tidal interaction was proposed to study the formation of super-Earth systems, and it was shown that up to 95% of resonant chains become dynamically unstable after the gas disk dispersal, leading to a phase of late collisions that breaks the original resonant configurations.
Abstract: At least 30\% of main sequence stars host planets with sizes of between 1 and 4 Earth radii and orbital periods of less than 100 days. We use N-body simulations including a model for gas-assisted pebble accretion and disk--planet tidal interaction to study the formation of super-Earth systems. We show that the integrated pebble mass reservoir creates a bifurcation between hot super-Earths or hot-Neptunes ($\lesssim15M_{\oplus}$) and super-massive planetary cores potentially able to become gas giant planets ($\gtrsim15M_{\oplus}$). Simulations with moderate pebble fluxes grow multiple super-Earth-mass planets that migrate inwards and pile up at the inner edge of the disk forming long resonant chains. We follow the long-term dynamical evolution of these systems and use the period ratio distribution of observed planet-pairs to constrain our model. Up to $\sim$95\% of resonant chains become dynamically unstable after the gas disk dispersal, leading to a phase of late collisions that breaks the original resonant configurations. Our simulations naturally match observations when they produce a dominant fraction ($\gtrsim95\%$) of unstable systems with a sprinkling ($\lesssim5\%$) of stable resonant chains (the Trappist-1 system represents one such example). Our results demonstrate that super-Earth systems are inherently multiple (${\rm N\geq2}$) and that the observed excess of single-planet transits is a consequence of the mutual inclinations excited by the planet--planet instability. In simulations in which planetary seeds are initially distributed in the inner and outer disk, close-in super-Earths (abridged).
114 citations
TL;DR: In this paper, the authors show evidence that Kuiper belt planetesimals formed by the streaming instability, a process in which aerodynamically concentrated clumps of pebbles gravitationally collapse into 100kilometre-class bodies.
Abstract: A critical step toward the emergence of planets in a protoplanetary disk is the accretion of planetesimals, bodies 1–1,000 km in size, from smaller disk constituents. This process is poorly understood, partly because we lack good observational constraints on the complex physical processes that contribute to planetesimal formation1. In the outer Solar System, the best place to look for clues is the Kuiper belt, where icy planetesimals survive to this day. Here we report evidence that Kuiper belt planetesimals formed by the streaming instability, a process in which aerodynamically concentrated clumps of pebbles gravitationally collapse into 100-kilometre-class bodies2. Gravitational collapse has previously been suggested to explain the ubiquity of equal-sized binaries in the Kuiper belt3–5. We analyse new hydrodynamical simulations of the streaming instability to determine the model expectations for the spatial orientation of binary orbits. The predicted broad inclination distribution with approximately 80% of prograde binary orbits matches the observations of trans-Neptunian binaries6. The formation models that imply predominantly retrograde binary orbits (for example, ref. 7) can be ruled out. Given its applicability over a wide range of protoplanetary disk conditions8, it is expected that the streaming instability also seeded planetesimal formation elsewhere in the Solar System, and beyond. The predominantly prograde orientation and broad inclination distribution of trans-Neptunian binary objects is reproduced by a three-dimensional hydrodynamical simulation of planetesimal formation driven by the streaming instability, showing evidence of the activation of the streaming instability in the solar protoplanetary disk.
109 citations
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01 Jan 1966TL;DR: In this paper, a simulation program for particle-mesh force calculation is presented, based on a one-dimensional plasma model and a collisionless particle model, which is used to simulate collisionless particle models.
Abstract: Computer experiments using particle models A one-dimensional plasma model The simulation program Time integration schemes The particle-mesh force calculation The solution of field equations Collisionless particle models Particle-particle/particle-mesh algorithms Plasma simulation Semiconductor device simulation Astrophysics Solids, liquids and phase changes Fourier transforms Fourier series and finite Fourier transforms Bibliography Index
6,376 citations
2,001 citations
"Concentrating small particles in pr..." refers background in this paper
...The gas interacts with each of the particles via their mutual drag force, which is characterized by the stopping time ts (Whipple 1972; Weidenschilling 1977a) or its dimensionless counterpart τs ≡ ΩKts (Youdin & Goodman 2005)....
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...For example, the timescale for the radial drift of meter-sized boulders at ∼1 au of the minimum-mass solar nebula (MMSN; Weidenschilling 1977b; Hayashi 1981) is ∼100 yr, significantly shorter than the typical lifetime of protoplanetary disks....
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...Solid particles marginally coupled to the gas via drag force drift radially inwards and are quickly removed from protoplanetary disks due to the gaseous head wind (Adachi et al. 1976; Weidenschilling 1977a)....
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1,928 citations
"Concentrating small particles in pr..." refers background in this paper
...For example, the timescale for the radial drift of meter-sized boulders at ∼1 au of the minimum-mass solar nebula (MMSN; Weidenschilling 1977b; Hayashi 1981) is ∼100 yr, significantly shorter than the typical lifetime of protoplanetary disks....
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TL;DR: In this paper, the authors report the results of the first sensitive L-band survey of the intermediate-age (2.5-30 Myr) clusters NGC 2264, NGC 2362, and NGC 1960.
Abstract: We report the results of the first sensitive L-band survey of the intermediate-age (2.5-30 Myr) clusters NGC 2264, NGC 2362, and NGC 1960. We use JHKL colors to obtain a census of the circumstellar disk fractions in each cluster. We find disk fractions of 52% ± 10%, 12% ± 4%, and 3% ± 3% for the three clusters, respectively. Together with our previously published JHKL investigations of the younger NGC 2024, Trapezium, and IC 348 clusters, we have completed the first systematic and homogeneous survey for circumstellar disks in a sample of young clusters that both span a significant range in age (0.3-30 Myr) and contain statistically significant numbers of stars whose masses span nearly the entire stellar mass spectrum. Analysis of the combined survey indicates that the cluster disk fraction is initially very high (≥80%) and rapidly decreases with increasing cluster age, such that one-half the stars within the clusters lose their disks in 3 Myr. Moreover, these observations yield an overall disk lifetime of ~6 Myr in the surveyed cluster sample. This is the timescale for essentially all the stars in a cluster to lose their disks. This should set a meaningful constraint for the planet-building timescale in stellar clusters. The implications of these results for current theories of planet formation are briefly discussed.
1,886 citations
"Concentrating small particles in pr..." refers background in this paper
...This process of growing planetary cores covers more than 30 orders of magnitude in mass and more than 13 orders of magnitude in size, required to be completed within the 1–5 Myr lifetime of their natal protoplanetary disks (e.g., Haisch et al. 2001; Mamajek 2009)....
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1,268 citations
"Concentrating small particles in pr..." refers background in this paper
...The standard sheared periodic boundary conditions are imposed (Brandenburg et al. 1995; Hawley et al. 1995), and we assume the vertical dimension is also periodic....
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