Streaming instability in the quasi-global protoplanetary discs

ABSTRACT The streaming instability (SI) has been extensively studied in the linear and non-linear regimes as a mechanism to concentrate solids and trigger planetesimal formation in the mid-plane of protoplanetary discs. A related dust settling instability (DSI) applies to particles while settling towards the mid-plane. The DSI has previously been studied in the linear regime, with predictions that it could trigger particle clumping away from the mid-plane. This work presents a range of linear calculations and non-linear simulations, performed with fargo3d, to assess conditions for DSI growth. We expand on previous linear analyses by including particle size distributions and performing a detailed study of the amount of background turbulence needed to stabilize the DSI. When including binned size distributions, the DSI often produces converged growth rates with fewer bins than the standard SI. With background turbulence, we find that the most favourable conditions for DSI growth are weak turbulence, characterized by α ≲ 10−6 with intermediate-sized grains that settle from one gas scale height. These conditions could arise during a sudden decrease in disc turbulence following an accretion outburst. Ignoring background turbulence, we performed a parameter survey of local 2D DSI simulations. Particle clumping was either weak or occurred slower than particles settle. Clumping was reduced by a factor of 2 in a comparison 3D simulation. Overall, our results strongly disfavour the hypothesis that the DSI significantly promotes planetesimal formation. Non-linear simulations of the DSI with different numerical methods could support or challenge these findings.

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Physical models of streaming instabilities in protoplanetary discs

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/staa2311 ◽

2020 ◽

Vol 498 (1) ◽

pp. 1239-1251 ◽

Cited By ~ 2

Author(s):

Jonathan Squire ◽

Philip F Hopkins

Keyword(s):

Growth Rate ◽

Sudden Change ◽

Physical Models ◽

Physical Processes ◽

Slow Growth Rate ◽

Drag Forces ◽

Streaming Instability ◽

Fluid Instability ◽

Gas Drag ◽

Protoplanetary Discs

ABSTRACT We develop simple, physically motivated models for drag-induced dust–gas streaming instabilities, which are thought to be crucial for clumping grains to form planetesimals in protoplanetary discs. The models explain, based on the physics of gaseous epicyclic motion and dust–gas drag forces, the most important features of the streaming instability and its simple generalization, the disc settling instability. Some of the key properties explained by our models include the sudden change in the growth rate of the streaming instability when the dust-to-gas mass ratio surpasses one, the slow growth rate of the streaming instability compared to the settling instability for smaller grains, and the main physical processes underlying the growth of the most unstable modes in different regimes. As well as providing helpful simplified pictures for understanding the operation of an interesting and fundamental astrophysical fluid instability, our models may prove useful for analysing simulations and developing non-linear theories of planetesimal growth in discs.

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Dust clearing by radial drift in evolving protoplanetary discs

Astronomy and Astrophysics ◽

10.1051/0004-6361/202037650 ◽

2020 ◽

Vol 638 ◽

pp. A156 ◽

Cited By ~ 1

Author(s):

Johan Appelgren ◽

Michiel Lambrechts ◽

Anders Johansen

Keyword(s):

Accretion Rate ◽

Stellar Mass ◽

Dust Particles ◽

Occurrence Rate ◽

Linear Scaling ◽

Streaming Instability ◽

Dust Mass ◽

Gas Accretion ◽

Gas Ratio ◽

Protoplanetary Discs

Recent surveys have revealed that protoplanetary discs typically have dust masses that appear to be insufficient to account for the high occurrence rate of exoplanet systems. We demonstrate that this observed dust depletion is consistent with the radial drift of pebbles. Using a Monte Carlo method we simulate the evolution of a cluster of protoplanetary discs using a 1D numerical method to viscously evolve each gas disc together with the radial drift of dust particles that have grown to 100 μm in size. For a 2 Myr-old cluster of stars, we find a slightly sublinear scaling between the gas disc mass and the gas accretion rate (Mg ∝ Ṁ0.9). However, for the dust mass we find that evolved dust discs have a much weaker scaling with the gas accretion rate, with the precise scaling depending on the age at which the cluster is sampled and the intrinsic age spread of the discs in the cluster. Ultimately, we find that the dust mass present in protoplanetary discs is on the order of 10–100 M⊕ in 1–3 Myr-old star-forming regions, a factor of 10–100 depleted from the original dust budget. As the dust drains from the outer disc, pebbles pile up in the inner disc and locally increase the dust-to-gas ratio by up to a factor of four above the initial value. In these regions of high dust-to-gas ratio we find conditions that are favourable for planetesimal formation via the streaming instability and subsequent growth by pebble accretion. We also find the following scaling relations with stellar mass within a 1–2 Myr-old cluster: a slightly super-linear scaling between the gas accretion rate and stellar mass (Ṁ ∝ M⋆1.4), a slightly super-linear scaling between the gas disc mass and the stellar mass (Mg ∝ M⋆1.4), and a super-linear relation between the dust disc mass and stellar mass (Md ∝ M⋆1.4−4.1).

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Pebble drift and planetesimal formation in protoplanetary discs with embedded planets

Astronomy and Astrophysics ◽

10.1051/0004-6361/201937037 ◽

2020 ◽

Vol 635 ◽

pp. A110 ◽

Cited By ~ 4

Author(s):

Linn E. J. Eriksson ◽

Anders Johansen ◽

Beibei Liu

Keyword(s):

Spatial Distribution ◽

Time Scale ◽

Particle Sizes ◽

Dust Trapping ◽

Nominal Model ◽

Streaming Instability ◽

Dust Evolution ◽

Strong Depletion ◽

Protoplanetary Discs

Nearly axisymmetric gaps and rings are commonly observed in protoplanetary discs. The leading theory regarding the origin of these patterns is that they are due to dust trapping at the edges of gas gaps induced by the gravitational torques from embedded planets. If the concentration of solids at the gap edges becomes high enough, it could potentially result in planetesimal formation by the streaming instability. We tested this hypothesis by performing global 1D simulations of dust evolution and planetesimal formation in a protoplanetary disc that is perturbed by multiple planets. We explore different combinations of particle sizes, disc parameters, and planetary masses, and we find that planetesimals form in all of these cases. We also compare the spatial distribution of pebbles from our simulations with protoplanetary disc observations. Planets larger than one pebble isolation mass catch drifting pebbles efficiently at the edge of their gas gaps, and depending on the efficiency of planetesimal formation at the gap edges, the protoplanetary disc transforms within a few 100 000 yr to either a transition disc with a large inner hole devoid of dust or to a disc with narrow bright rings. For simulations with planetary masses lower than the pebble isolation mass, the outcome is a disc with a series of weak ring patterns but there is no strong depletion between the rings. By lowering the pebble size artificially to a 100 micrometer-sized “silt”, we find that regions between planets get depleted of their pebble mass on a longer time-scale of up to 0.5 million years. These simulations also produce fewer planetesimals than in the nominal model with millimeter-sized particles and always have at least two rings of pebbles that are still visible after 1 Myr.

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Resonant drag instabilities in protoplanetary discs: the streaming instability and new, faster growing instabilities

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/sty854 ◽

2018 ◽

Vol 477 (4) ◽

pp. 5011-5040 ◽

Cited By ~ 41

Author(s):

Jonathan Squire ◽

Philip F Hopkins

Keyword(s):

Streaming Instability ◽

Protoplanetary Discs

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MRI-active inner regions of protoplanetary discs. I. A detailed model of disc structure

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/stab920 ◽

2021 ◽

Vol 504 (1) ◽

pp. 280-299

Author(s):

Marija R Jankovic ◽

James E Owen ◽

Subhanjoy Mohanty ◽

Jonathan C Tan

Keyword(s):

Energy Transport ◽

Threshold Temperature ◽

Mass Star ◽

Dust Grains ◽

Solar Mass ◽

Detailed Model ◽

Short Period ◽

Pressure Maximum ◽

Ion Emission ◽

Protoplanetary Discs

ABSTRACT Short-period super-Earth-sized planets are common. Explaining how they form near their present orbits requires understanding the structure of the inner regions of protoplanetary discs. Previous studies have argued that the hot inner protoplanetary disc is unstable to the magnetorotational instability (MRI) due to thermal ionization of potassium, and that a local gas pressure maximum forms at the outer edge of this MRI-active zone. Here we present a steady-state model for inner discs accreting viscously, primarily due to the MRI. The structure and MRI-viscosity of the inner disc are fully coupled in our model; moreover, we account for many processes omitted in previous such models, including disc heating by both accretion and stellar irradiation, vertical energy transport, realistic dust opacities, dust effects on disc ionization, and non-thermal sources of ionization. For a disc around a solar-mass star with a standard gas accretion rate ($\dot{M}\, \sim \, 10^{-8}$ M⊙ yr−1) and small dust grains, we find that the inner disc is optically thick, and the accretion heat is primarily released near the mid-plane. As a result, both the disc mid-plane temperature and the location of the pressure maximum are only marginally affected by stellar irradiation, and the inner disc is also convectively unstable. As previously suggested, the inner disc is primarily ionized through thermionic and potassium ion emission from dust grains, which, at high temperatures, counteract adsorption of free charges on to grains. Our results show that the location of the pressure maximum is determined by the threshold temperature above which thermionic and ion emission become efficient.

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