Planetesimal Formation by the

Streaming Instability in a Magnetized Disc

Chao-Chin Yang Lund Observatory

Department of Astronomy and Theoretical Physics Lund University

Meter-size Barrier (Adachi, Hayashi, & Nakazawa 1976; Weidenschilling 1977)

vgas

vK

Fdrag

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R

Meter-size Barrier (Adachi, Hayashi, & Nakazawa 1976; Weidenschilling 1977)

vgas

vK

Fdrag

Youdin (2010)

Disk lifetime

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R

Streaming Instability Youdin & Goodman (2005)

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R

Streaming Instability Youdin & Goodman (2005)

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R

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What We Know• It can create Ceres-sized or smaller planetesimals by direct

gravitational collapse (Johansen et al. 2007, 2012).

• There exists a critical solid-to-gas ratio (Johansen et al. 2009; Bai & Stone 2010b).

• This ratio depends on the radial pressure gradient of the gas (Johansen et al. 2007; Bai & Stone 2010a).

• The initial mass function of planetesimals (Johansen et al. 2015; Schäfer, Yang, & Johansen, in prep.).

• Dependence on the particle size (Carrera, Johansen, & Davies 2015; see Carrera’s talk next).

• Streaming instability on large scales and its interaction with the gas (Yang & Johansen 2014; see also Rixin Li’s poster).

Model Setup

• Local shearing box approximation

• Gas and particles with vertical gravity and two-way friction. • Non-magnetized, isothermal equation of state. • Radial pressure gradient with Δv = 0.05cs. • Solid-to-gas ratio: 2%. • Frictional stopping time: 0.05P (τs ~ 0.3). • Box dimensions: 0.2H×0.2H×0.2H to 1.6H×1.6H×1.6H.

• The Pencil Code

r, x

ϕ, y

⊙z✹

Lz = 0.2H

Lz = 0.2H

1.6H×1.6H×0.2H Yang & Johansen 2014

1.6H×1.6H×1.6H Yang & Johansen 2014

0 2 0 4 0 6 0 8 0− 0 .7

− 0 .6

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0 .0

0 .1

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t

− 0 .7

− 0 .6

− 0 .5

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0 .0

0 .1

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Tim

ea

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rag

ed

Co

rre

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Gas-solid Correlation

Yang & Johansen 2014

The Side View

The Side View

Towards Even Lager Scales: Challenges

• Drag timescales

• On the particles ~ ts ~ ΩK for cm-sized (outer disk) or m-sized (inner disk)

• On the gas ~ ts / (ρp / ρg)

• Explicit integration is severely limited by

• Small particle sizes (ts ≪ ΩK)

• Strong local solid concentration (ρp / ρg ~ 103)

• Our new method (Yang & Johansen, in prep.; see also Lorén-Aguilar & Bate 2014)

• Operator-split, simultaneous integration of the gas and particle velocities.

Linear Test of the Streaming Instability

Yang & Johansen, in prep.

Nonlinear Evolution of the Streaming Instability

Yang & Johansen, in prep.

Nonlinear Evolution of the Streaming Instability

Yang & Johansen, in prep.

Streaming Instability in Magnetized Disks

• Ideal MHD & turbulence • Remains relevant for R ≲ 1 au. • Results are still inconsistent

(c.f. Johansen et al. 2007; Balsara et al. 2009). • Box-size effects on turbulence

in local shearing box (Johansen et al. 2009; Yang, Mac Low, & Menou 2009, 2012; Simon et al. 2012).

• Zonal flow ⤴

• Particle concentration ⤴

• Turbulence ⤴

• particle concentration ⤵

• Non-ideal MHD & dead zone • Perturbations in the mid-

plane remain significant. • With only Ohmic resistivity

• δv ~ a few % of cs (Oishi & Mac Low 2009).

• With both Ohmic and ambipolar diffusion resistivities

• δv ~ a few % of cs (Bai 2015). • Zonal flow still exists

(Simon et al. 2013).

See also A. Schreiber’s poster

2H×8H×8H α ~ 10-2

Concluding Remarks• Radial separation of planetesimal formation

• Size of the initial feeding zone of the planetesimals.

• Axisymmetric filamentary structure in solid particles.

• Large-scale gas-solid interaction

• Non-trivial dynamics of the streaming instability when in MHD/HD unstable disks.

• New numerical method for strong solid concentration and/or small particle sizes.