Self-induced dust traps: overcoming planet formation barriers - - PowerPoint PPT Presentation

Jean-François Gonzalez Guillaume Laibe Centre de Recherche Astrophysique de Lyon, France Sarah Maddison Swinburne University of Technology, Melbourne, Australia

Self-induced dust traps:

• vercoming planet formation

barriers

• Core accre)on paradigm
• Small dust grains ➞ pebbles ➞ planetesimals ➞ planets

Planet formation

Weidenschilling1977, Nakagawa+1986, Birns9el+2010, Laibe+2012,2014 Dullemond+Dominik2005, Blum+Wurm2008 Zsom+2010, Windmark+2012

• The barriers of planet forma)on
• Radial dri:
• Fragmenta)on
• Bouncing

➞

easy

➞

easy

➞

bo>leneck

The radial drift barrier

vd,r(z = 0) = St 1 + St2 ✓H r ◆2 d ln Pg d ln r vK

• Sub-Keplerian gas drags Keplerian dust ⇒ dust se>ling and dri:
• Dust dynamics controlled by the Stokes number St
• St≪1, small sizes (1-10 µm): dust coupled to gas
• St~1, median sizes (100 µm-10 cm): strong influence of gas drag
• St≫1, large sizes (1-10 m): dust insensi)ve to gas

St = ρsΩKs ρgcs Stmid = √ 2πρss Σg

The fragmentation and bouncing barriers

• Grain collisional evolu)on: fragmenta)on threshold Vfrag
• Growth when Vrel < Vfrag
• Bouncing when Vrel ≲ Vfrag
• Fragmenta)on when Vrel > Vfrag

Seizinger2011

Pinilla+2012, Bethune+2016 Barge+Sommeria1995, Lyra+Mac Low2012, Regály+2012, Méheut+2013, Zhu+2014 de Val-Borro+2007, Fouchet+2007,2010, Gonzalez+2012, Zhu2012,2014 Dzyurkevich+2010

Possible solution: dust traps

➡ Dust concentra)ons

• ! = "d/"g ↗, Vrel ↘ ⇒ solves planet forma)on barriers
• …but need for special condi)ons
• Pressure maxima in the disk
• Vor)ces
• Dead zone inner edge
• Planet gap edges
• ‘‘Bumpy’’ gas surface density

Simulations

• Ini)al disk model
• Σg ∝ r−p

T ∝ r−q Stmid ∝ s rp cs ∝ r−q/2

• SPH 3D two-phase (gas+dust) global simula)ons
• Aerodynamic drag
• self-consistent, grain-size dependent dynamics
• backreac)on of dust on gas
• Grain growth
• Stepinski & Valageas (1997)
• compact par)cles
• perfect s)cking
• Fragmenta)on
• when Vrel > Vfrag
• conserva)ve model

Vrel ∝ cs √ St 1 + St

ds dt ∝ ✏ Vrel ✏ = ⇢d ⇢g

Barrière-Fouchet+2005, Laibe+2008, Gonzalez+2015, Pignatale+2017

Flat disk

• Setup
• CTTS disk
• M✰ = 1 M⊙, Mdisk = 0.01 M⊙
• p = 0, q = 1
• Rout = 160 AU
• α = 10-2
• Ini)al dust/gas ra)o
• !0 = 1%, uniform
• Ini)al grain size
• s0 = 10 µm, uniform
• Fragmenta)on threshold
• Vfrag = 10, 15, 20, 25 m.s-1

Vrel ∝ cs ∝ r−1/2 Stmid ∝ s

Inner disk ↓ Vrel > Vfrag ↓ fragmentation Outer disk ↓ Vrel < Vfrag ↓ growth

Flat disk, Vfrag = 15 m.s-1

Coupled grains D e c

• u

p l e d g r a i n s

Without backreac)on Resul)ng size distribu)on similar to Brauer+2008, Birns)el+2010, …

Gonzalez+2017

• Drag of dust on gas
• o:en neglected when ! = "d/"g is small
• becomes important when dust concentrates
• slows down dust radial dri:

The importance of back-reaction

vd,r(z = 0) = St (1 + ✏)2 + St2 ✓H r ◆2 d ln Pg d ln r vK

Youdin+Goodman2005, Johansen+2007, Bai+Stone2010, Yang+Johansen2014, Drążkowska+Dullemond2014

• Consequences
• Streaming instability
• Self-induced dust traps
• modifies the gas mo)on

vg,r(z = 0) = vvisc

g,r −

✏ St (1 + ✏)2 + St2 ✓H r ◆2 d ln Pg d ln r vK

Flat disk, Vfrag = 15 m.s-1

With backreac)on Without backreac)on

Coupled grains D e c

• u

p l e d g r a i n s

Gonzalez+2017

large grains slow drift

St

small grains slow drift St = 1 fast drift without back-reaction with back-reaction, slower drift vd,r(z = 0) = St (1 + ✏)2 + St2 ✓H r ◆2 d ln Pg d ln r vK

Formation of the self-induced dust trap

Gonzalez+2017

Formation of the self-induced dust trap

Gonzalez+2017

vg,r(z = 0) = vvisc

g,r −

✏ St (1 + ✏)2 + St2 ✓H r ◆2 d ln Pg d ln r vK

rpu ∝ V −2/q

frag

Pile-up loca)on: largest grains have St ~ 1 and Vrel ~ Vfrag ⟹

Influence of Vfrag

Gas pressure Gas pressure gradient

Gonzalez+2017

Steep disk

• Setup
• CTTS disk
• M✰ = 1 M⊙, Mdisk = 0.01 M⊙
• p = 1, q = 1/2
• Rout = 400 AU
• α = 10-2
• Ini)al dust/gas ra)o
• !0 = 1%, 3%, 5%, uniform
• Ini)al grain size
• s0 = 10 µm, uniform
• Fragmenta)on threshold
• Vfrag = 10, 15, 20, 25 m.s-1

Steep disk

Vfrag = 10 m.s-1 Vfrag = 15 m.s-1 Vfrag = 20 m.s-1 Vfrag = 25 m.s-1

Influence of the fragmenta)on threshold

!0 = 1% !0 = 5%

Influence of the dust-to-gas ra)o

!0 = 1% !0 = 3% !0 = 5% Vfrag = 10 m.s-1

Gonzalez+2017

Pressure maxima in the steep disk

Gas pressure

Gonzalez+2017

Conclusion

• Self-induced dust traps: robust mechanism
• Traps can cause rings and gaps in disk images
• Easier dust growth and planetesimal forma)on

⟹ solu)on to the radial-dri: and fragmenta)on barriers

• Influence of snow lines ⟹ see Arnaud’s poster

Plans

• Switch to PHANTOM !
• Add dust growth and fragmenta)on
• 1st step: Stepinski & Valageas formalism, two-fluid
• Arnaud’s PhD project
• 2nd step: Smoluchowski equa)on
• Maxime Lombart’s PhD project (with Guillaume Laibe)
• Ul)mate goal: unify with mul)grain, in one-fluid and mul)-fluid

Thank you!