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

Self-induced dust traps: overcoming planet formation barriers Jean-François Gonzalez Guillaume Laibe Centre de Recherche Astrophysique de Lyon, France Sarah Maddison Swinburne University of Technology, Melbourne, Australia

Planet formation • Core accre)on paradigm • Small dust grains ➞ pebbles ➞ planetesimals ➞ planets ➞ ➞ ➞ easy bo>leneck easy • The barriers of planet forma)on • Radial dri: Weidenschilling1977, Nakagawa+1986, Birns9el+2010, Laibe+2012,2014 • Fragmenta)on Dullemond+Dominik2005, Blum+Wurm2008 • Bouncing Zsom+2010, Windmark+2012

The radial drift barrier • Sub-Keplerian gas drags Keplerian dust ⇒ dust se>ling and dri: • Dust dynamics controlled by the Stokes number St √ St = ρ s Ω K s 2 πρ s s St mid = Σ g ρ g c s ◆ 2 d ln P g ✓ H St v d ,r ( z = 0) = d ln r v K 1 + St 2 r • 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

The fragmentation and bouncing barriers • Grain collisional evolu)on: fragmenta)on threshold V frag • Growth when V rel < V frag • Fragmenta)on when V rel > V frag • Bouncing when V rel ≲ V frag Seizinger2011

Possible solution: dust traps • Pressure maxima in the disk • Vor)ces Barge+Sommeria1995, Lyra+Mac Low2012, Regály+2012, Méheut+2013, Zhu+2014 • Dead zone inner edge Dzyurkevich+2010 • Planet gap edges de Val-Borro+2007, Fouchet+2007,2010, Gonzalez+2012, Zhu2012,2014 • ‘‘Bumpy’’ gas surface density Pinilla+2012, Bethune+2016 ➡ Dust concentra)ons • ! = " d / " g ↗ , V rel ↘ ⇒ solves planet forma)on barriers • …but need for special condi)ons

Simulations • SPH 3D two-phase (gas+dust) global simula)ons Barrière-Fouchet+2005, Laibe+2008, Gonzalez+2015, Pignatale+2017 • Aerodynamic drag • self-consistent, grain-size dependent dynamics • backreac)on of dust on gas • Grain growth • Stepinski & Valageas (1997) ✏ = ⇢ d • compact par)cles d s ⇢ g d t ∝ ✏ V rel √ • perfect s)cking St V rel ∝ c s • Fragmenta)on 1 + St • when V rel > V frag • conserva)ve model • Ini)al disk model • Σ g ∝ r − p c s ∝ r − q/ 2 St mid ∝ s r p • T ∝ r − q

Flat disk • Setup • CTTS disk St mid ∝ s • M ✰ = 1 M ⊙ , M disk = 0.01 M ⊙ V rel ∝ c s ∝ r − 1 / 2 • p = 0, q = 1 • R out = 160 AU • α = 10 -2 • Ini)al dust/gas ra)o Inner disk Outer disk • ! 0 = 1% , uniform ↓ ↓ • Ini)al grain size V rel > V frag V rel < V frag ↓ ↓ • s 0 = 10 µm , uniform fragmentation growth • Fragmenta)on threshold • V frag = 10, 15, 20, 25 m.s -1

Flat disk, V frag = 15 m.s -1 s n i a r g d e l p Resul)ng size distribu)on similar to u o c Brauer+2008, Birns)el+2010, … e D Coupled grains Without backreac)on Gonzalez+2017

The importance of back-reaction • Drag of dust on gas • o:en neglected when ! = " d / " g is small • becomes important when dust concentrates • slows down dust radial dri: ◆ 2 d ln P g ✓ H St v d ,r ( z = 0) = d ln r v K (1 + ✏ ) 2 + St 2 r • modifies the gas mo)on ◆ 2 d ln P g ✓ H ✏ St v g ,r ( z = 0) = v visc d ln r v K g ,r − (1 + ✏ ) 2 + St 2 r • Consequences • Streaming instability Youdin+Goodman2005, Johansen+2007, Bai+Stone2010, Yang+Johansen2014, Drążkowska+Dullemond2014 • Self-induced dust traps

Flat disk, V frag = 15 m.s -1 With backreac)on s n i a r g d e l p u o c e D Coupled grains Without backreac)on Gonzalez+2017

Formation of the self-induced dust trap ◆ 2 d ln P g ✓ H St St v d ,r ( z = 0) = d ln r v K (1 + ✏ ) 2 + St 2 r large grains slow drift with back-reaction, slower drift St = 1 fast drift without back-reaction small grains slow drift Gonzalez+2017

Formation of the self-induced dust trap ◆ 2 d ln P g ✓ H ✏ St v g ,r ( z = 0) = v visc d ln r v K g ,r − (1 + ✏ ) 2 + St 2 r Gonzalez+2017

Influence of V frag r pu ∝ V − 2 /q Pile-up loca)on: largest grains have St ~ 1 and V rel ~ V frag ⟹ frag Gas pressure Gas pressure gradient Gonzalez+2017

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

Steep disk Influence of the dust-to-gas ra)o ! 0 = 1% ! 0 = 3% V frag = 10 m.s -1 ! 0 = 5% Influence of the fragmenta)on threshold V frag = 10 m.s -1 V frag = 15 m.s -1 V frag = 20 m.s -1 V frag = 25 m.s -1 Gonzalez+2017 ! 0 = 1% ! 0 = 5%

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!