From Pebbles to Planets

. From pebbles to planets

Anders Johansen (Lund University) with Michiel Lambrechts, Katrin Ros, Andrew Youdin, Yoram Lithwick

From Atoms to Pebbles – Herschel’s View of Star and Planet Formation Grenoble, March 2012

1 / 11 Anders Johansen From pebbles to planets Overview of topics

Size and time Dust Pebbles Planetesimals Planets µ m cm 10−1,000 km 10,000 km

1 From dust to pebbles by ice condensation Ros & Johansen (in preparation); poster by Katrin Ros

2 From pebbles to planetesimals by streaming instabilities Johansen, Youdin, & Lithwick (2012)

3 From planetesimals to gas-giant cores by pebble accretion Lambrechts & Johansen (submitted); poster by Michiel Lambrechts

2 / 11 Anders Johansen From pebbles to planets Classical core accretion scenario

1 Dust grains and ice particles collide to form km-scale planetesimals

2 Large protoplanet grows by run-away accretion of planetesimals

3 Protoplanet attracts hydrostatic gas envelope

4 Run-away gas accretion as Menv ≈ Mcore

5 Form gas giant with Mcore ≈ 10M⊕ and Matm ∼ MJup 3 / 11 Anders Johansen From pebbles to planets Planetesimal accretion

Planetesimals passing within the Hill sphere get signiﬁcantly scattered by the protoplanet The size of the protoplanet relative to the Hill sphere is R r −1 α ≡ p ≈ 0.001 RH 5 AU Rate of planetesimal accretion ˙ 2 M = πRpFH

Without gravitational focusing ˙ 2 2 M = α RHFH Planet With gravitational focusing Gravitational cross section ˙ 2 Hill sphere M = αRHFH

4 / 11 Anders Johansen From pebbles to planets x=0 x Core formation time-scales

The size of the protoplanet relative to the Hill sphere: R r −1 p ≡ α ≈ 0.001 RH 5 AU

Maximal growth rate ˙ 2 M = αRHFH

⇒ Only 0.1% (0.01%) of planetesimals entering the Hill sphere are accreted at 5 AU (50 AU)

⇒ Time to grow to 10 M⊕ is ∼10 Myr at 5 AU ∼50 Myr at 10 AU ∼5,000 Myr at 50 AU 5 / 11 Anders Johansen From pebbles to planets Directly imaged exoplanets

(Marois et al. 2008; 2010) (Kalas et al. 2008)

HR 8799 (4 planets at 14.5, 24, 38, 68 AU) Fomalhaut (1 planet at 113 AU) ⇒ No way to form the cores of these planets within the life-time of the protoplanetary gas disc by standard core accretion 6 / 11 Anders Johansen From pebbles to planets Pebble accretion

Most planetesimals are simply scattered by the protoplanet

Planetesimal is scattered by protoplanet Pebbles spiral in towards the protoplanet due to gas friction ⇒ Pebbles are accreted from the entire Hill sphere Pebble spirals towards protoplanet due to gas friction Growth rate by planetesimal accretion is ˙ 2 M = αRHFH

Growth rate by pebble accretion is ˙ 2 M = RHFH

7 / 11 Anders Johansen From pebbles to planets Time-scale of pebble accretion

∆=0.05, Z=0.01 1 0.10 0.10 −1 −1 10 5.0 0.05 t=0.0 Ω t=120 Ω > Hill p 0.00 0.05 z/H 0 /< Σ Drift p −0.05 10 Σ −0.10 0.0 −0.10 −0.05 0 0.05 0.10 PA 50AU 0.00 x/H y/H −1 10 5.0AU

0.5AU −0.05 50AU 50AU ⊕ 10−2

/ M 5.0AU 5.0AU −0.10 c 0.10 −1 −1 M Pluto t=131 Ω t=134 Ω 10−3 0.05 10−4 Ceres 0.00 y/H 5.0AU −5 0.5AU −0.05 10

−0.10 100 101 102 103 104 105 106 107 108 −0.10 −0.05 0.00 0.05 0.10 −0.05 0.00 0.05 0.10 x/H x/H t/yr ⇒ Pebble accretion speeds up core formation by a factor 1,000 at 5 AU and a factor 10,000 at 50 AU (Lambrechts & Johansen, submitted to A&A; see also Ormel & Klahr 2010) ⇒ Cores form well within the life-time of the protoplanetary gas disc, even at large orbital distances But requires large planetesimals to begin with... 8 / 11 Anders Johansen From pebbles to planets Formation of large planetesimals

t=120.4 t=130.4 t=140.4 0.10 Streaming instabilities lead to 1283

0.05 No collisions concentration of cm-sized pebbles 20.0

N=13 N=7 (Johansen & Youdin 2007; Bai & Stone 2010) 0.00 Σp/<Σp> y / H Mbound= 1.34 Mbound= 1.35 0.0 M1= 0.44 M1= 0.95 −0.05 M2= 0.19 M2= 0.16

M13= 0.0061 M7= 0.029 Planetesimals with d ∼ 1000 km −0.10 0.10 Collisions with shear form by gravitational collapse 0.05 ε =0.3 0.00 N=7 N=3 y / H Mbound= 1.35 Mbound= 1.47

M1= 0.59 M1= 0.75 ⇒ Asteroids born big? −0.05 M2= 0.49 M2= 0.70

(Morbidelli et al. 2009) M7= 0.020 M3= 0.014 −0.10 0.10 Collisions without shear Scaling to Kuiper belt gives twice 0.05 ε =0.3 0.00 N=9 N=6 y / H as large planetesimals Mbound= 1.42 Mbound= 1.46

M1= 0.45 M1= 0.63 (Johansen, Youdin, & Lithwick 2012) −0.05 M2= 0.33 M2= 0.59

M9= 0.012 M6= 0.021 −0.10 0.10 Collisions with shear ⇒ Explains why Kuiper belt objects 0.05 ε =1.0 are larger than asteroids 0.00 N=7 N=3 y / H Mbound= 1.37 Mbound= 1.44

M1= 0.54 M1= 0.63 −0.05 M2= 0.31 M2= 0.59

M7= 0.0052 M3= 0.22 ⇒ Largest planetesimals can grow to −0.10 −0.10 −0.05 0.00 0.05 −0.10 −0.05 0.00 0.05 −0.10 −0.05 0.00 0.05 0.10 cores by pebble accretion x/H x/H x/H

9 / 11 Anders Johansen From pebbles to planets Formation of icy pebbles

Pebbles are observed in abundance in nearby protoplanetary discs (e.g. Testi et al. 2003; Wilner et al. 2005) How do pebbles form so eﬃciently? Near ice lines pebbles can form like hail stones ⇒ Eﬃcient formation of cm-dm sized icy pebbles near ice lines (Ros & Johansen, in preparation; poster by Katrin Ros) 10 / 11 Anders Johansen From pebbles to planets Summary of talk

Dust Pebbles Planetesimals Cores Ice condensation Gravitational instability Pebble accretion

1 Ice condensation leads to eﬃcient formation of pebbles near ice lines (Ros & Johansen, in preparation; poster by Katrin Ros)

2 Streaming instabilities form large planetesimals (∼Ceres or ∼Pluto) (Johansen, Youdin, & Lithwick 2012)

3 Large planetesimals grow rapidly by pebble accretion, explaining the giants of the solar system as well as gas giants in wide orbits (Lambrechts & Johansen, submitted; poster by Michiel Lambrechts)

⇒ Icy pebbles may play important role in planet formation ⇒ Planet formation can be probed and constrained through observations of water vapour and pebbles 11 / 11 Anders Johansen From pebbles to planets