How asteroids grow Anders Johansen (Lund University) “Star and Planet Formation For All”, Lund, February 2014 1 / 14
Planets and exoplanets ◮ First exoplanet was discovered in 1995 ( Mayor & Queloz , 1995) ◮ The Kepler satellite identified over 2300 exoplanet candidates in the 16-months data ( Batalha et al. , 2013) ⇒ 50% of stars have planets within 0.4 AU ( Fressin et al. , 2013) ⇒ Most exoplanets in close orbits are super-Earths or small Neptunes ⇒ Nature is very efficient at turning dust and ice into planets 2 / 14
Classical picture of planet formation Planetesimal hypothesis of Viktor Safronov 1969: Planets form in protoplanetary discs around young stars as planetes- imals collide to form ever larger bodies 1. Dust to planetesimals µ m → km: contact forces 2. Planetesimals to protoplanets km → 1,000 km: gravity (run-away accretion) 3. Protoplanets to planets (10 7 –10 8 years) Terrestrial planets: protoplanets collide Gas and ice giants: 10 M ⊕ core accretes gas ( < 10 6 ... 7 years) Severe problems with classical model: 1 Growth of macroscopic particles is frustrated by erosion and bouncing 2 Planetesimals colliding at high speeds will shatter each other 3 Core formation takes much longer time than the life-time of the nebula 3 / 14
Planet formation with pebbles Pebble hypothesis: Planetesimals form by gravitational collapse of dense clumps of peb- bles and planets form mainly by pebble accretion onto planetesimals 1. Dust to pebbles µ m → cm: coagulation and condensation 2. Pebbles to planetesimals km → 100–1,000 km: particle concentration and gravitational collapse 3. Planetesimals to planets Terrestrial planets: pebble accretion, giant impacts (10 6 –10 8 years ?) ( ≪ 10 6 years) Gas and ice giants: pebble accretion to 10 M ⊕ See Protostars and Planets VI reviews by Johansen et al. (2014) and Chabrier, Johansen, et al. (2014) 4 / 14
Dust to pebbles ( Zsom et al. , 2010) ◮ Collisions between dust aggregates can lead to sticking, bouncing or fragmentation ( G¨ uttler et al. , 2010) ◮ Sticking for low collision speeds and small aggregates ◮ Bouncing prevents growth beyond mm sizes ( bouncing barrier ) ◮ Further growth may be possible by mass transfer in high-speed collisions ( Windmark et al. , 2012) or by ice condensation ( Ros & Johansen , 2012) → SPFFA talk by Katrin Ros 5 / 14
Pebbles to planetesimals t =40.0 Ω −1 t =80.0 Ω −1 +20.0 +20.0 +10.0 +10.0 z /( η r ) z /( η r ) +0.0 +0.0 −10.0 −10.0 −20.0 −20.0 v (1− ) η −20.0 −10.0 +0.0 +10.0 +20.0 −20.0 −10.0 +0.0 +10.0 +20.0 Kep x /( η r ) x /( η r ) t =120.0 Ω −1 t =160.0 Ω −1 +20.0 +20.0 F G F +10.0 +10.0 P z /( η r ) z /( η r ) +0.0 +0.0 −10.0 −10.0 −20.0 −20.0 −20.0 −10.0 +0.0 +10.0 +20.0 −20.0 −10.0 +0.0 +10.0 +20.0 x /( η r ) x /( η r ) ◮ The radial drift flow of particles is linearly unstable to streaming instability 0.10 0.10 ( Youdin & Goodman , 2005; Youdin & Johansen , 2007) 0.05 0.05 y / H y / H 0.00 0.00 ◮ Particles pile up in dense filaments −0.05 −0.05 ( Johansen & Youdin , 2007; Bai & Stone , 2010a) −0.10 −0.10 −0.10 −0.05 0.00 0.05 0.10 −0.10 −0.05 0.00 0.05 0.10 x / H x / H ◮ Particle concentration triggered above a 0.10 10 −6 10 −6 269 t = 337.5 Ω −1 Z = 0.020 0.05 threshold metallicity around Z ≈ 0 . 015 162 R /km z / H 0.00 µ 10 −7 10 −7 ( Johansen et al. , 2009, 2012; Bai & Stone , 2010b,c) 97 −0.05 ◮ Possible to concentrate particles down to mm −0.10 10 −8 10 −8 58 −0.10 −0.05 0.00 0.05 0.10 325 330 335 t / Ω −1 x / H sizes at 2.5 AU ( Carrera, Johansen, & Davies , in prep) → SPFFA talk by Daniel Carrera 6 / 14
Planetesimals to planets 0.10 0.10 t =0.0 Ω −1 t =120 Ω −1 5.0 0.05 Σ p /< Σ p > z/H 0.00 0.05 −0.05 −0.10 Core growth to 10 M ⊕ 0.0 −0.10 −0.05 0 0.05 0.10 y/H 0.00 x/H 10 8 Planetesimals 10 7 −0.05 −0.10 10 6 0.10 ∆ t /yr t =131 Ω −1 t =134 Ω −1 s t n e m 10 5 0.05 g a r F Pebbles y/H 10 4 0.00 10 3 −0.05 10 −1 10 0 10 1 10 2 −0.10 −0.10 −0.05 0.00 0.05 0.10 −0.05 0.00 0.05 0.10 r /AU x/H x/H ⇒ Pebble accretion speeds up core formation by a factor 1,000 at 5 AU and a factor 10,000 at 50 AU ( Lambrechts & Johansen , 2012; also Ormel & Klahr , 2010; Morbidelli & Nesvorny , 2012) ⇒ Cores form well within the life-time of the protoplanetary gas disc, even at large orbital distances ◮ Requires large planetesimal seeds, consistent with turbulence-aided planetesimal formation → SPFFA talk by Michiel Lambrechts 7 / 14
Evidence for giant impact stage ( Wetherill , 1985) ◮ The Moon’s mean density is very low, with uncompressed density ρ = 3 . 3 g cm − 3 [Earth’s uncompressed density: ρ = 4 . 4 g cm − 3 ] ◮ The Moon is highly differentiated – with a dense core, a mantle, and a crust – but must be lacking iron and volatiles ⇒ Moon formed from the impact debris after Mars-sized protoplanet impacted the young, differentiated Earth ⇒ Taken as evidence for giant impact stage of classical planet formation ? Any evidence for pebble accretion? YES – encoded in the asteroid sizes 8 / 14
Asteroid birth sizes Asteroid size distribution 10 3 10 2 10 1 d N /d R [km −1 ] 10 0 10 −1 10 −2 10 −3 100 1000 D [km] ◮ Size distribution of asteroids shows distinct bumps at diameters D = 120 km and D = 350 km ◮ Forming asteroids from km-sized planetesimals does not reproduce the first bump – bump is primordial ( Bottke et al. , 2005) ◮ Asteroids must be born BIG (100 – 1000 km) in order to not overproduce asteroids with diameters less than 100 km ( Morbidelli et al. , 2010) 9 / 14
Planetesimal formation R [km] 25 50 100 200 400 10 9 q M = 1.31 +/− 0.07 10 8 10 7 −1 ] d N /d M [M 22 10 6 10 5 10 4 128 3 , 5.0 × MMSN 256 3 , 5.0 × MMSN 512 3 , 5.0 × MMSN 10 3 256 3 , 2.5 × MMSN 256 3 , 1.0 × MMSN 10 2 10 20 10 21 10 22 10 23 10 24 M [g] ◮ Streaming instability leads to concentration of pebbles and to planetesimal formation ( Johansen et al. , 2014, Protostars and Planets VI, arXiv:1402.1344 ) ◮ Higher resolution gives smaller planetesimals (PRACE grant “PLANETESIM”) ◮ Birth sizes of planetesimals show no sign of a bump – most of the planetesimals are small but most mass is in the largest bodies ◮ Powerlaw in d N / d M ∝ M − q is approximately q = 1 . . . 1 . 5 ◮ Gravitational collapse of clumps → SPFFA talk by Kalle Jansson 10 / 14
Chondrules ◮ Meteorites recovered on Earth are fragments of asteroids ◮ Oldest condensates in the Solar System are CAIs with a narrow age range of 4567 . 30 ± 0 . 16 Myr ( Connelly et al. , 2012) ◮ Primitive meteorites ( chondrites ) contain a large fraction of 0.1-1-mm-sized chondrules (formed over the first 3 Myr) ◮ Chondrites contain up to 80% of their mass in chondrules ◮ What role did chondrules play in asteroid formation? 11 / 14
Chondrule accretion ∆ v ≈ 50 m/s Chondrule spirals towards asteroid due to gas friction Bondi radius: GM R B = (∆ v ) 2 Large chondrule is scattered by protoplanet ˙ M = π R 2 B ρ c ∆ v ∝ R 6 ( Lambrechts & Johansen , 2012) 12 / 14
Planetesimal size distribution R [km] R [km] 10 100 1000 10 100 1000 10 6 10 5 Nominal model Lower pressure support 10 5 10 4 10 4 10 3 d N /d R [km −1 ] d N /d R [km −1 ] 10 3 10 2 10 2 10 1 10 1 10 0 10 0 10 −1 10 −1 10 −2 10 5 10 5 Steeper chondrule size distribution Larger chondrules 10 4 10 4 10 3 10 3 d N /d R [km −1 ] d N /d R [km −1 ] 10 2 10 2 10 1 10 1 10 0 10 0 10 −1 10 −1 10 −2 10 −2 10 100 1000 10 100 1000 R [km] R [km] ◮ The nominal model reproduces four features of the asteroid size distribution: the bump at R = 60 km, the steep size distribution up to R = 200 km, the bump at R = 200 km and the shallow size distribution for the largest sizes ( Johansen, Mac Low, Lacerda, & Bizzarro , in prep) ◮ Variation in the parameters gives different realisations of the asteroid belt 13 / 14
Implications ( Elkins-Tanton et al. , 2011) ◮ Asteroids grew primarily by chondrule accretion ◮ Size distribution of asteroids shows evidence of this chondrule accretion ◮ General validation that pebble accretion occurred in the Solar System ◮ Pebble accretion likely driven by icy pebbles beyond the ice line ◮ Planetesimals in the terrestrial planet formation region grew by accreting chondrules – could this explain rapid formation of Mars? 14 / 14
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