Other Topics 1 / 43 Topics

Lecture 3: Recent topics

0.10 0.10 Ω−1 Ω−1 5.0 0.05 t=0.0 t=120 > p

Σ 0.00 0.05 z/H /<

p −0.05

Σ −0.10 0.0 −0.10 −0.05 0 0.05 0.10 0.00 x/H y/H

−0.05

−0.10 0.10 t=131 Ω−1 t=134 Ω−1

0.05

0.00 y/H

−0.05

−0.10 −0.10 −0.05 0.00 0.05 0.10 −0.05 0.00 0.05 0.10 x/H x/H

“NBI summer School on Protoplanetary Disks and Planet Formation” August 2015

Anders Johansen (Lund University)

Copenhagen 2015 (Lecture 3) Other topics 1 / 43 Topics

1 Wide-orbit exoplanets

2 Pebble accretion

3 Size distribution of asteroids

4 Nice model

5 Grand Tack model

6 Population synthesis with pebbles

7 Chondrule accretion

Copenhagen 2015 (Lecture 3) Other topics 2 / 43 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 (Safronov, 1969; Mizuno, 1980; Pollack et al., 1996) All steps must happen within 1–3 Myr while there is gas orbiting the star Copenhagen 2015 (Lecture 3) Other topics 3 / 43 Life-times of protoplanetary discs Stars in a star-forming region are pretty much the same age Compare disc fraction between regions of diﬀerent age

(Haisch et al., 2001) (Mamajek, 2009)

⇒ Protoplanetary discs live for 1–3 Myr

Copenhagen 2015 (Lecture 3) Other topics 4 / 43 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 by gravitational focussing ˙ 2 M = αRHFH

⇒ Only 0.1% (0.01%) of planetesimals entering

the Hill sphere are accreted at 5 AU (50 AU) Planet Gravitational cross section ⇒ Time to grow to 10 M⊕ is Hill sphere ∼10 Myr at 5 AU ∼50 Myr at 10 AU ∼5,000 Myr at 50 AU x=0 x

Copenhagen 2015 (Lecture 3) Other topics 5 / 43 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 controversial 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

Copenhagen 2015 (Lecture 3) Other topics 6 / 43 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

Copenhagen 2015 (Lecture 3) Other topics 7 / 43 Relevant parameters for pebble accretion

2 1/3 Hill radius RH = [GM/(3Ω )] Distance over which the gravity of the protoplanet dominates over the the tidal force of the central star

2 Bondi radius RB = GM/(∆v) Distance over which a particle with approach speed ∆v is signiﬁcantly deﬂected by the protoplanet (in absence of drag)

Sub-Keplerian speed ∆v Orbital speed of gas and pebbles relative to Keplerian speed

Hill speed vH = ΩRH Approach speed of gas and pebbles at the edge of the Hill sphere

Copenhagen 2015 (Lecture 3) Other topics 8 / 43 Pebble accretion regimes 2 0 Weak Strong 10 τf=0.1 τf=0.01 τ =1 1 f

10−1 B H

r x/r r

/ B

/ 0 d

−4 −2 0 2 4 y r −4

−2 −2

10 B r

/ 0 −1 y 2 4 10−3 −2 10−3 10−2 10−1 100 101 102 −2 −1 0 1 2 / tB/tf x rH

Two main pebble accretion regimes: (Lambrechts & Johansen, 2012)

1 Bondi regime (when ∆v vH) ˙ 2 2 Particles pass the core with speed ∆v, giving M ∝ RB ∝ M 2 Hill regime (when ∆v vH) 2/3 Particles enter Hill sphere with speed vH ≈ ΩRH, giving M˙ ∝ M

Copenhagen 2015 (Lecture 3) Other topics 9 / 43 Time-scale of pebble accretion 0.10 0.10 Ω−1 Ω−1 5.0 0.05 t=0.0 t=120 > p

Σ 0.00 0.05 z/H /<

p −0.05

Σ −0.10 0.0 −0.10 −0.05 0 0.05 0.10 0.00 x/H Core growth to 10 M⊕ y/H 108 Planetesimals −0.05 107 −0.10 0.10 6 t=131 Ω−1 t=134 Ω−1 10 /yr t 0.05 5 ∆ 10 Fragments Pebbles 0.00 4 y/H 10 3 −0.05 10 −1 0 1 2 −0.10 10 10 10 10 −0.10 −0.05 0.00 0.05 0.10 −0.05 0.00 0.05 0.10 x/H x/H r/AU ⇒ Pebble accretion speeds up core formation by a factor 1,000 at 5 AU and a factor 10,000 at 50 AU (Ormel & Klahr, 2010; Lambrechts & Johansen, 2012; Nesvorny & Morbidelli, 2012) ⇒ Cores form well within the life-time of the protoplanetary gas disc, even at large orbital distances Requires large planetesimal seeds to accrete in Hill regime, consistent with planetesimal formation by gravitational collapse

Copenhagen 2015 (Lecture 3) Other topics 10 / 43 The asteroid belt

1–2 million asteroids larger than 1 km in main belt between Mars and Jupiter

Total mass is only 0.0005 ME

Interpolation between terrestrial planets and giant planets gives 2.5 ME in the primordial asteroid belt between 2 and 3 AU

Asteroid belt depleted by resonances with Jupiter

Copenhagen 2015 (Lecture 3) Other topics 11 / 43 Growth of asteroids by pebble accretion

Put large (500 km) planetesimal in an ocean of pebbles:

0.02 t=0.0 2.0 t=2.0 g ρ /

0.01 p ρ 0.0 H

/ 0.00 y

−0.01

−0.02 0.02 ρ log p: t=6.0 t=12.0

0.01 H

/ 0.00 y

−0.01

−0.02 −0.02 −0.01 0.00 0.01 0.02 −0.01 0.00 0.01 0.02 x/H x/H

⇒ Prograde accretion disc forms around the protoplanet (Johansen & Lacerda, 2010)

Copenhagen 2015 (Lecture 3) Other topics 12 / 43 Asteroid rotation

The majority of large asteroids have axial tilt Body α o α < 90◦ Ceres 2 2 Pallas 60o Called “direct” or “prograde” rotation 3 Juno 50o 4 Vesta 29o 5 Astraea 33o 6 Hebe 42o

NP α

Copenhagen 2015 (Lecture 3) Other topics 13 / 43 Asteroid poles

Plot of asteroid pole axes (from Johansen & Lacerda, 2010)

Largest asteroids have a tendency to rotate prograde (1-2 σ)

... but there is a very large scatter

The two large retrograde asteroids, 2 Pallas and 10 Hygiea, are actually spinning on the side

Planetesimal accretion yields slow, retrograde rotation (Lissauer & Kary, 1991)

Prograde spin can also arise from random eﬀect of large impacts (Dones & Tremaine, 1993) or due to collisions between planetesimals within the Hill sphere (Schlichting & Sari, 2007)

Copenhagen 2015 (Lecture 3) Other topics 14 / 43 Primordial spin of planetesimals

A B 2·10−5

1·10−5 z l 0 Ω τ K f=0.1 −1·10−5 ε=10.0 Ω τ Average K f=0.1 Cumulative −5 −2·10 ε=1.0 Keplerian

C D 2·10−5

1·10−5 z l 0

−1·10−5 Ω τ K f=0.1 Ω τ =∞ −5 K f −2·10 ε=0.1

0 2 4 6 8 10 12 0 2 4 6 8 10 12 14 Ω−1 Ω−1 t/ K t/ K

Prograde rotation with P ≈ (5 ... 10) h induced for particles between centimeters and a few meters Spin can be randomised later in giant impacts ⇒ Predict that pristine Kuiper belt objects formed by gravitational collapse should have prograde spin

Copenhagen 2015 (Lecture 3) Other topics 15 / 43 Orbits of Kuiper belt objects

(Chiang et al., 2007; de Pater & Lissauer, 2010)

Kuiper belt objects reside beyond the orbit of Neptune Pluto trapped in 3:2 resonance with Neptune – result of outwards migration of Neptune Scattered disc objects have high e and perihelion between 33 and 40 AU Centaurs have perihelion within 30 AU – source of Jupiter family comets Classical KBOs have low e and semimajor axes between 37 and 48 AU – future target of New Horizons

Copenhagen 2015 (Lecture 3) Other topics 16 / 43 Nice model

(Gomes et al., 2005)

Pluto’s resonant orbit with Neptune is explained by trapping during the migration of Neptune through a primordial, massive Kuiper belt (Malhotra, 1993, 1995) Planetesimals scattered inwards by N, U and S are ejected from the Solar System by J, leading to a net outwards migration of the three outer giants As Jupiter and Saturn cross their 2:1 mean motion resonance, the orbits of Uranus and Neptune are excited and the primordial Kuiper belt is depleted (Tsiganis et al., 2005) Explains modern architecture of the Kuiper belt and Late Heavy Bombardment of the terrestrial planets and the Moon (Gomes et al., 2005) Copenhagen 2015 (Lecture 3) Other topics 17 / 43 Kuiper belt binaries

(Nesvorny et al., 2010)

At least 30% of 100-km classical KBOs are binaries (Noll et al., 2008)

Nesvorny et al. (2010) modelled gravitational collapse of particle clumps to explain why binary KBO can have similar colors

Found good statistical agreement in orbital parameters between simulations and observed KBO binary systems

Almost no binaries in scattered disc – ionised by close encounters?

Copenhagen 2015 (Lecture 3) Other topics 18 / 43 Cloud collapse to pebble piles

Simulate cloud collapse in 0-D collision code (Wahlberg Jansson & Johansen, 2014) High collision rates ⇒ Rapid energy dissipation ⇒ Contraction to solid density (Wahlberg Jansson & Johansen, 2014) ⇒ High pebble fraction after collapse ⇒ Predict that comets like 67P/ Churyumov-Gerasimenko are pebble piles Large Kuiper belt objects likely lost their porosity by gravitational compression (Brown, 2013) Copenhagen 2015 (Lecture 3) Other topics 19 / 43 Goosebumps on 67P

(Sierks et al., 2015) (Mottola et al., 2015)

The Rosetta mission arrived at the comet 67P/Churyumov-Gerasimenko in 2014 Orbiter will follow 67P beyond perihelion

Structures in deep pits resemble goosebumps (Sierks et al., 2015) Could be the primordial pebbles from the solar protoplanetary disc But meter-sized pebbles hard to explain in light of radial drift Philae’s ﬁrst landing site shows characteristic particle scale of cm in smooth terrains (Mottola et al., 2015)

Copenhagen 2015 (Lecture 3) Other topics 20 / 43 Pebbles in the media!

Copenhagen 2015 (Lecture 3) Other topics 21 / 43 Missing intermediate-size planetesimals

Sheppard & Trujillo (2010) searched for Neptune Trojans

Sensitive to planetesimals larger than 16 km

Found no Trojans with radius less than 45 kilometers

Dubbed them the missing intermediate-size planetesimals (MISPs)

Copenhagen 2015 (Lecture 3) Other topics 22 / 43 Asteroid size distribution

Diﬀerential size distribution of asteroids shows several bumps

Can be used to infer the degree of depletion and collisional grinding in the asteroid belt

Divide the history of the asteroid belt into an early accretion phase followed by an extended depletion phase

Bottke et al. (2005a,b) evolved the asteroid belt over billions of years, starting from a size distribution which matches the current one for bodies larger than 120 km in diameter

Copenhagen 2015 (Lecture 3) Other topics 23 / 43 Evolution of asteroid size distribution

Depletion factor of 100–200 gives good ﬁt to (Bottke et al., 2005) observed size distribution after 4600 Myr of evolution Also satisﬁes the two constraints: (i) Vesta only has a single large crater and (ii) there are only 9 large asteroid familes Observed size distribution of large asteroids is a fossil of the size distribution at the end of the accretion phase

Copenhagen 2015 (Lecture 3) Other topics 24 / 43 Accretion phase of asteroids

Size distribution of asteroids shows distinct bumps at D = 120 km and at D = 350 km

The ﬁrst bump must be primordial (Bottke et al., 2005) Starting accretion phase with km-sized planetesimals produces way too many asteroids with D < 100 km (Morbidelli et al., 2009)

Copenhagen 2015 (Lecture 3) Other topics 25 / 43 Starting from planetesimals with D = 100 km

Starting with planetesimals with D = 100 km produces very few fragments during the accretion stage

But the resulting size distribution is too steep for D > 100 km (Morbidelli et al., 2009; Weidenschilling, 2011)

Copenhagen 2015 (Lecture 3) Other topics 26 / 43 Asteroids are born big

The best results are obtained by setting the birth size distribution of asteroids equal to the current observed size distribution of large asteroids

Asteroids are born BIG (Morbidelli et al., 2009) Can we connect birth sizes to planetesimal formation models?

Copenhagen 2015 (Lecture 3) Other topics 27 / 43 Birth sizes of planetesimals

R [km] 25 50 100 200 400 109

8 Asteroids (rescaled) 10 qM = 1.6

107 ] −1 22 106 [M M 5 /d 10 N d 4 3 Σ −2 10 128 , p = 23.9 g cm 3 Σ −2 256 , p = 23.9 g cm 3 Σ −2 512 , p = 23.9 g cm 3 3 Σ −2 10 256 , p = 12.0 g cm 3 Σ −2 256 , p = 6.0 g cm Binary 2563, Σ = 2.4 g cm−2 102 p 1020 1021 1022 1023 1024 M [g] Streaming instability leads to concentration of pebbles and to planetesimal formation Higher resolution yields smaller and smaller planetesimals −q Powerlaw in dN/dM ∝ M with q ≈ 1.6 (Johansen et al., 2015) Most of the planetesimals are small but most mass is in the largest bodies Birth sizes of planetesimals show no sign of a bump at 50 km radii

Copenhagen 2015 (Lecture 3) Other topics 28 / 43 Chondrules

Primitive meteorite parent bodies contain a large fraction of 0.1-1-mm-sized chondrules (formed over the ﬁrst 3 million years) Ordinary chondrites contain up to 80% of their mass in chondrules What role did chondrules play in asteroid formation and growth?

Copenhagen 2015 (Lecture 3) Other topics 29 / 43 4 10 R R × −4 R R × −1 / B= 1.0 10 / B= 1.0 10 R R × −4 R R × −1 / B= 3.2 10 / B= 3.2 10 R R × −3 R R × 0 Bondi accretion of chondrules / B= 1.0 10 / B= 1.0 10 R R × −3 R R × 0 / B= 3.2 10 / B= 3.2 10 R R × −2 R R × 1 / B= 1.0 10 / B= 1.0 10 2 −2 R/R = 3.2×10 Geometric ∆v ≈ 50 m/s 10 B B R

/ 0 10 Weak acc coupling R Sedimentation overshootR R × 1 / B= 3.2 10 R R × 2 / B= 1.0 10 Strong coupling R R × 2 / B= 3.2 10 −2 R R × 3 / B= 1.0 10 10 R R × 3 Grav. focusing / B= 3.2 10 R R × 4 / B= 1.0 10 Perfect sticking 10−4 10−3 10−2 10−1 100 101 102 103 104 t t f/ B

Chondrule spirals towards asteroid due to gas friction Bondi radius: GM RB = (∆v)2

Large chondrule is scattered by asteroid

˙ 2 2 6 M = πfB RBρc∆v ∝ R (Ormel & Klahr, 2010; Lambrechts & Johansen, 2012)

Copenhagen 2015 (Lecture 3) Other topics 30 / 43 Asteroid sizes after chondrule accretion

106 1027 10−1 Nominal model (t=5.0 Myr) R = 3119 km R5 Myr Initial size distribution 5 Myr = 498 km Asteroid belt (× 540) 26 R = 199 km Embryos 10 5 Myr 4 No chondrule accretion Collisions 10 Smallest body i 25 i −2 Ceres Moon Mars Largest body ] 10 10 −1

2 24 i [km 10 [g] 10 R M /d N

d Smaller planetesimals 23 −3 Larger chondrules 10 10 (t=2.0 Myr) 100 1022

21 −4 10−2 10 10 10 100 1000 0 1 2 3 4 5 R [km] t [Myr] Chondrule accretion reproduces both the bump at R = 120 km and the steep size distribution up to R = 200 km (Johansen et al., 2015) Embryos with sizes between the Moon and Mars are also formed by rapid chondrule accretion Direct planetesimal accretion contributes only a minor amount of mass to the embryos and the largest asteroids

Copenhagen 2015 (Lecture 3) Other topics 31 / 43 Embryos in the asteroid belt

(Bottke et al., 2005) Both planetesimal accretion and chondrule accretion models produce embryos in the asteroid belt

The embryos excite the eccentricities and inclinations of asteroids to their high values (Wetherill, 1991; Petit et al., 2001)

Embryos also scattered asteroids to Jupiter resonances

Embryos entirely removed from the asteroid belt by perturbation from Jupiter

Copenhagen 2015 (Lecture 3) Other topics 32 / 43 The Grand Tack scenario

(Walsh et al., 2011) The small mass of Mars (11% of Earth’s) is hard to explain in terrestrial planet formation models Jupiter could have migrated suﬃciently far in to perturb the embryos in the terrestrial planet formation region As Jupiter and Saturn come to share a gap, they migrate outwards together (the Grand Tack scenario of Walsh et al., 2011) Best alternative to embedded embryos model for asteroid stirring, particularly if one is concerned about Mars’ small size

Copenhagen 2015 (Lecture 3) Other topics 33 / 43 Terrestrial planet formation with chondrules

100 t 0 =0 Myr 10 t=1 Myr t=3 Myr 10−1 t=5 Myr

−2 ] 10−2 10 −1 ] Ceres Moon Mars E M [km −3 [ R 10 M /d

N −4

d 10 M −4 max 10 Chondrule contribution Planetesimal contribution −5 −6 No chondrules 10 10 Isolation mass 10−6 10 100 1000 0 1 2 3 4 5 R [km] t [Myr]

100 t 0 =0.0 Myr 10 t=0.5 Myr t=1.0 Myr 10−1 t=2.0 Myr

−2 ] 10−2 10 −1 ] Ceres Moon Mars E M [km −3 [ R 10 M /d

N −4

d 10 10−4 M max −5 −6 Chondrule contribution 10 10 Planetesimal contribution 10−6 10 100 1000 0.0 0.5 1.0 1.5 2.0 R [km] t [Myr] (Johansen et al., 2015) Chondrule accretion leads to rapid formation of Mars-sized embryos in the terrestrial planet formation region Planetesimal accretion nevertheless more important than in the asteroid belt Larger chondrules are accreted more eﬃciently

Copenhagen 2015 (Lecture 3) Other topics 34 / 43 From planetesimals to planets

103 103 5AU 5AU 8AU 8AU 2 2 10 15AU 10 15AU 20AU 20AU 101 101 Z=0.02 E E /M /M c c M 100 M 100

10−1 10−1 Z=0.005

10−2 10−2 105 106 107 105 106 107 t/yr t/yr(Lambrechts & Johansen, 2014)

The largest planetesimals accrete the remaining pebbles and grow to planets in the next 1–5 Myr Growth depends strongly on the amount of heavy elements in the protoplanetary disc (Z = 0.01 in the Sun’s photosphere) (Lambrechts & Johansen, 2014) Gas-giant planets like Jupiter form if Z is high, in agreement with exoplanet surveys (Buchhave, Latham, Johansen, et al., 2012) Copenhagen 2015 (Lecture 3) Other topics 35 / 43 The critical core mass

10−2

80% 60% 40% 20% 0% 10−3

−4 10 5AU ⋅ Mpeb 10−5 30AU 5AU /yr) E

/(M −6

⋅ 10 M ⋅ 30AU Mplan 10−7

−8 τ <τ 10 τacc τdisc acc> disc 10−9 10−1 100 101 102 103 M c/ME (Ikoma et al., 2000) (Lambrechts, Johansen, & Morbidelli, 2014)

The critical core mass for envelope collapse increases when the accretion rate increases Planetesimal accretion rates at 5–10 AU yield core masses of 10-20 Earth masses – but the growth rate is too low to compete with gas dissipation Pebble accretion rates yield very high critical core masses of 100–200 Earth masses – in disagreement with measured core masses Copenhagen 2015 (Lecture 3) Other topics 36 / 43 Halting pebble accretion

Pebble accretion is stopped when the protoplanet grows massive enough to carve a gap in the pebble distribution

Gap formation known for Jupiter-mass planets (Paardekooper & Mellema, 2006) Lambrechts et al. (2014) demonstrate that pebble accretion is stopped already at 20 M⊕ at 5 AU, with isolation mass scaling as r 3/4 M = 20 M iso 5AU ⊕

Copenhagen 2015 (Lecture 3) Other topics 37 / 43 The critical core mass revisited

10−2

80% 60% 40% 20% 0% 10−3

−4 10 5AU ⋅ Mpeb 10−5 30AU 5AU /yr) E

/(M −6

⋅ 10 M ⋅ 30AU Mplan 10−7

−8 τ <τ 10 τacc τdisc acc> disc 10−9 10−1 100 101 102 103 M c/ME (Lambrechts et al., 2014) Protoplanets grow at the pebble accretion rate until pebble accretion is halted abruptly The envelope is then supercritical and collapses onto the core Gives an excellent ﬁt to Jupiter’s and Saturn’s heavy elements (Lambrechts et al., 2014)

Gas giants in wide orbits must have large cores masses (50-100 ME) Explains dichotomy between ice giants and gas giants

Copenhagen 2015 (Lecture 3) Other topics 38 / 43 Including planetary migration

1000 3.0x106

1000 100 2.5x106 10.0 20.0 10 10 2.0x106 100 ] 2

Z=1.0% E ]

E 1 1 t0=2 Myr 5.0

[yr] 6 [g/cm in M

0 1.5x10 t P M [M 10 peb M

0.1 0.1 Σ r = 5.0 AU 1.0 0 1.0x106 0.1 0.5 r0 = 10 AU 0.01 r = 15 AU 0.01 0 1 r0 = 25 AU r = 40 AU 0 0.5x106 0.001 r0 = 50 AU t =3.0Myr Σ D peb at 2 Myr 0.1 0.1 1 5 10 20 30 40 50 5 10 15 20 25 30 35 40 45 50

r [AU] r0 [AU]

Pebble accretion combined with protoplanetary disc evolution and planetary migration (Bitsch, Lambrechts, & Johansen, 2015) Jupiter analogue forms late (after 2 Myr) and far out (beyond 15 AU)

Migrates into 3 AU orbit while growing to 300 ME Growth tracks can be bundled into a growth map Early formed planets migrate to become hot and warm Jupiters Formation after 2 Myr yields a range of planetary classes

Copenhagen 2015 (Lecture 3) Other topics 39 / 43 Growth map with planetesimal accretion

5.0x106 1.0x106

6 4.5x10 1000 0.9x106 1000 6 4.0x10 0.8x106 3.5x106 100 0.7x106 100 6

3.0x10 E E 0.6x106 6 [yr] [yr] 2.5x10 in M in M 0 0 t t 10 P 0.5x106 10 P M M 2.0x106 0.4x106 1.5x106 1 0.3x106 1 1.0x106 6 6 0.2x10 5.0 0.5x10 0.1 0.1 0.1x106 0.1 5 10 15 20 25 30 35 40 45 50 4 6 8 10 12 14

r0 [AU] r0 [AU]

Accretion of planetesimals can not form cores within 5 Myr, even if planetesimal surface density enhanced by factor 8 (Bitsch et al., 2015) Hard to form Jupiter at 5 AU due to the slow accretion rate and the high migration rate

Copenhagen 2015 (Lecture 3) Other topics 40 / 43 Emergence regions of planetary classes

(Bitsch et al., 2015)

Copenhagen 2015 (Lecture 3) Other topics 41 / 43 Reaching the initial conditions for the Nice model

1000

100

10 ] E

[M 1 P M

0.1

Jupiter 0.01 Saturn Uranus Neptune tD=3.0Myr 0.001 5 10 15 20 25 (Bitsch et al., 2015) (Gomes et al., 2005) r [AU] In the Nice model the giant planets orbit initially in a compact conﬁguration Natural consequence of planetary migration combined with rapid pebble accretion Orbital architecture of the Nice model can be explained if the planetary embryos emerge after 1.5–2 Myr in initial orbits between 20 and 25 AU What happened to the embryos that formed closer to the Sun?

Copenhagen 2015 (Lecture 3) Other topics 42 / 43 Summary

Models and experiments of dust coagulation / fragmentation / bouncing are very advanced now Ice condensation may be another necessary ingredient for eﬃcient formation of pebbles Particle clumping by streaming instabilities / pressure bumps / vortices is by now a robust phenomenon studied by several groups with independent codes Pebble accretion is very eﬃcient at growth from planetesimals to planets – the full importance of this new growth mechanism is still being explored Asteroid belt and Kuiper belt may be sculpted by gravitational collapse, pebble accretion and planetesimal collisions Copenhagen 2015 (LectureFUTURE 3) : COMBINEOther topics IT ALL 43 / 43