Bertram Bitsch: Formation of Giant Planets Via Pebble Accretion

Formation of giant planets via pebble accretion

Bertram Bitsch

Lund Observatory

October 2016

Bertram Bitsch (Lund) Formation of giant planets October 2016 1 / 25 The four steps of planet formation

1 Dust to pebbles µm dm: contact forces during collision lead to sticking → 2 Pebbles to planetesimals dm km: gravitational collapse of pebble clouds form planetesimals → 3 Planetesimals to protoplanets km 1,000 km: gravity (run-away accretion) → 4 Protoplanets to planets 7 Gas giants: 10 M⊕ core accretes gas (< 10 years) Terrestrial planets: protoplanets collide (107–108 years)

Bertram Bitsch (Lund) Formation of giant planets October 2016 2 / 25 The four steps of planet formation

Bertram Bitsch (Lund) Formation of giant planets October 2016 2 / 25 Outline

Pebble and gas accretion Planet migration Planet formation

Bertram Bitsch (Lund) Formation of giant planets October 2016 3 / 25 Classical scenario of giant planet formation

(Pollack et al. 1996)

Large planetesimals used for accretion Planesimal density of a few MMSN needed to make cores at 5AU Growth timescale increases strongly× with orbital distance Making giant planet cores at large r with Z = Z very tough! ⇒ Bertram Bitsch (Lund) Formation of giant planets October 2016 4 / 25 Accretion of small planetesimals

accretion of small planetesimals (1km in size) very ineﬃcient accretion scattering of planetesimals by embryos: aerodynamic drag removes planesimals from the embryos and places them outside their orbits Migration of embryo results in more scattering and not accretion (Tanaka & Ida 1999) Growth only possible if cores stocastically jump into new feeding zones? ⇒ Core accretion via planetesimals very tough! (Levison et al. 2010) But what about even smaller objects? ⇒ Bertram Bitsch (Lund) Formation of giant planets October 2016 5 / 25 Remember radial drift v Kep (1− η )

F F G P

Disc is hotter and denser close to the star: radial pressure gradient

Radial pressure gradient force mimics decreased gravity ⇒ gas orbits slower than Keplerian:

1 H 2 ∂ ln(P) η = − 2 r ∂ ln(r)

Particles do not feel the pressure gradient force and want to orbit Keplerian

Headwind from sub-Keplerian gas drains angular momentum from particles, so they spiral in through the disc

Bertram Bitsch (Lund) Formation of giant planets October 2016 6 / 25 Pebble accretion in the Hill regime

Most planetesimals are simply scattered by the protoplanet Pebbles spiral in towards the protoplanet due to gas friction Pebbles are accreted from ⇒ the entire Hill sphere Accretion rate by pebble accretion in Hill regime

τ 2/3 M˙ = 2 f r v Σ c 0.1 H H Peb

(Ormel & Klahr 2010; Ormel 2013; Lambrechts &

Johansen, 2012, 2014)

Bertram Bitsch (Lund) Formation of giant planets October 2016 7 / 25 Pebble accretion regimes

∆v: Orbital speed of gas and pebbles relative to Keplerian speed vH = ΩRH: Approach speed of gas and pebbles at the edge of the Hill sphere Two main pebble accretion regimes: (Lambrechts & Johansen, 2012)

1 Bondi regime (when ∆v vH) Particles pass the core with speed ∆v, giving M˙ R2 M2 ∝ B ∝ 2 Hill regime (when ∆v vH) Particles enter Hill sphere with speed v ΩR , giving M˙ M2/3 H ≈ H ∝ Bertram Bitsch (Lund) Formation of giant planets October 2016 8 / 25 Importance of the initial seed mass

(Visser & Ormel, 2016)(Lambrechts & Johansen, 2012) Minimum mass for pebble accretion to work: 100 km Maximum sizes of planetesimals from Streaming∼ Instability are in that regime: see T. Birnstiel! Growth in⇒ Bondi (drift) regime slow; Pebble transition mass: q 3 1 (ηvK) Mt = 3 GΩK

Bertram Bitsch (Lund) Formation of giant planets October 2016 9 / 25 Pebble accretion in turbulent discs

(Xu, Bai & Murray-Clay, to be submitted; courtesy of Xuening Bai)

Pebble accretion in 3D discs with pure hydro, ideal MHD and ambipolar diﬀusion (AD) Accretion rates match very well for diﬀerent disc set-ups Simulations follow trend of the theoretical predictions of pebble accretion for both accretion regimes

Bertram Bitsch (Lund) Formation of giant planets October 2016 10 / 25 Dust gaps in discs: Pebble isolation mass

Gaps in dust disc are wider than in the gas disc (Paardekooper & Mellema, 2006)

Pebble isolation mass:

H/r 3 Miso = 20 M 0.05 Earth

(Lambrechts et al., 2014) Pebble accretion self-terminates: no accretion of solids any more! ⇒ After pebble isolation mass is reached, gas accretion can start! ⇒ Bertram Bitsch (Lund) Formation of giant planets October 2016 11 / 25 The critical core mass

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

Bertram Bitsch (Lund) Formation of giant planets October 2016 12 / 25 tdisc = 0.0 Myr tdisc = 0.1 Myr 0.08 tdisc = 0.2 Myr tdisc = 0.5 Myr t = 1.0 Myr 0.07 disc tdisc = 2.0 Myr tdisc = 3.0 Myr 0.06 MMSN

0.05 H/r 0.04

0.03

0.02

0.01

1 2 5 10 20 r [AU]

Disc structure: opacity transition at the water ice line 2D (r-z) hydro disc model with 1 radiative cooling, viscous and 0.5 stellar heating 0

/g) -0.5 2

˙ 2 -1 M = 3πνΣ = 3παH Ω Σ in cm g K g κ -1.5 log (

Bump in κR at the ice line -2

less cooling (D 1/κ ) -2.5 R Transition κ ⇒ ∝ R bump in T -3 ⇒ 10 100 1000 dip in Σ T in K ⇒ g 8 500 M˙ =3.5 10− M / yr × MMSN⊙ 1000 200

500 100

2 50 Transition 200 8 M˙ =3.5 10− M /yr × MMSN⊙ in g/cm

100 T in K G

Σ 10 50

10 1 2 345 10 20 1 234510 20 r [AU] r [AU]

(Bitsch et al., 2014, 2015a)

Bertram Bitsch (Lund) Formation of giant planets October 2016 13 / 25 Disc structure: opacity transition at the water ice line 2D (r-z) hydro disc model with 1 radiative cooling, viscous and 0.5 tdisc = 0.0 Myr 0 stellar heatingtdisc = 0.1 Myr

/g) -0.5 0.08 tdisc = 0.2 Myr 2 t = 0.5 Myr ˙ disc 2 -1 M = 3πνΣ = 3παH Ω Σ in cm g t = 1.0 Myr K g κ 0.07 disc t = 2.0 Myr -1.5 disc log ( t = 3.0 Myr Bump in κR discat the ice line -2 0.06 MMSN less cooling (D 1/κ ) -2.5 R Transition κ ⇒ ∝ R bump0.05 in T -3 ⇒ 10 100 1000 H/r dip in Σg T in K ⇒ 0.04 8 500 M˙ =3.5 10− M / yr × MMSN⊙ 1000 0.03 200

500 100 0.02 2 50 Transition 200 8 M˙ =3.5 10− M /yr × MMSN⊙ in g/cm 0.01 100 T in K G

Σ 10 50 1 2 5 10 20 r [AU] 10 1 2 345 10 20 1 234510 20 r [AU] r [AU]

(Bitsch et al., 2014, 2015a)

Bertram Bitsch (Lund) Formation of giant planets October 2016 13 / 25 Planet Migration in a slide

Lindblad torques drive strong inward migration:a ˙ q ∝ Corotation torque can drive outward migration, but depends on gradients in Σg and T (Paardekooper & Mellema, 2006; Baruteau & Masset, 2008) Giant planets open gaps in disc, where the gap opening depends on H/r and α (Crida et al. 2006; Crida & Morbidelli 2007)

Giant planets migrate (maybe) with viscous accretion rate (Lin & Papaloizou, 1986)

Bertram Bitsch (Lund) Formation of giant planets October 2016 14 / 25 Type-I migration in evolving discs ˙ 8 M = 3.5 10− M /yr 0.06 ×

0.05

0.04 H/r 0.03

0.02 7 M˙ =1.0 10− × 8 M˙ =7.0 10− × 8 M˙ =3.5 10− 0.01 × 8 M˙ =1.75 10− × 9 M˙ =8.75 10− × 9 M˙ =4.375 10− 0 ×

1000 500

200

2 100 50 in g/cm G Σ

10 7 M˙ =1.0 10− × 8 M˙ =7.0 10− × 8 M˙ =3.5 10− × 8 M˙ =1.75 10− × 9 M˙ =8.75 10− × 9 M˙ =4.375 10− 1 × 1 2 345 10 20 ˙ 9 M = 8.75 10− M /yr r [AU] × Outward migration in regions where H/r drops with increasing r!

(Bitsch et al., 2015a)

Bertram Bitsch (Lund) Formation of giant planets October 2016 15 / 25 tdisc = 0.0 Myr tdisc = 0.1 Myr 0.08 tdisc = 0.2 Myr tdisc = 0.5 Myr t = 1.0 Myr 0.07 disc tdisc = 2.0 Myr tdisc = 3.0 Myr 0.06 MMSN

0.05 H/r 0.04

0.03

0.02

0.01

1 2 5 10 20 r [AU]

Evolution tracks 1000

100

10 ]

E 1 t0=2 Myr M [M 0.1

r0 = 5.0 AU r0 = 10 AU 0.01 r0 = 15 AU r0 = 25 AU r0 = 40 AU 0.001 r0 = 50 AU tD=3.0Myr Zero torque 3 Myr 0.5 1 5 10 20 30 40 50 r [AU]

(Bitsch et al., 2015b)

Bertram Bitsch (Lund) Formation of giant planets October 2016 16 / 25 Evolution tracks 1000

100

10 ]

E 1 t0=2 Myr M [M

0.1 tdisc = 0.0 Myr tdisc = 0.1 Myr 0.08 tdisc = 0.2 Myr r = 5.0 AU tdisc = 0.5 Myr 0 tdisc = 1.0 Myr r0 = 10 AU 0.07 t = 2.0 Myr 0.01 disc r0 = 15 AU tdisc = 3.0 Myr 0.06 MMSN r0 = 25 AU r0 = 40 AU 0.05 0.001 r0 = 50 AU t =3.0Myr H/r D 0.04 Zero torque 3 Myr

0.03 0.5 1 5 10 20 30 40 50

0.02 r [AU]

0.01 (Bitsch et al., 2015b)

1 2 5 10 20 r [AU] Bertram Bitsch (Lund) Formation of giant planets October 2016 16 / 25 Planet formation in evolving disc Everything below blue line: pebble isolation reached Everything above white line: Mcore > Menv

3.0x106

1000 2.5x106 10.0 20.0

2.0x106 100

Z=1.0% E 5.0

[yr] 6 in M

0 1.5x10 t 10 P M

1.0 1.0x106 0.1 0.5 1

0.5x106

0.1 5 10 15 20 25 30 35 40 45 50

r0 [AU]

t0 formation time of planetary seed; r0 starting orbital distance (Bitsch et al.,2015b) Bertram Bitsch (Lund) Formation of giant planets October 2016 17 / 25 Randomization of parameters

Gaussian distribution with median at [Fe/H] = 0.0678 (Cassagrande et al. 2011) Time parameters: I Lifetime of the disc, median at 3 Myr with [1-5] Myr I Starting time of planetary seed is [0-5] Myr Starting location of planetary seed: [0.1:50] AU

10000 0.6

0.4 1000

0.2 100 ] E

[M 0 P [Fe/H] M 10 -0.2

1 -0.4

0.1 -0.6 0.1 1 10 100 r [AU] (Bitsch & Johansen, submitted) Bertram Bitsch (Lund) Formation of giant planets October 2016 18 / 25 MMSN 10000 0.6

0.4 1000

0.2 100 ] E

[M 0 P [Fe/H] M 10 -0.2

1 -0.4

0.1 -0.6 0.1 1 10 100 r [AU] (Bitsch & Johansen, submitted)

−3/2 MMSN disc is very steep (Σg r ): fast inward migration MMSN disc can not explain exoplanet∝ observations ⇒ Bertram Bitsch (Lund) Formation of giant planets October 2016 19 / 25 Late formation

Starting time at t0 > 2 Myr (remember to reach Mt!)

10000 0.6

0.4 1000

0.2 100 ] E

[M 0 P [Fe/H] M 10 -0.2

1 -0.4

0.1 -0.6 0.1 1 10 100 r [AU] (Bitsch & Johansen, submitted)

Bertram Bitsch (Lund) Formation of giant planets October 2016 20 / 25

Accreted material of growing planets

✶

✵✵☎ ✵

✡

☛

❈

✠

✎

✏

✑

✶

✵☎ ✵

☞

✌

✍

✟

✞

✝

✆

✖

✗

✒

✓

✔

✙

✛

✶

☎ ✵

✚

❍

❖

✘

✸ ✺

☎

❧✜✢✣❚✮

✩ ✂ ✧

✜

❊ ✤✦✧ ★✧

❧✜

✺

✵☎

✶

✵☎

✶ ✷ ✸ ✹ ✺

✥ ✁✂✄

(Madhusudhan, Bitsch, et al., in review)

Bertram Bitsch (Lund) Formation of giant planets October 2016 21 / 25 Growth of Jupiter planets

10 HJ, 3 Myr CJ, 3 Myr CJ, 5 Myr 1 CO CH4 CO2 H2O 0.1 ] J 0.01 M [M

0.001

0.0001

1e-05 5 10 15 20 25 30 35 40 45 50 r [AU]

(Bitsch et al. 2015b & Madhusudhan, Bitsch, et al., in review) Bertram Bitsch (Lund) Formation of giant planets October 2016 22 / 25 Composition of the disc

Species Tcond [K] X/H CO 20 0.45 C/H (0.9 C/H for T < 70 K) × × CH4 30 0.45 C/H (0 for T < 70 K) × CO2 70 0.1 C/H × H2O 150 O/H - (3 Si/H + CO/H + 2 CO2/H) Silicates 1500× Si/H ×

Volume fractions of species in terms of elemental volume fractions for solar composition (Asplund et al. 2009): O/H = 4.9 10−4 × C/H = 2.7 10−4 × Si/H = 3.2 10−5 ×

Bertram Bitsch (Lund) Formation of giant planets October 2016 23 / 25 But: photoevaporation and late-stage planetesimal accretion could change the atmospheric composition as well!

Planetary composition compared to solar

{C/H} of Jupiter

1 {C/H}

HJ CJ, 3 Myr CJ, 5 Myr HJ, core erosion CJ, 3 Myr, core erosion CJ, 5 Myr, core erosion

C/O = 0.54 (Solar) 0.1 0.1 1 10 {O/H}

(Madhusudhan, Bitsch, et al., in review)

Bertram Bitsch (Lund) Formation of giant planets October 2016 24 / 25 Planetary composition compared to solar

{C/H} of Jupiter

1 {C/H}

HJ CJ, 3 Myr CJ, 5 Myr HJ, core erosion CJ, 3 Myr, core erosion CJ, 5 Myr, core erosion

C/O = 0.54 (Solar) 0.1 0.1 1 10 {O/H}

(Madhusudhan, Bitsch, et al., in review) But: photoevaporation and late-stage planetesimal accretion could change the atmospheric composition as well! Bertram Bitsch (Lund) Formation of giant planets October 2016 24 / 25 Summary Migration requires large initial orbital distances to form cold gas giants Formation of giant planets at wide orbits including planet migration possible with pebble accretion in discs with solar Z (Bitsch et al. 2015b) Formation of giant planets depends on the underlying disc model and on the chemical composition of the disc itself (Bitsch & Johansen 2016) Missing links: Planets cross (multiple) ice lines during their formation, which changes the chemical composition of the accreted material Predictions for Jupiter’s formation with core erosion:

I Initial formation at r0 > rCO! Solar C/O ratio for Jupiter’s atmosphere! Hot Jupiters (by migration) have roughly solar C/H, but by scattering they have sub-solar C/H or slightly super-solar C/H (if core erosion)

Bertram Bitsch (Lund) Formation of giant planets October 2016 25 / 25