Evolution of protoplanetary discs and why it is important for planet formation Bertram Bitsch

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Evolution of protoplanetary discs

and why it is important for planet formation

Bertram Bitsch

Lund Observatory

April 2015

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Observations of planets

⇒ How can we explain this diversity?

Data from exoplanet.org

Bertram Bitsch (Lund) Evolution of protoplanetary discs April 2015 2 / 41

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Outline

Introduction

Protoplanetary disc structure

Planet growth and migration

Planet formation in evolving

protoplanetary discs

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Planetary system evolution

(a) Collapse of interstellar cloud

(b) Formation of protostar with protoplanetary disc made out of dust and gas (c) Small particles stick and

form bigger objects

(c)-(e) Formation of planetesimals and planetary embryos (f) Formation of planets,

clearing of gas in disc in

≈ 10 Myr

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Protoplanetary discs in the Orion Nebula

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Observations of protoplanetary discs

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Composition of the disc

The inner regions of the disc are hotter than the outer regions:

⇒ Icy particles only in the outer parts of the disc!

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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

Gas giants: 10 M⊕ core accretes gas (< 10⁷ years) Terrestrial planets: protoplanets collide (10⁷–10⁸ years)

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Time-scale to build gas giants

Mamajek (2009)

Giant planet formation has to happen within the disc’s lifetime of a few Myr!

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Important quantities in the disc

Temperature T

Viscosityν = αH²Ω_K with:

I H is the thickness of the disc

I Ω_Kis the Keplerian frequency, Ω_K=pGM_?/r³

I α≈ 10⁻²− 10⁻⁴

Gas densityρg and gas surface density Σg: Σg=ρgH√

2π

0.5 1 1.5 2 2.5

r [a_Jup] -0.3

-0.2 -0.1 0 0.1 0.2 0.3

z in [aJup]

1e-11 2e-11 3e-11 4e-11 5e-11 6e-11 7e-11

ρ in g/cm3

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Importance of the disc structure

Growth and formation of planets relies on the disc structure:

Growth of dust particles to pebbles (Zsom et al., 2010; Birnstiel et al., 2012)

Movements of pebbles inside the gas disc (Brauer et al., 2008) Formation of planetesimals via streaming instability (Johansen &

Youdin, 2007)

Formation of planetary cores from embryos and planetesimals (Levison et al., 2010) or pebble accretion (Lambrechts & Johansen, 2012) Migration of planetary cores in the disc (Ward, 1997; Paardekooper &

Mellema, 2006; Kley et al., 2009)

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Radial drift of dust particles

P

v

_Kep

(1− ) η

F F

G

Disc is hotter and denser close to the star

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

η = −1 2

H r

2

∂ ln(P)

∂ 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

Particles sublimate when reaching higher temperatures close to the star

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Streaming instability: planetesimal formation

Gas orbits slightly slower than Keplerian

Particles lose angular momentum due to headwind

Particle clumps locally reduce headwind and are fed by isolated particles

v _Kep(1− )η

F FG P

Streaming instabilities feed on velocity difference between two components (gas and particles) at the same location

Interested in details of the S.I.? Ask Anders Johansen or Chao-Chin Yang!

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Streaming instability: lots of literature!

This is just a tiny example of literature to the streaming instabilty!

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Streaming instability: a movie

(Johansen et al. 2011)

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Protoplanetary disc structure

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The Minimum Mass Solar Nebula - MMSN

Spread appropriate mass of solids around the orbit of each planet in the solar system and multiply by 100 (add gas)

Power law through data (Hayashi (1981), Weidenschilling (1977)):

Σ_g(r ) = 1700 r 1AU

−3/2

g/cm² The planets accreted all solids (hence

”Minimum”)

The planets formed on their present orbits and did not move

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Constraints from Observations

Σ∝ R^−γ with γ = 0.4− 1.1

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Time evolution of the star and the disc

Accretion rate ˙M (∝ Σg) changes with time (Hartmann et al., 1998)

⇒ Accretion rate changes by a factor of 100 in 5Myr!

Star changes luminosity in time (Baraffe et al., 1998)

⇒ Stellar luminosity changes by a factor of 3 in 5Myr!

0 0.5 1 1.5 2

2 5

0.1 1 10

10⁻⁹ 5× 10⁻⁹ 10⁻⁸ 5× 10⁻⁸ 10⁻⁷

LinL⊙

˙ MinM/yr⊙

t in Myr L M˙

⇒ The disc is subject to massive changes in its lifetime!

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Disc Model

2D hydrodynamical disc model with viscous heating, radiative cooling and stellar irradiation with S ∝ L?:

1 2 3 4 5 6 7 8 9 r [a_Jup]

0 0.5 1 1.5 2 2.5 3

z in [aJup]

-13 -12.5 -12 -11.5 -11 -10.5 -10 -9.5 -9

log ( ρ in g/cm3 )

Bitsch et al., 2013

Mass flux through disc: ˙M constant at each r withα viscosity:

M = 3πνΣ = 3παH˙ ²Ω_KΣ

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Influence of opacity on cooling

Cooling of the disc:

F=− λc ρκ_R∇ER

Grey area marks transition in opacity at the ice line Change of opacity:

⇒ change of cooling Change of cooling:

⇒ change in T (r)

log (κ in cm2/g)

T in K

Transition κR = κP κ* -3

-2.5 -2 -1.5 -1 -0.5 0 0.5 1

10 100 1000

TinK

r [AU]

Transition M = 3.5˙ × 10⁻⁸M⊙/yr MMSN 50

200 500

1 10 100

2 3 4 5 20

1 10

Bitsch et al., 2015

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Influence of viscosity and ˙ M

Hydrostatic equilibrium:

T = H r

2

GM_? r

µ R bump in T : bump in H/r M disc:˙

M = 3πνΣ = 3παH˙ ²ΩKΣ M constant at each r :˙

⇒ dip in Σ

Σing/cm2

r [AU]

H/r

M = 3.5× 10˙ ⁻⁸M⊙/yr MMSN

50 200 500

10 100 1000

2 3 4 5 10 20

1

M = 3.5× 10˙ ⁻⁸M⊙/yr 0 MMSN

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

Bitsch et al., 2015

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Importance for the streaming instability

Streaming instabilities feed on velocity difference between two components (gas and particles) at the same location, caused by a reduction of the effective gravitational force by the radially outwards pointing force of the radial pressure gradient:

∆ =ηvK

c_s =−1 2

H r

∂ ln(P)

∂ ln(r ) Reduced ∆ helps the formation of large clumps via streaming instability (Bai & Stone, 2010b)

∆

r [AU]

H/r

M = 3.5˙ × 10⁻⁸M⊙/yr 0 MMSN

0.02 0.04 0.06 0.08 0.1 0.12

2 3 4 5 10 20

1

M = 3.5˙ × 10⁻⁸M⊙/yr 0 MMSN

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

Bitsch et al., 2015

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Change of ˙ M in time

TinK

r [AU]

Transition M = 1.0˙˙ × 10⁻⁷ M = 7.0× 10⁻⁸ M = 3.5˙ × 10⁻⁸ M = 1.75˙ × 10⁻⁸ M = 8.75˙ × 10⁻⁹ M = 4.375× 10˙ ⁻⁹

50 200 500

10 100

2 3 4 5 20

1 10

M decreases with decreasing Σ˙ M = 3πνΣ = 3παH˙ ²ΩKΣ Inner disc dominated by viscous heating for high ˙M, dominated by stellar heating for low ˙M

ΣGing/cm2

r [AU]

H/r

M = 1.0× 10˙ ⁻⁷ M = 7.0× 10˙ ⁻⁸ M = 3.5× 10˙ ⁻⁸ M = 1.75× 10˙ ⁻⁸ M = 8.75× 10˙ ⁻⁹ M = 4.375× 10˙ ⁻⁹ 1

10 50 100 200 500 1000

2 3 4 5 10 20

1

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

0.01 0.02 0.03 0.04 0.05 0.06

Bitsch et al., 2015

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Time evolution of the disc

Evolution in time follows Hartmann et al. 1998 equation:

log M˙ M/yr

!

=−8.00 − 1.40 log t_disc+ 10⁵yr 10⁶yr

.

TinK

r [AU]

Transition M = 1.0˙ × 10⁻⁷ M = 7.0˙ × 10⁻⁸ M = 3.5˙ × 10⁻⁸ M = 1.75˙ × 10⁻⁸ M = 8.75˙ × 10⁻⁹ M = 4.375˙ × 10⁻⁹

50 200 500

10 100

2 3 4 5 20

1 10

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Planet growth and migration

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Pebble accretion

Small pebbles (τ_f < 1) can be easily accreted by planetesimals (Lambrechts & Johansen, 2012)

Stokes number τ_f and friction time t_f: τ_f = t_fΩ_K= ρ•R

ρGc_sΩ_K = ρ•R ρGH

”Pebbles are weakly enough bound to the gas to feel the gravitational pull from the core, but strongly enough to deposit their kinetic energy through drag forces, when passing the core.”

Lambrechts & Johansen, 2012

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Scaling of pebble accretion

Core growth via pebbles

(Lambrechts & Johansen, 2014):

M˙_c= 2 τ_f 0.1

2/3

r_Hv_HΣ_Peb Growth faster in inner regions of the disc

Red dotsmark pebble isolation mass: Pebble accretion does not continue forever!

Lambrechts & Johansen, 2014

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Pebble isolation mass

Pebble isolation mass:

M_iso= 20 H/r 0.05

3

M_Earth

⇒ After pebble isolation mass is reached, gas accretion can start!

Lambrechts et al., 2014

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Gas accretion

0 10 20 30 40 50 60 70 80 90 100

1 10⁵ 2 10⁵ 3 10⁵ 4 10⁵ 5 10⁵

M [ME]

t [yr]

M_c M_env M_tot

Phase 1: accretion of solid core until pebble isolation (≈ 2 × 10⁵ yr) Phase 2: envelope contraction (≈ 4 × 10⁵ yr, following Piso &

Youdin, 2014), when M_c> Menv

Phase 3: rapid accretion of gas onto core when Mc< Menv (Machida et al. 2010)

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Planets in discs

Planet embedded in a disc creates a wake

Wake directed forwards in inner disc and backwards in outer disc Planetpushes inner (outer) discinwards (outwards),

inner (outer) discpushes planetoutwards (inwards)

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Type-II-migration

High mass planets (M_P > M_Jup) open gaps in discs (Crida et al.

2007):

P = h/q^1/3+ 50α/qh² < 1 with h = H/r Planet is locked in the disc

Planet moves with disc on ”accretion timescale”:

τν = r_p²/ν (up to a few Myrs) It is called Type-II-migration

0 50 100 150 200 250 300 350 400 450 500 550

0.5 1 1.5 2 2.5

Σ in g/cm2

r [a_Jup]

initial 200 Orbits

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Type-I-migration

Planet fully embedded in the disc, free to migrate with respect to the gas Waves carry energy and angular momentum

Torque calculated through Lindblad Resonances (e.g. Goldreich & Tremaine, 1980)

ILR: positive torque, OLR: negative torque OLR stronger than ILR:

⇒ inward migration( ˙a∝ q)

120 140 160 180 200 220 240 260 280 300 320 340

0.5 1 1.5 2 2.5

Σ in g/cm2

r [a_Jup]

initial 200 Orbits

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Migration map

Paardekooper et al. (2011): Analytic torque estimate of embedded low mass planets using gradients in the disc (Σ∝ r^−α^Σ; T ∝ r^−β^T)

γΓtot/Γ0=−0.9 − 3.22αΣ+ 3.92βT Γ₀ =q h

2

Σ_Pr_P⁴Ω²_K

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Planet formation in evolving

protoplanetary discs

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Evolution track starting at t

0

= 2 Myr

0.0001 0.001 0.01 0.1 1 10 100 1000

5 20 30 40

0.1 1 10

M [ME]

r [AU]

r₀ = 4 AU r₀ = 10 AU r₀ = 20 AU r₀ = 30 AU r₀ = 40 AU t_D=3.0Myr

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Planet formation at all orbital distances r

0

at t

0

= 2 Myr

M [ME] rf [AU]

r₀ [AU]

M_core M_env M_tot r_f r₀

0.1 1 10 100 1000

5 10 15 20 25 30 35 40 45 50

0.1 1 10 100 1000

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

2 5 20

1 10

H/r

r [AU] tdisc= 0.0Myr

tdisc= 0.1Myr tdisc= 0.2Myr tdisc= 0.5Myr tdisc= 1.0Myr tdisc= 2.0Myr tdisc= 3.0Myr

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Planet formation at all orbital distances r

0

at t

0

= 2 Myr

M [ME] rf [AU]

r₀ [AU]

M_core M_env M_tot r_f r₀

0.1 1 10 100 1000

5 10 15 20 25 30 35 40 45 50

0.1 1 10 100 1000

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

2 5 20

1 10

H/r

r [AU]

tdisc= 0.0Myr tdisc= 0.1Myr tdisc= 0.2Myr tdisc= 0.5Myr tdisc= 1.0Myr tdisc= 2.0Myr tdisc= 3.0Myr

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Planet formation in evolving disc

Everything below blue line: pebble isolation reached Everything above white line: M_core> Menv

0.5x10⁶ 1.0x10⁶ 1.5x10⁶ 2.0x10⁶ 2.5x10⁶ 3.0x10⁶

5 10 15 20 25 30 35 40 45 50 t0 [yr]

r₀ [AU]

0.1 1 10 100 1000

MP in ME 0.1 0.5 1.0

5.0 10.

20.

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Power law disc: MMSN

0.5x10⁶ 1.0x10⁶ 1.5x10⁶ 2.0x10⁶ 2.5x10⁶ 3.0x10⁶

5 10 15 20 25 30 35 40 45 50 t0 [yr]

r₀ [AU]

0.1 1 10 100 1000

MP in ME

0.1 20.

10.

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Schematic view of planet formation

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Summary

Protoplanetary discs evolve in time and change their properties (Σ, T , H), which matters for all processes inside the disc!

Resulting planetary systems depend crucially on the underlying disc structure

Early planet formation produces mainly gas giants

Giant planets form far out in the disc: no in-situ formation Smaller planets can form in-situ, but form late

Late formation scenario preferred: larger diversity of planetary types as predicted by observations