Evolution of protoplanetary discs - and why it is ...home.thep.lu.se/~anders/ATP_slides/150415-BertB.pdf · Bitsch et al., 2013 Mass ux through disc: M_ constant at each r with viscosity:

Evolution of protoplanetary discsand why it is important for planet formation

Bertram Bitsch

Lund Observatory

April 2015

Bertram Bitsch (Lund) Evolution of protoplanetary discs April 2015 1 / 41

Observations of planets

⇒ How can we explain this diversity?

Data from exoplanet.org


Outline

Introduction

Protoplanetary disc structure

Planet growth and migration

Planet formation in evolvingprotoplanetary discs


Planetary system evolution

(a) Collapse of interstellarcloud

(b) Formation of protostarwith protoplanetary discmade out of dust and gas

(c) Small particles stick andform bigger objects

(c)-(e) Formation of planetesimalsand planetary embryos

(f) Formation of planets,clearing of gas in disc in≈ 10 Myr


Protoplanetary discs in the Orion Nebula


Observations of protoplanetary discs


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!


The four steps of planet formation

1 Dust to pebblesµm → dm: contact forces during collision lead to sticking

2 Pebbles to planetesimalsdm → km: gravitational collapse of pebble clouds form planetesimals

3 Planetesimals to protoplanetskm → 1,000 km: gravity (run-away accretion)

4 Protoplanets to planetsGas giants: 10 M⊕ core accretes gas (< 107 years)Terrestrial planets: protoplanets collide (107–108 years)


Time-scale to build gas giants

Mamajek (2009)

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


Important quantities in the disc

Temperature TViscosity ν = αH2ΩK with:

I H is the thickness of the discI ΩK is the Keplerian frequency, ΩK =

√GM?/r3

I α ≈ 10−2 − 10−4

Gas density ρg and gas surface density Σg:

Σg = ρgH√

2π

0.5 1 1.5 2 2.5

r [aJup]

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

z in

[a

Jup]

1e-11

2e-11

3e-11

4e-11

5e-11

6e-11

7e-11

ρ in

g/c

m3


Importance of the disc structureGrowth and formation of planets relies on the disc structure:

Growth of dust particles to pebbles (Zsom et al., 2010; Birnstiel etal., 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 (Levisonet al., 2010) or pebble accretion (Lambrechts & Johansen, 2012)

Migration of planetary cores in the disc (Ward, 1997; Paardekooper &Mellema, 2006; Kley et al., 2009)


Radial drift of dust particles

P

v η(1− )Kep

FFG

Disc is hotter and denser close to the star

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

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, sothey spiral in through the disc

Particles sublimate when reaching higher temperatures close to the star


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 isolatedparticles

v η(1− )Kep

FFG P

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

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


Streaming instability: lots of literature!

This is just a tiny example of literature to the streaming instabilty!Bertram Bitsch (Lund) Evolution of protoplanetary discs April 2015 14 / 41

Streaming instability: a movie

(Johansen et al. 2011)


Protoplanetary disc structure


The Minimum Mass Solar Nebula - MMSN

Spread appropriate mass of solidsaround the orbit of each planet in thesolar system and multiply by 100 (addgas)

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

Σg(r) = 1700( r

1AU

)−3/2g/cm2

The planets accreted all solids (hence”Minimum”)

The planets formed on their presentorbits and did not move


Constraints from Observations

Σ ∝ R−γ with γ = 0.4− 1.1


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 50.1 1 10

10−9

5× 10−9

10−8

5× 10−8

10−7

Lin

L⊙

Min

M⊙/yr

t in Myr

LM

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


Disc Model

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

1 2 3 4 5 6 7 8 9

r [aJup]

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

/cm

3 )

Bitsch et al., 2013

Mass flux through disc: M constant at each r with α viscosity:

M = 3πνΣ = 3παH2ΩKΣ


Influence of opacity on cooling

Cooling of the disc:

F = − λc

ρκR∇ER

Grey area marks transition inopacity at the ice line

Change of opacity:⇒ change of cooling

Change of cooling:⇒ change in T (r)

log (

κ in c

m2/g

)

T in K

TransitionκR = κP

κ*-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

10 100 1000

Tin

K

r [AU]

TransitionM = 3.5× 10−8M⊙/yr

MMSN

50

200

500

1

10

100

2 3 4 5 201 10

Bitsch et al., 2015


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 constant at each r :⇒ dip in Σ

Σin

g/cm

2

r [AU]

H/r

M = 3.5× 10−8M⊙/yrMMSN

50

200

500

10

100

1000

2 3 4 5 10 201

M = 3.5× 10−8M⊙/yrMMSN

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

Bitsch et al., 2015


Importance for the streaming instabilityStreaming instabilities feed onvelocity difference between twocomponents (gas and particles)at the same location, caused bya reduction of the effectivegravitational force by theradially outwards pointing forceof the radial pressure gradient:

∆ = ηvKcs

= −1

2

H

r

∂ ln(P)

∂ ln(r)

Reduced ∆ helps the formationof large clumps via streaminginstability (Bai & Stone, 2010b)

∆

r [AU]

H/r

M = 3.5× 10−8M⊙/yrMMSN

0

0.02

0.04

0.06

0.08

0.1

0.12

2 3 4 5 10 201

M = 3.5× 10−8M⊙/yrMMSN

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

Bitsch et al., 2015


Change of M in timeT

inK

r [AU]

TransitionM = 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 5 201 10

M decreases with decreasing Σ


Inner disc dominated by viscousheating for high M, dominatedby stellar heating for low M

ΣG

ing/cm

2

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 10 201

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


Time evolution of the disc

Evolution in time follows Hartmann et al. 1998 equation:

log

(M

M/yr

)= −8.00− 1.40 log

(tdisc + 105yr

106yr

).

Tin

K

r [AU]

TransitionM = 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 5 201 10


Planet growth and migration


Pebble accretionSmall pebbles (τf < 1) can be easily accreted by planetesimals(Lambrechts & Johansen, 2012)Stokes number τf and friction time tf :

τf = tfΩK =ρ•R

ρGcsΩK =

ρ•R

ρGH

”Pebbles are weakly enough boundto the gas to feel the gravitationalpull from the core, but stronglyenough to deposit their kineticenergy through drag forces, whenpassing the core.”

Lambrechts & Johansen, 2012


Scaling of pebble accretion

Core growth via pebbles(Lambrechts & Johansen, 2014):

Mc = 2( τf

0.1

)2/3rHvHΣPeb

Growth faster in inner regions ofthe disc

Red dots mark pebble isolationmass: Pebble accretion does notcontinue forever!

Lambrechts & Johansen, 2014


Pebble isolation mass

Pebble isolation mass:

Miso = 20

(H/r

0.05

)3

MEarth

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

Lambrechts et al., 2014


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]

McMenvMtot

Phase 1: accretion of solid core until pebble isolation (≈ 2× 105 yr)

Phase 2: envelope contraction (≈ 4× 105 yr, following Piso &Youdin, 2014), when Mc > Menv

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


Planets in discs

Planet embedded in a disc creates a wake

Wake directed forwards in inner disc and backwards in outer disc

Planet pushes inner (outer) disc inwards (outwards),inner (outer) disc pushes planet outwards (inwards)


Type-II-migrationHigh mass planets (MP > MJup) open gaps in discs (Crida et al.2007):

P = h/q1/3 + 50α/qh2 < 1 with h = H/r

Planet is locked in the discPlanet moves with disc on ”accretion timescale”:τν = r2

p/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/c

m2

r [aJup]

initial200 Orbits


Type-I-migrationPlanet 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/c

m2

r [aJup]

initial200 Orbits


Migration mapPaardekooper et al. (2011): Analytic torque estimate of embedded lowmass planets using gradients in the disc (Σ ∝ r−αΣ ; T ∝ r−βT)

γΓtot/Γ0 = −0.9− 3.22αΣ + 3.92βT Γ0 =(qh

)2ΣPr

4PΩ2

K


Planet formation in evolvingprotoplanetary discs


Evolution track starting at t0 = 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 AUr0 = 10 AUr0 = 20 AUr0 = 30 AUr0 = 40 AUtD=3.0Myr


Planet formation at all orbital distances r0 at t0 = 2 MyrM

[M

E]

r f [

AU

]

r0 [AU]

McoreMenvMtot

rfr0

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 5 201 10

H/r

r [AU]

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


Planet formation at all orbital distances r0 at t0 = 2 MyrM

[M

E]

r f [

AU

]

r0 [AU]

McoreMenvMtot

rfr0

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 5 201 10

H/r

r [AU]

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


Planet formation in evolving discEverything below blue line: pebble isolation reachedEverything above white line: Mcore > Menv

0.5x106

1.0x106

1.5x106

2.0x106

2.5x106

3.0x106

5 10 15 20 25 30 35 40 45 50

t 0 [

yr]

r0 [AU]

0.1

1

10

100

1000

MP in

ME

0.1 0.51.0

5.0

10.

20.


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

t 0 [

yr]

r0 [AU]

0.1

1

10

100

1000

MP in

ME

0.1 20.

10.


Schematic view of planet formation


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 discstructure

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 typesas predicted by observations


Documents

Evolution of protoplanetary discs - and why it is ...home.thep.lu.se/~anders/ATP_slides/150415-BertB.pdf · Bitsch et al., 2013 Mass ux through disc: M_ constant at each r with viscosity: