in evolving protoplanetary discs Bertram Bitsch · Planet formation in evolving protoplanetary discs Bertram Bitsch Lund Observatory July 2015 Bertram Bitsch (Lund) Planet formation

Planet formationin evolving protoplanetary discs

Bertram Bitsch

Lund Observatory

July 2015

Bertram Bitsch (Lund) Planet formation July 2015 1 / 18

OutlineTime evolving discs, planet migration and pebble & gas accretion!

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

Bitsch et al. (2015), Lambrechts & Johansen (2012), Machida et al. (2010)


Time-scale to build gas giants

Mamajek (2009) Hartmann et al. (1998)

The protoplanetary disc evolves during time of a few Myr

Giant planet formation has to happen within the disc’s 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


Cooling of the disc

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

cm

2/g

)

T in K

TransitionκR

-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., 2014, 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 = 3πνΣ = 3παH2ΩKΣ

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., 2014, 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

M = 3πνΣ = 3παH2ΩKΣEvolution in time followsHartmann et al. 1998 equation:

log

(M

M/yr

)= −8.00 − 1.40 log

(tdisc + 105yr

106yr

).

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

See also: K. Baillie et al. (2015) and his poster!

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

2 5 201 10

H/r

r [AU]



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

M = 3πνΣ = 3παH2ΩKΣEvolution in time followsHartmann et al. 1998 equation:

log

(M

M/yr

)= −8.00 − 1.40 log

(tdisc + 105yr

106yr

).

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

See also: K. Baillie et al. (2015) and his poster!

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

2 5 201 10

H/r

r [AU]



Pebble accretionSmall pebbles (τf < 1) can be easily accreted by planetesimals(see X. Bai and for planetesimal formation see C.-C. Yang and D. Carrera)

Stokes number τf and frictiontime tf :

τf = tfΩK =ρ•R

ρGcsΩK =

ρ•R

ρGH

Core growth via pebbles:

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, 2012, 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


Planet growth

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

Phase 2: envelope contraction until Menv ≈ Mc, faster for larger Mc

(Piso & Youdin, 2014)

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


Planet migration

Paardekooper et al. (2011):Analytic torque estimate ofembedded low mass planetsusing gradients in the disc(Σ ∝ r−αΣ ; T ∝ r−βT):

γΓtot

Γ0= −0.9− 3.22αΣ + 3.92βT

Γ0 =(qh

)2ΣPr

4PΩ2

K

Gap opening planets migratein type-II migration

M = 3.5× 10−8M/yr

M = 8.75× 10−9M/yr

Bitsch et al., 2015

See also: talk by A. Crida (yesterday)!


Evolution track starting at t0 = 2 Myr until tf = 3 Myr

0.0001

0.001

0.01

0.1

1

10

100

1000

5 20 30 4050 0.1 1 10

M [

ME]

r [AU]

r0 = 5.0 AUr0 = 10 AUr0 = 15 AUr0 = 25 AUr0 = 40 AUr0 = 50 AUtD=3.0Myr

(Bitsch et al., in review)

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

2 5 201 10

H/r

r [AU]



Evolution track starting at t0 = 2 Myr until tf = 3 Myr

0.0001

0.001

0.01

0.1

1

10

100

1000

5 20 30 4050 0.1 1 10

M [

ME]

r [AU]

r0 = 5.0 AUr0 = 10 AUr0 = 15 AUr0 = 25 AUr0 = 40 AUr0 = 50 AUtD=3.0Myr

(Bitsch et al., in review)

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

2 5 201 10

H/r

r [AU]



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

10.0

20.0

Z=1.0%

t0 formation time of planetary seed; r0 starting orbital distance (Bitsch et al., in review)


Link to observations

r/AU 5.2 9.6 19.2 30.1M/M⊕ 318 95.2 14.5 17.1

Nice model:

Compact configuration of planets that then went unstable:

r/AU ≈ 5 ≈ 8 ≈ 19 ≈ 17



r/AU 5.2 9.6 19.2 30.1M/M⊕ 318 95.2 14.5 17.1

Nice model:


r/AU ≈ 5 ≈ 8 ≈ 19 ≈ 17



r/AU 5.2 9.6 19.2 30.1M/M⊕ 318 95.2 14.5 17.1

Nice model:


r/AU ≈ 5 ≈ 8 ≈ 19 ≈ 17


Power law disc: MMSNEverything 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 20.0

10.0



Planet formation via planetesimal growth with Zpla = 8.0%Everything below red line: planetesimal isolation reachedEverything above white line: Mcore > Menv

0.5x106

1.0x106

1.5x106

2.0x106

2.5x106

3.0x106

3.5x106

4.0x106

4.5x106

5.0x106

5 10 15 20 25 30 35 40 45 50

t 0 [

yr]

r0 [AU]

0.1

1

10

100

1000

MP in

ME


0.1x106

0.2x106

0.3x106

0.4x106

0.5x106

0.6x106

0.7x106

0.8x106

0.9x106

1.0x106

4 6 8 10 12 14

t 0 [yr]

r0 [AU]

0.1

1

10

100

1000

MP in M

E

0.1

5.0


Planet formation via planetesimal growth with Zpla = 8.0%Everything below red line: planetesimal isolation reachedEverything above white line: Mcore > Menv

0.5x106

1.0x106

1.5x106

2.0x106

2.5x106

3.0x106

3.5x106

4.0x106

4.5x106

5.0x106

5 10 15 20 25 30 35 40 45 50

t 0 [

yr]

r0 [AU]

0.1

1

10

100

1000

MP in

ME


0.1x106

0.2x106

0.3x106

0.4x106

0.5x106

0.6x106

0.7x106

0.8x106

0.9x106

1.0x106

4 6 8 10 12 14

t 0 [yr]

r0 [AU]

0.1

1

10

100

1000

MP in M

E

0.1

5.0


Summary

Protoplanetary discs evolve in time and change their properties (Σ,T , H), which matters for all processes inside the disc (Bitsch et al. 2014, 2015)

Resulting planetary systems depend crucially on the underlyingprotoplanetary disc structure

Early planet formation produces mainly gas giants

Giant planets form far out in the disc and migrate into the inner disc

Smaller planets can form in-situ, but form late

Late formation scenario preferred: larger diversity of planetary types

Formation with planetesimals not efficient and can not explain gasgiants at r > 0.2 AU!


Graphical summary

Bitsch et al., in reviewBertram Bitsch (Lund) Planet formation July 2015 18 / 18

Documents

in evolving protoplanetary discs Bertram Bitsch · Planet formation in evolving protoplanetary discs Bertram Bitsch Lund Observatory July 2015 Bertram Bitsch (Lund) Planet formation