planet formation in a disk with a dead zone

Planet Formation in a disk with a Dead ZoneSoko Matsumura (Northwestern University)

Ralph Pudritz (McMaster University)Edward Thommes (Northwestern University)

Planet formation and migration in an evolving disk with a dead zone Pollack et al. (1996), Hubickyj et al. (2005): giant planet

formation at a fixed orbital radius (~ 5.2 AU) with no disk evolution

Alibert et al. (2005) studied giant planet formation with migration and disk evolution, and found that planet migration can speed up the formation. Jupiter can be made within about 106 years. Planet migration has to be at least 10 times slower.

One of the problems of the core accretion scenario: planet migration seems to be too fast.

Planet formation and migration in an evolving disk with a dead zone

If a planet is made outside the dead zone, we may not need to artificially slow down the planet migration.

Time [years]

30

20

10

0

Dis

k ra

dius

[AU

]

0 2x106 4x106 6x106 8x106 107

α = 10-2

α = 10-5

Evolution of Dead Zones

Gammie (1996): Mass accretion through the surface layers can explain the observed mass accretion rate onto the central star.

Dead Zone

αactiveαdead

Evolution of Dead Zones

Averaged viscosity

2/12/16 rt

rdtdM

hchc sdeaddeadactivecrit

s

2

1810~

yearM

dtdM

dtdM

solardeadactive

Evolution of Dead Zones

104 105 106 107

Time [years]

100

10

1

0.1

0.01

Dis

k ra

dius

[AU

]

Time [years]

30

20

10

0

Dis

k ra

dius

[AU

]

0 2x106 4x106 6x106 8x106 107

Evolution of Dead Zones

104 105 106 107

Time [years]

100

10

1

0.1

0.01

Dis

k ra

dius

[AU

]

106

104

102

1

10-2

10-4

Sur

face

mas

s de

nsity

Σ [g

cm

-2]

Disk radius [AU]0.01 0.1 1. 10. 100.

104 yrs

105 yrs

106 yrs107 yrs

Mdisk< MJ

Mdisk~ 0.01 Msolar

Pollack et al. (1996)

Planet Formation (core accretion scenario)

Core accretion + Gas accretion

Planet Formation (core accretion scenario)

Core accretion Rapid core growth upto ~10-3 - 10-2 ME (Ida & Makino 1993) Oligarchic growth (e.g. Kokubo & Ida 1998, Thommes et al. 2003)

Gas accretion Scaled with Kelvin-Helmholtz timescale (e.g. Pollack et al. 1996,

Ikoma et al. 2000, Bryden et al. 2000, Ida & Lin 2004)

yeargcmM

M grain

Earth

plgas

12

5.28

1106~

Planet Formation (core accretion scenario)

Pollack et al. (1996): Jupiter can be made within 8 x 106 years at 5.2 AU.

Use the solid surface mass density:

Σs = 300(r/AU)-2 g cm-2

and a planetesimal size (10km).

Oligarchic growth is slower than runaway growth.

100

10

1

0.1

0.01

0.001

Mas

s [M

E]

Time [years]0 2x106 4x106 6x106 8x106 107

Core

Envelope

Total

Planet Formation (core accretion scenario)

Lower opacity speeds up gas accretion (e.g. Ikoma et al. 2000, Hubickyj et al. 2005).

Hubickyj et al. (2005): Jupiter can be made within a few 106 years.

Use a fixed opacity of 0.03 cm2 g-1.

100

10

1

0.1

0.01

0.001

Mas

s [M

E]

Time [years]0 2x106 4x106 6x106 8x106 107

Core

Envelope

Total

Planet Formation in a disk with a dead zone

Initial disk mass is Md ~ 0.01 Msolar and disk temperature is calculated as in Chiang et al. (2001).

Dead zone is initially stretched out to ~ 13 AU.

Planetary core with 0.6 ME is placed at 10 AU.

Standard opacity (1 cm2 g-1) assumed. 0 2x106 4x106 6x106 8x108

Time [years]

100

10

1

0.1

0.01

Dis

k ra

dius

[AU

]

Planet Formation in a disk with a dead zone

0 2x106 4x106 6x106 8x108

Time [years]

100

10

1

0.1

0.01

Dis

k ra

dius

[AU

]

0 2x106 4x106 6x106 8x108

Time [years]

100

10

1

0.1

0.01

Dis

k ra

dius

[AU

]

Decreased opacity (0.03 cm2 g-1) Standard opacity (1 cm2 g-1)

Planet Formation in a disk with a dead zone

100

10

1

0.1

0.01

0.001

Mas

s [M

E]

Time [years]0 2x106 4x106 6x106 8x106

Core

Envelope

Total

100

10

1

0.1

0.01

0.001

Mas

s [M

E]

Time [years]0 2x106 4x106 6x106 8x106

Standard opacity (1 cm2 g-1)Decreased opacity (0.03 cm2 g-1)

Planet Formation in a disk with a dead zone

Planetary core with 0.6 ME is placed at 15 AU.

Core accretion is truncated at 10 ME.

Standard opacity is assumed.

0 2x106 4x106 6x106 8x106 107

Time [years]

100

10

1

0.1

0.01

Dis

k ra

dius

[AU

]

Planet Formation in a disk with a dead zone

0 2x106 4x106 6x106 8x106 107

Time [years]

100

10

1

0.1

0.01

Dis

k ra

dius

[AU

]

Time [years]104 105 106 107

100

10

1

0.1

Mas

s [M

E]

1000

Summary Dead zones evolve rapidly.

From 13 AU to 1 AU within ~ 2 x 106 years.

Dead zones help planet formation by slowing down the migration.

Core mass as well as the difference in viscosities between active and dead zones may affect the evolution of a planet.