Planet formation in a disk with a dead zone
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Planet Formation in a disk with a Dead Zone. Soko Matsumura (Northwestern University) Ralph Pudritz (McMaster University) Edward Thommes (Northwestern University). Planet formation and migration in an evolving disk with a dead zone.

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Planet formation in a disk with a dead zone

Planet Formation in a disk with a Dead Zone

Soko Matsumura (Northwestern University)

Ralph Pudritz (McMaster University)

Edward Thommes (Northwestern University)


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

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 zone1

30

α = 10-2

20

Disk radius [AU]

10

α = 10-5

0

0 2x106 4x106 6x106 8x106 107

Time [years]

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.


Evolution of dead zones

Dead Zone

Evolution of Dead Zones

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


Evolution of dead zones1

αactive

αdead

Evolution of Dead Zones

  • Averaged viscosity


Evolution of dead zones2

100

30

10

20

1

Disk radius [AU]

Disk radius [AU]

10

0.1

0.01

0

104 105 106 107

0 2x106 4x106 6x106 8x106 107

Time [years]

Time [years]

Evolution of Dead Zones


Evolution of dead zones3

100

106

104

10

102

Surface mass density Σ [g cm-2]

1

Disk radius [AU]

1

10-2

0.1

10-4

0.01 0.1 1. 10. 100.

0.01

Disk radius [AU]

104 105 106 107

Time [years]

Evolution of Dead Zones

Mdisk~ 0.01 Msolar

107 yrs

106 yrs

105 yrs

104 yrs

Mdisk< MJ


Planet formation core accretion scenario

Pollack et al. (1996)

Planet Formation (core accretion scenario)

  • Core accretion + Gas accretion


Planet formation core accretion scenario1

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)


Planet formation core accretion scenario2

100

Total

10

Core

1

Mass [ME]

0.1

Envelope

0.01

0.001

0 2x106 4x106 6x106 8x106 107

Time [years]

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.


Planet formation core accretion scenario3

100

Total

10

Core

1

Mass [ME]

0.1

Envelope

0.01

0.001

0 2x106 4x106 6x106 8x106 107

Time [years]

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.


Planet formation in a disk with a dead zone1

100

10

1

Disk radius [AU]

0.1

0.01

0 2x106 4x106 6x106 8x108

Time [years]

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.


Planet formation in a disk with a dead zone2

100

100

10

10

1

1

Disk radius [AU]

Disk radius [AU]

0.1

0.1

0.01

0.01

0 2x106 4x106 6x106 8x108

0 2x106 4x106 6x106 8x108

Time [years]

Time [years]

Planet Formation in a disk with a dead zone

Decreased opacity (0.03 cm2 g-1)

Standard opacity (1 cm2 g-1)


Planet formation in a disk with a dead zone3

100

100

10

10

1

1

Mass [ME]

Mass [ME]

0.1

0.1

0.01

0.01

0.001

0.001

0 2x106 4x106 6x106 8x106

0 2x106 4x106 6x106 8x106

Time [years]

Time [years]

Planet Formation in a disk with a dead zone

Standard opacity (1 cm2 g-1)

Decreased opacity (0.03 cm2 g-1)

Core

Total

Envelope


Planet formation in a disk with a dead zone4

100

10

1

Disk radius [AU]

0.1

0.01

0 2x106 4x106 6x106 8x106 107

Time [years]

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.


Planet formation in a disk with a dead zone5

100

1000

10

100

Mass [ME]

10

1

Disk radius [AU]

1

0.1

0.1

104 105 106 107

0.01

0 2x106 4x106 6x106 8x106 107

Time [years]

Time [years]

Planet Formation in a disk with a dead zone


Summary

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.


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