1. Planet Formation in a disk with a Dead Zone Soko Matsumura (Northwestern University) Ralph Pudritz (McMaster University) Edward Thommes (Northwestern University)

2. Outline Evolution of the Dead Zones Planet Formation  Reproduce the standard models  What happens with a dead zone? Summary

3. 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 10 6 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.

4. Motivation One of the problems of the core accretion scenario: planet migration seems to be too fast. 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 10 6 years.  Planet migration has to be at least 10 times slower.

5. 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 Disk radius [AU] 0 2x10 6 4x10 6 6x10 6 8x10 6 10 7 α = 10 -2 α = 10 -5

6. Evolution of Dead Zones There is a critical surface mass density below which the MRI becomes active.  Cosmic ray attenuation length ~ 100 g cm -2  In our fiducial model: Σ crit ~ 16 g cm -2 Gammie (1996): Mass accretion through the surface layers can explain the mass accretion rate onto the central star. Dead Zone

7. 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

8. Evolution of Dead Zones Gammie (1996): Mass accretion through the surface layers can explain the mass accretion rate onto the central star. There is a critical surface mass density below which the MRI becomes active.  Cosmic ray attenuation length ~ 100 g cm -2  In our fiducial model: Σ crit ~ 16 g cm -2 Dead Zone

9. Evolution of Dead Zones There is a critical surface mass density below which the MRI becomes active.  Cosmic ray attenuation length ~ 100 g cm -2  In our fiducial model: Σ crit ~ 16 g cm -2 Gammie (1996): Mass accretion through the surface layers can explain the mass accretion rate onto the central star. Turner et al. (2006): Gas in the dead zone accretes toward the star only slightly slower than that in the surface layers.

10. α active α dead Evolution of Dead Zones Averaged viscosity alpha

11. α active α dead Evolution of Dead Zones Averaged viscosity

12. α active α dead Evolution of Dead Zones Averaged viscosity

13. Evolution of Dead Zones 10 4 10 5 10 6 10 7 Time [years] 100 10 1 0.1 0.01 Disk radius [AU] Time [years] 30 20 10 0 Disk radius [AU] 0 2x10 6 4x10 6 6x10 6 8x10 6 10 7

14. Evolution of Dead Zones 10 4 10 5 10 6 10 7 Time [years] 100 10 1 0.1 0.01 Disk radius [AU] 10 6 10 4 10 2 1 10 -2 10 -4 Surface mass density Σ [g cm -2 ] Disk radius [AU] 0.01 0.1 1. 10. 100. 10 4 yrs 10 5 yrs 10 6 yrs 10 7 yrs M disk < M J M disk ~ 0.01 M solar

15. Pollack et al. (1996) Planet Formation (core accretion scenario) Core accretion + Gas accretion

16. Planet Formation (core accretion scenario) Core accretion + Gas accretion  Pollack et al. (1996): in-situ planet formation  Planetary core of 0.6 M E

17. Planet Formation (core accretion scenario) Core accretion  Rapid core growth upto ~10 -3 - 10 -2 M E (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)

18. Planet Formation (core accretion scenario) Core accretion  Rapid core growth upto ~10 -3 - 10 -2 M E (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)

19. Planet Formation (core accretion scenario) Wide-range in gas accretion timescale 10 10 8 10 6 10 4 Timescale [ years ] 10 2 1 10 100 Mass [ M E ] Bryden et al. (2000) & Pollack et al. (1996) Ikoma et al. (2000) Ikoma et al. (2000): core accretion is stopped Ida & Lin (2004) Chambers (2007) Dashed lines include the effect of lowered opacity

20. Planet Formation (core accretion scenario) Pollack et al. (1996): Jupiter can be made within 8 x 10 6 years at 5.2 AU. Use the solid surface mass density: Σ s = 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 Mass [M E ] Time [years] 0 2x10 6 4x10 6 6x10 6 8x10 6 10 7 Core Envelope Total

21. 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 10 6 years. Use a fixed opacity of 0.03 cm 2 g -1. 100 10 1 0.1 0.01 0.001 Mass [M E ] Time [years] 0 2x10 6 4x10 6 6x10 6 8x10 6 10 7 Core Envelope Total

22. Planet Formation in a disk with a dead zone Initial disk mass is M d ~ 0.01 M solar 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 M E is placed at 10 AU. Standard opacity (1 cm 2 g -1 ) assumed. 0 2x10 6 4x10 6 6x10 6 8x10 8 Time [years] 100 10 1 0.1 0.01 Disk radius [AU]

23. Planet Formation in a disk with a dead zone 0 2x10 6 4x10 6 6x10 6 8x10 8 Time [years] 100 10 1 0.1 0.01 Disk radius [AU] 0 2x10 6 4x10 6 6x10 6 8x10 8 Time [years] 100 10 1 0.1 0.01 Disk radius [AU] Decreased opacity (0.03 cm 2 g -1 )Standard opacity (1 cm 2 g -1 )

24. Planet Formation in a disk with a dead zone 100 10 1 0.1 0.01 0.001 Mass [M E ] Time [years] 0 2x10 6 4x10 6 6x10 6 8x10 6 Core Envelope Total 100 10 1 0.1 0.01 0.001 Mass [M E ] Time [years] 0 2x10 6 4x10 6 6x10 6 8x10 6 Standard opacity (1 cm 2 g -1 ) Decreased opacity (0.03 cm 2 g -1 )

25. Planet Formation in a disk with a dead zone Planetary core with 0.6 M E is placed at 15 AU. Core accretion is truncated at 10 M E. Standard opacity is assumed. 0 2x10 6 4x10 6 6x10 6 8x10 6 10 7 Time [years] 100 10 1 0.1 0.01 Disk radius [AU]

26. Planet Formation in a disk with a dead zone 0 2x10 6 4x10 6 6x10 6 8x10 6 10 7 Time [years] 100 10 1 0.1 0.01 Disk radius [AU] Time [years] 10 4 10 5 10 6 10 7 100 10 1 0.1 Mass [M E ] 1000

27. Planet Formation in a disk with a dead zone Formation with a dead zone takes about 8x10 6 years. Time [years] 10 4 10 5 10 6 10 7 100 10 1 0.1 Mass [M E ] 1000

28. Planet Formation (core accretion scenario) Is there an optimized place to form planets? Ikoma et al. (2000)

29. Summary Dead zones evolve rapidly.  From 13 AU to 1 AU within ~ 2 x 10 6 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.