1. Origin of the Different Architectures
of the Jovian and Saturnian Satellite Systems
Takanori Sasaki, Shigeru Ida (Tokyo Tech)
Glen R. Stewart (U. Colorado)

2. Jovian System v.s. Saturnian System
rocky rocky icy icy, undiff.
Io Europa Ganymede Callisto
mutual mean motion resonances (MMR)
icy
only one big body
(~95% of total satellite mass)
Titan

3. Questions; Motivation of this study
Satellites’ size, number, and location
Jovian: 4 similar mass satellites in MMR
Saturnian: only 1 large satellite far from Saturn
What is the origin of the different architecture?
Among Galilean satellites
Io & Europa: rocky satellite
Ganymede & Callisto: icy satellite
Callisto: undifferentiated
What is the origin of the satellites’ diversity?

4. Overview of this study
Circum-Planetary Disk Satellite Formation
Canup & Ward, 2002, 2006 Ida & Lin, 2004, 2008, in prep.
Satellites formed in c.-p. disk Analytical solution for
Actively-supplied accretion disk accretion timescale
Supplied from circum-stellar disk type I migration timescale
→ Analytical solution for T, Σ trapping condition in MMR

5. Overview of this study
Circum-Planetary Disk Satellite Formation
Canup & Ward, 2002, 2006 Ida & Lin, 2004, 2008, in prep.
Satellites formed in c.-p. disk Analytical solution for
Actively-supplied accretion disk accretion timescale
Supplied from circum-stellar disk type I migration timescale
→ Analytical solution for T, Σ trapping condition in MMR
Adding New Ideas Disk boundary conditions
Difference of Jovian/Saturnian systems is naturally reproduced?

6. Overview of this study
Circum-Planetary Disk Satellite Formation
Canup & Ward, 2002, 2006 Ida & Lin, 2004, 2008, in prep.
Satellites formed in c.-p. disk Analytical solution for
Actively-supplied accretion disk accretion timescale
Supplied from circum-stellar disk type I migration timescale
→ Analytical solution for T, Σ trapping in MMR
Adding New Ideas Disk boundary conditions
Difference of Jovian/Saturnian system is naturally reproduced

7. Canup & Ward (2002, 2006)
Actively-Supplied Accretion Disk
Uniform mass infall Fin from the circum-stellar disk
Infall regions: rin < r < rc (rc ~ 30Rp)
Diffuse out at outer edge: rd ~ 150Rp
Infall rate decays exponentially with time
Temperature: balance of viscous heating and blackbody radiation
Viscosity: α model

8. Canup & Ward (2002, 2006) +α
Inflow flux Fin = Fin (t = 0)exp("t # in ) [g/s]
12 +1 4 +3 4
# Mp & # )G & # r &
Temperature Td " 160% ( % 6 ( % ( [K]
$ M J ' $ 5 *10 yrs ' $ 20RJ '
!
Gas density [g/cm2]
!
Dust density [g/cm2]
(2 3 (1 (1 34
Increasing rate df d " Mp % " f % " )G % " r %
= 0.029$ ' $ ' $ 6 ' $ ' [/years]
of dust density dt # MJ & #100 & # 5 *10 yrs & # 20RJ &

9. Overview of this study
Circum-Planetary Disk Satellite Formation
Canup & Ward, 2002, 2006 Ida & Lin, 2004, 2008, in prep.
Satellites formed in c.-p. disk Analytical solution for
Actively-supplied accretion disk accretion timescale
Supplied from circum-stellar disk type I migration timescale
→ Analytical solution for T, Σ trapping in MMR
Adding New Ideas Disk boundary conditions
Difference of Jovian/Saturnian system is naturally reproduced

10. Ida & Lin (2004, 2008, in prep.)
Timescales of satellite’s accretion & type I migration
M ' & *1 3 ' M *1 3 ' M *$5 / 6 ' - * 2 ' r * 5 4
" acc = # 10 6 f d$1%$1 ) , ) $4
ice ) , ) p, ) , )
, )10 M , M , [years]
˙
M ( 10 + ( 20RJ +
( &p + ( p+ ( J +
r 1 % M ($1% M ($1% r (1 2 % " ($1 4
" mig = # 10 5 ' $4 * ' p* '
' 10 M * M * '
G
6* [years]
! ˙
r fg & p) & J ) & 20RJ ) & 5 +10 )
Resonant trapping width of migrating proto-satellites
!
1/6 −1/4
m i + mj vmig
btrap = 0.16 rH
M⊕ vK
These approximate analytical solutions
are based on the results of N-body simulations

11. Overview of this study
Circum-Planetary Disk Satellite Formation
Canup Ward, 2002, 2006 Ida Lin, 2004, 2008, in prep.
Satellites formed in c.-p. disk Analytical solution for
Actively-supplied accretion disk accretion timescale
Supplied from circum-stellar disk type I migration timescale
→ Analytical solution for T, Σ trapping condition in MMR
Adding New Ideas Disk boundary conditions
Difference of Jovian/Saturnian systems is naturally reproduced?

12. The Ideas
Jupiter
inner cavity opened up gap in c.-s. disk
→ infall to c.-p. disk stop abruptly
Saturn
no cavity did not open up gap in c.-s. disk
→ c.-p. disk decay with c.-s. disk
Difference of “inner cavity” is from Königl (1991) and Stevenson (1974)
Difference of gap conditions is from Ida Lin (2004)

13. Inner Cavity (Analogy with T-Tauri stars)
974 HERBST MUNDT
number of stars
Herbst Mundt (2005)
spin period [day]

14. Inner Cavity (Analogy with T-Tauri stars)
weak magnetic field strong magnetic field → coupling with disk
No Cavity Cavity
974 HERBST MUNDT
If the magnetic torque is stronger
than the viscous torque, the disk
would be truncated at the
number of stars
corotation radius
Herbst Mundt (2005)
spin period [day]

15. Inner Cavity (Analogy with T-Tauri stars)
weak magnetic field strong magnetic field → coupling with disk
No Cavity Cavity
974 HERBST MUNDT
Saturnian Jovian
number of stars
Herbst Mundt (2005)
spin period [day]

16. Estimates of Cavity Opening
Cavity
Stevenson (1974)
proto-Jovian magnetic field 1000 Gauss
Königl (1991)
magnetic field for the magnetic coupling
accretion rate 10-6MJ/yr → a few hundred Gauss
Present Saturnian magnetic field 1 Gauss No Cavity
≒ late stage of Saturnian satellite formation

17. Jovian System
inner cavity outer proto-satellite
@corotation radius grow faster migrate earlier
Because the infall mass flux per unit area is constant,
the total mass flux to satellite feeding zones is larger in outer regions.

18. Jovian System
Type I migration is
halted near the inner edge
The outer most satellite migrates and sweeps up
the inner small satellites.

19. Jovian System
MMR
Proto-satellites grow migrate repeatedly
They are trapped in MMR with the innermost satellite

20. Jovian System
Total mass of the trapped satellites Disk mass
→ the halting mechanism is not effective
→ Innermost satellite is released to the host planet

21. Jovian System
after the gap opening → c.-p. disk deplete quickly

22. Saturnian System
No inner cavity outer proto-satellite
grow faster migrate earlier

23. Saturnian System
fall to Saturn
Large proto-satellites migrate from the outer regions
and fall to the host planet with inner smaller satellites

24. Saturnian System
c.-p. disk depleted slowly
with the decay of c.-s. disk

25. Monte Carlo Simulation (n=100)
Parameters:
Disk viscosity (α model) α = 10−3 − 10−2
Disk decay timescale τin = 3 × 10 − 5 × 10
6 6 yr
Number of “satellite seeds” N = 10 − 20

26. Results: Distribution of the number of large satellites
Jovian Saturnian
40 80
Total count of the case
60
20 40
20
0 0
0 1 2 3 4 5 6 7 0 1 2 3 4
number of produced satellites

27. Results: Distribution of the number of large satellites
Jovian Saturnian
40 80
Total count of the case
60
20 40
20
0 0
0 1 2 3 4 5 6 7 0 1 2 3 4
number of produced satellites
inner two bodies: rocky icy satellite
outer two bodies: icy large enough (~MTitan)

28. Results: Properties of produced satellite systems
Jovian Saturnian
1e-3
Galilean Satellites
Titan
1e-4
Ms/Mp
1e-5 rocky component
icy component
1e-6
0 10 20 30 0 10 20 30
a/Rp

29. Results: Properties of produced satellite systems
Jovian Saturnian
1e-3
Galilean Satellites
Titan
1e-4
Ms/Mp
1e-5 rocky component
icy component
1e-6
0 10 20 30 0 10 20 30
a/Rp
inner three bodies the largest satellite
are trapped in MMR has ~90% of total satellite mass

32. Summary
• Jovian Satellite System v.s. Saturnian Satellite System
Difference of size, number, location, and compositions
• Satellite Accretion/Migration in Circum-Planetary Disk
Canup Ward (2002, 2006) + Ida Lin (2004, 2008, in prep.)
• The Ideas of Disk Boundary Conditions
Difference of inner cavity opening and gap opening conditions
• Monte Carlo Simulations
Difference of Jovian/Saturnian system are naturally reproduced
• Application to Solar/Super-Earths Systems