1. Formation 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, undiff.
only one big body Inside Titan. Global gravity field and sha
pletely separated within Titan’s deep inter
may contain a cold water-ammonia ocean
water ice below (gray) and a floating ice/cl
images show that the extent of separation
density that is predominantly affected by t
Titan
dial ice-rock mixtures may display distinct
degrees of internal differentiation. Impact-
induced melting and/or intense tidal heating
of Ganymede, locked in orbital resonances
with the inner neighboring satellites Io and
ries and gradual unmixing of ice and rock may
also play a role for incomplete differentiation
of icy satellites.
References and Notes
1. L. Iess et al., Science 327, 1367 (2010).
Europa, may have triggered runaway differ- 2. R. Jaumann et al., in Titan from Cassini-Huygens, R.H.
Brown, J.-P. Lebreton, J. Hunter Waite, Eds. (Springer,
entiation, but Callisto farther out from Jupiter New York, 2009), pp. 75–140.

3. Circum-planetary disk models
Actively-Supplied Accretion Disk “Minimum Mass” Disk
[Canup & Ward, 2002] [Mosqueira & Estrada, 2003]
Inflow (gas + small solids)
H
RP ν = αcH
ro rd
× Only for Jovian system
Figure 8: Left: Idealization of the initial Σ and assumed photospheric
○ Msatellites/Mplanet ~ 10-4 subnebula. The re-constituted mass of Io, Europa, and Ganymede det
thick inner disk, while the mass of Callisto is spread out over the opticall
inflow-produced accretion disk. [Canup & Ward, 2006]
Inflowing gas and solids initially achieve
just inside the centrifugal radius rc , while Callisto lies outside a transitio
× Unrealistic initial conditions
and outer disks. The transition region between in the inner and outer
e balance across a region extending from the surface of the planet out to distance
temperature is set to agree with the compositional constraints of the Ga
ccrete into satellites throughout this region. The gas spreads viscously onto the [Tanigawa et al., 2012 JpGU]
Stevenson, 1982; Mosqueira and Estrada, 2003a,b), which implies a Jovi
○ removal distance, rd with rd >> ro. Saturnian
a planetary radius of ∼ 1.5 − 2 RJ consistent with planet formation mo
ward to aDifference b/w ,Jovian and The half-thickness of the gas disk is 1a). Upper left: Critical mass at which migration stalls as a function of J
using both vertically thermally stratified (solid and dotted curves), and v
c is gas satellite systemsorbital frequency, with H/r ~ 0.1. After Canup and
sound speed and Ω is
× Difficult to make satellites(?)
dashed curve). Gas drag is included. The solid curve corresponds to the
dotted and dashed curves correspond to the SEMM model. The short-d
[Sasaki et al., 2010; Ogihara et al., 2012] T model. Lower right: Migration and growth models for proto-Ganyme
[Miguel, Sasaki & Ida, in prep.];
evolved backward in time from the location where it opens a gap to th
size (∼ 1000 km) for a SEMM disk. Two models for growth are used. S
Dotted curve: growth rate proportional to the disk surface density. Grow

4. Circum-planetary disk models
Actively-Supplied Accretion Disk “Minimum Mass” Disk
[Canup & Ward, 2002] [Mosqueira & Estrada, 2003]
Inflow (gas + small solids)
H
RP ν = αcH
ro rd
× Only for Jovian system
○ Msatellites/Mplanet ~ 10-4
inflow-produced accretion disk. [Canup & Ward, 2006]
Inflowing gas and solids initially achieve
× Unrealistic initial conditions
e balance across a region extending from the surface of the planet out to distance
ccrete into satellites throughout this region. The gas spreads viscously onto the [Tanigawa et al., 2012 JpGU]
○ removal distance, rd with rd >> ro. Saturnian
ward to aDifference b/w ,Jovian and The half-thickness of the gas disk is
c is gas satellite systemsorbital frequency, with H/r ~ 0.1. After Canup and
sound speed and Ω is
× Difficult to make satellites(?)
[Sasaki et al., 2010; Ogihara et al., 2012] [Miguel, Sasaki & Ida, in prep.];

5. 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 Inflow (gas + small solids)
H
RP ν = αcH
ro rd

6. Overview of Sasaki et al. (2010)
Circum-Planetary Disk Satellite Formation
Canup & Ward, 2002, 2006 Ida & Lin, 2004, 2008, 2010
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.

7. The New 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)

8. 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.

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

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

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

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

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

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

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

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

17. 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

18. 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)

19. 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

20. 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

21. 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, 2010)
• 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
[Sasaki, Stewart & Ida (2010) ApJ 714, 1052]