![Satellite Properties
a/Rp M/Mp [10-5] ρ [g/cm3] C/MR2
Io 5.9 4.70 3.53 0.378
Europa 9.4 2.53 2.99 0.346
Ganymede 15.0 7.80 1.94 0.312
Callisto 26.4 5.69 1.83 0.355
Titan 20.3 23.7 1.88 0.34
Callisto and Titan’s undifferentiated interiors
→ accretion timescale > 5×105 years [Barr & Canup, 2008]](https://image.slidesharecdn.com/2010aogssatellite-100712211958-phpapp02/85/2010-aogs-satellite-3-320.jpg)
![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 &](https://image.slidesharecdn.com/2010aogssatellite-100712211958-phpapp02/85/2010-aogs-satellite-9-320.jpg)
![Ida & Lin (2004, 2008, 2010)
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](https://image.slidesharecdn.com/2010aogssatellite-100712211958-phpapp02/85/2010-aogs-satellite-11-320.jpg)
![Inner Cavity (Analogy with T-Tauri stars)
974 HERBST MUNDT
number of stars
Herbst Mundt (2005)
spin period [day]](https://image.slidesharecdn.com/2010aogssatellite-100712211958-phpapp02/85/2010-aogs-satellite-16-320.jpg)
![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]](https://image.slidesharecdn.com/2010aogssatellite-100712211958-phpapp02/85/2010-aogs-satellite-17-320.jpg)
![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]](https://image.slidesharecdn.com/2010aogssatellite-100712211958-phpapp02/85/2010-aogs-satellite-18-320.jpg)
![Results: Other features of produced satellite systems
Callisto and Titan’s undifferentiated interior
→ accretion timescales 5×105 years [Barr Canup, 2008]
Accretion timescales in our simulations
Callisto: 105-106 years
Titan: ~106 years
dial ice-rock mixtures may display distinct ries and
Saturn’s ring formed from an ancient satellite at Roche Zone
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
also pla
of icy s
Ref
1. L. Ie
→ RRoche RSynch is required [Charnoz et al., 2009]
Europa, may have triggered runaway differ- 2. R. Ja
Brow
entiation, but Callisto farther out from Jupiter New
remained unaffected (11). Titan’s interior must 3. R. M
have stayed relatively cold and less dissipative 4. J. Lu
to avoid tidal heating and damping of Titan’s R. H
(Spr
notable orbital eccentricity (12). Prolonged 5. G. To
accretion times farther away from their prima- 6. G. S
Jovian: RRoche RSynch OCEANS
Interesting Times for
Saturnian: RRoche RSynch Louis A. Codispoti
Uranian, Neptunian: RRoche RSynch A
lthough present in minute concentra- Cru
tions in Earth’s atmosphere, nitrous ships b
oxide (N2O) is a highly potent green- their va
house gas (1). It is also becoming a key factor Under w
in stratospheric ozone destruction (2). For the produc
past ~400,000 years, changes in atmospheric during
N2O appear to have roughly paralleled changes NO2−).
in CO2 and to have had modest impacts on cli- fiers m
mate (1), but this may change. Human activi- cess re](https://image.slidesharecdn.com/2010aogssatellite-100712211958-phpapp02/85/2010-aogs-satellite-34-320.jpg)
![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]](https://image.slidesharecdn.com/2010aogssatellite-100712211958-phpapp02/85/2010-aogs-satellite-35-320.jpg)
2010 aogs satellite
- 1. Origin of the Difference of the Jovian and Saturnian Satellite Systems Takanori Sasaki, Shigeru Ida (Tokyo Tech) Glen R. Stewart (U. Colorado) Sasaki, Stewart & Ida (2010) ApJ 714, 1052
- 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. Satellite Properties a/Rp M/Mp [10-5] ρ [g/cm3] C/MR2 Io 5.9 4.70 3.53 0.378 Europa 9.4 2.53 2.99 0.346 Ganymede 15.0 7.80 1.94 0.312 Callisto 26.4 5.69 1.83 0.355 Titan 20.3 23.7 1.88 0.34 Callisto and Titan’s undifferentiated interiors → accretion timescale > 5×105 years [Barr & Canup, 2008]
- 4. 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?
- 5. Overview of this study 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
- 6. Overview of this study 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. Overview of this study 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?
- 8. 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
- 9. 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 &
- 10. Overview of this study 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?
- 11. Ida & Lin (2004, 2008, 2010) 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
- 12. Comparison with N-body simulation Time evolution of total mass of satellites (time-constant inflow) N-body (Canup Ward) α=10-4, 5×10-3, 5×10-2
- 13. Comparison with N-body simulation Time evolution of total mass of satellites (time-constant inflow) N-body (Canup Ward) analytical (this study) α=10-4, 5×10-3, 5×10-2 Excellent agreement with N-body simulation!
- 14. Overview of this study 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?
- 15. 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)
- 16. Inner Cavity (Analogy with T-Tauri stars) 974 HERBST MUNDT number of stars Herbst Mundt (2005) spin period [day]
- 17. 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]
- 18. 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]
- 19. Estimates of Cavity Opening Stevenson (1974) proto-Jovian magnetic field 1000 Gauss Cavity (Jovian system should be correspond to the stage) 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
- 20. THE IDEAS Jupiter: open up gap in circum-stellar disk → infall to circum-planetary disk stop → c.-p. disk quickly depleted → frozen satellite system with “inner cavity” Saturn: did not open up the gap → c.-p. disk decay with c.-s. disk decay → c.-p. disk slowly depleted → satellite system without “inner cavity” difference of gap conditions are from Ida Lin (2004)
- 21. 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.
- 22. Jovian System Type I migration is halted near the inner edge The outer most satellite migrates and sweeps up the inner small satellites.
- 23. Jovian System MMR Proto-satellites grow migrate repeatedly They are trapped in MMR with the innermost satellite
- 24. Jovian System Total mass of the trapped satellites Disk mass → the halting mechanism is not effective → innermost satellite is released to the host planet
- 25. Jovian System after the gap opening → c.-p. disk deplete quickly
- 26. Saturnian System No inner cavity outer proto-satellite grow faster migrate earlier
- 27. Saturnian System fall to Saturn Large proto-satellites migrate from the outer regions and fall to the host planet with inner smaller satellites
- 28. Saturnian System c.-p. disk depleted slowly with the decay of c.-s. disk
- 29. 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
- 30. 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
- 31. 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)
- 32. 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
- 33. 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
- 34. Results: Other features of produced satellite systems Callisto and Titan’s undifferentiated interior → accretion timescales 5×105 years [Barr Canup, 2008] Accretion timescales in our simulations Callisto: 105-106 years Titan: ~106 years dial ice-rock mixtures may display distinct ries and Saturn’s ring formed from an ancient satellite at Roche Zone 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 also pla of icy s Ref 1. L. Ie → RRoche RSynch is required [Charnoz et al., 2009] Europa, may have triggered runaway differ- 2. R. Ja Brow entiation, but Callisto farther out from Jupiter New remained unaffected (11). Titan’s interior must 3. R. M have stayed relatively cold and less dissipative 4. J. Lu to avoid tidal heating and damping of Titan’s R. H (Spr notable orbital eccentricity (12). Prolonged 5. G. To accretion times farther away from their prima- 6. G. S Jovian: RRoche RSynch OCEANS Interesting Times for Saturnian: RRoche RSynch Louis A. Codispoti Uranian, Neptunian: RRoche RSynch A lthough present in minute concentra- Cru tions in Earth’s atmosphere, nitrous ships b oxide (N2O) is a highly potent green- their va house gas (1). It is also becoming a key factor Under w in stratospheric ozone destruction (2). For the produc past ~400,000 years, changes in atmospheric during N2O appear to have roughly paralleled changes NO2−). in CO2 and to have had modest impacts on cli- fiers m mate (1), but this may change. Human activi- cess re
- 35. 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]