Cps Hokudai
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Cps Hokudai Cps Hokudai Presentation Transcript

  • Origin of the Different Architectures of the Jovian and Saturnian Satellite Systems Takanori Sasaki, Shigeru Ida (Tokyo Tech) Glen R. Stewart (U. Colorado)
  • 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
  • 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?
  • 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
  • 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?
  • 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
  • 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
  • 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 &
  • 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
  • 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
  • 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?
  • 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)
  • Inner Cavity (Analogy with T-Tauri stars) 974 HERBST & MUNDT number of stars Herbst & Mundt (2005) spin period [day]
  • 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]
  • 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]
  • 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
  • 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.
  • Jovian System Type I migration is halted near the inner edge The outer most satellite migrates and sweeps up the inner small satellites.
  • Jovian System MMR Proto-satellites grow & migrate repeatedly They are trapped in MMR with the innermost satellite
  • Jovian System Total mass of the trapped satellites > Disk mass → the halting mechanism is not effective → Innermost satellite is released to the host planet
  • Jovian System after the gap opening → c.-p. disk deplete quickly
  • Saturnian System No inner cavity outer proto-satellite grow faster & migrate earlier
  • Saturnian System fall to Saturn Large proto-satellites migrate from the outer regions and fall to the host planet with inner smaller satellites
  • Saturnian System c.-p. disk depleted slowly with the decay of c.-s. disk
  • 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
  • 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
  • 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)
  • 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
  • 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
  • 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