A Numerical Study of the Problem is Challenging

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A Numerical Study of the Problem is Challenging

• 4.5 Billion Years 1012 orbits of Io!
• We use efficient new symplectic codes HNBody and
  HNDrag written by K. Rauch and D. Hamilton.
• We artificially speed up Io's migration by a
  factor of 100-1000. Adiabatic theory ensures that
  some results can be scaled to Io's true rate.

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Inclination History of Amalthea
Amalthea's Vertical Oscillation is 1160 /- 150
km. (i 0.37o)
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Kick Amplitude vs. Drag Rate
A Detailed Exploration of the Amalthea 42
Resonance
Io i 0.04o
Io i 0.01o
Io's actual migration rate is a few cm/yr.
Io i 0.001o
Amalthea's Inclination (degrees)
2.5 km/yr.
2.5 m/yr.
Io's Migration Rate
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Inclination History of Thebe?
Thebe's Vertical Oscillation is 4310 /- 150 km
(i 1.1o)
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Inclination History of Metis Adrastea?
The Vertical Oscillations of Metis and Adrastea
are unknown. The main ring is 30 km thick. (i
0.007o)
Just one of several possible 41 resonances
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Summary of Resonant Passages
Resonance Distance Comment
43 Thebe 21 Amalthea 32 Thebe 53 Thebe 41
Metis 21 Thebe 31 Amalthea
3.76 4.02 4.06 4.36 4.51 4.92 5.27
Did not occur - too strong Did not occur - too
strong Maybe Maybe Maybe Must have occurred Must
have occurred
The Inclinations of Amalthea Thebe are due to
Sweeping Io Resonances
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What Have We Learned About the Galilean
Satellites?
Satellite Current Distance
Formation Distance Formation Distance
(Previous Constraint) (New
Constraint)
aI 5.89 aE 9.35 aG 14.9
4.02 lt aI lt 4.92 aE gt 6.35 aG gt10.08
Io Europa Ganymede
aI gt 2.25 aE gt 3.58 aG gt 5.67
Much Stronger Constraints on Formation Distances
(Especially for Io)
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What Have We Learned About Jupiter?

• Q Tidal Dissipation Function of Jupiter
• Previous Constraint
• Lower Limit Q gt 1.12 x 106 (Goldreich Soter
  1966)
• New Constraint
• 1.22 x 106 lt Q lt 1.62 x 106
• (All numbers reduced by 4.3 if Laplace Resonance
  is old)
• Most Likely Value Q (3.30 /- 0.47) x 105
  

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Tidal Migration Resonances
Amalthea attained its Inclination 2.5-3.5
billion years ago
Thebe attained its Inclination 3.5-4.5 billion
years ago
Metis may or may not have been affected by Io
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Tidal Migration Movie
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Tidal Migration Movie
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What Else Have We Learned?

• Amalthea has existed (intact?) for gt 2.5
  billion years
• Thebe has existed (intact?) for gt 3.5
  billion years
• Question Could they have been catastrophically
  disrupted and yet still maintain their orbital
  inclinations?

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Best Images of the Inner Satellites
Amalthea
Thebe
Metis
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Catastrophic Disruption

• A disrupted satellite will maintain its
  inclination if the timescale for Reaccreation is
  faster than the timescale for Differential
  Precession.
• Differential Precession dominates when J2 gt
  (Rm/RJ)2. This inequality holds for all small
  satellites.

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Upper Limit on the flux of Km-Sized Comets to
Jupiter
Comet Radius 1.0 km 0.5 km
Frequency of Impact with Jupiter lt 1 every 1000
years lt 1 every 250 years
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What Have We Learned About the Galilean
Satellites?
Satellite Current Distance
Formation Distance Formation Distance
(Previous Constraint) (New
Constraint)
aI 5.89 aE 9.35 aG 14.9
4.02 lt aI lt 4.92 aE gt 6.35 aG gt10.08
Io Europa Ganymede
aI gt 2.25 aE gt 3.58 aG gt 5.67
Much Stronger Constraints on Formation Distances
(Especially for Io)
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Unseen Small Satellites?
This model can explain the absence of small
satellites between Amalthea Io - "kicked"
eccentricities would cause collisions between
more closely spaced moonlets. Sizes and spacings
of the small satellites determined by Io?
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Results of this Study
1. New Understanding for the Origin of the
Inclinations (Eccentricities?) of Amalthea,
Thebe, and (Metis?). 2. Improved Constraints of
the Formation Distances of Io and the Other
Galilean Satellites. 3. Best Constraint on Q for
any Giant Planet. 4. New Constraints on the Flux
of Comets to Jupiter. 5. Explanation for the
Spacing of Moonlets near Jupiter.