The Origin of Planetary Obliquities

1
The Origin of Planetary Obliquities
Doug Hamilton (U. Maryland) Saturn work done
in collaboration with Bill Ward (SwRI)
2
The Origin of Planetary Obliquities
Spin and Precession Saturn Jupiter Uranus and
Neptune Conclusions
3
Planetary Obliquities

• Mercury 0.1o
• Venus 177.4o
• Earth 23.5o
• Mars 25.2o
• Jupiter 3.1o
• Saturn 26.7o
• Uranus 97.9o
• Neptune 29.6o
• Pluto 119.6o

Tilts appear to be non-random Three tilts are
normal to orbit planes to within about 3o. Three
are gt 90o. Six are lt 90o. Four are between 20o
and 30o.
4
Planetary Spin States

• Mercury, Venus Tidally despun. Spin axis
  orientations not primordial.
• Earth Obliquity from Moon-forming impact?
• Mars 0-60o oscillations in planet's tilt.
• Jupiter Obliquity not from giant impact?
• Saturn Obliquity not from giant impact?
• Uranus, Neptune Giant Impacts?
• Pluto Obliquity from moon-forming impact?

5
Planetary Precession

• Cause the tidal torque from the Sun and
• distant massive satellites acting on the planet's
• bulge and its interior massive satellites.
• Effect the regression of the planet's spin axis
• (clockwise when viewed from above the
• positive spin axis).

6
Satellites Affect Precession Rates

• In two ways
• 1. As sources of external torque.
• 2. As an extended quadrupole bulge of the
  planet.

7
Laplace Plane

• Interior satellites are controlled by the Planet
• (Moon Orbit precesses around Planet's spin axis)
• Jupiter Io, Europa, Ganymede, Callisto
• Saturn Titan
• Neptune Triton
• Exterior satellites are controlled by the Sun
• (Moon Orbit precesses around Planet's orbit
  normal)
• Earth The Moon
• Saturn Iapetus

8
Satellites Affect Planetary Precession Rates
Saturn's Precession Period
Precession rate for "Titan"
9
Planetary Precession Rates

• Jupiter 0.48 million years
• Saturn 1.83 million years
• Uranus 276 million years
• Neptune 126 million years
• Pluto 9 million years

10
Spin Axis Precession of Saturn

• Saturn Ring Plane Crossings occur roughly every
  15 years. They are approximately 1 hour later
  than expected due to spin axis precession!
• Precession has been measured to 20 accuracy by
  precise timing of these ring plane crossings.

11
The Origin of Planetary Obliquities
Spin and Precession Saturn Jupiter Uranus and
Neptune Conclusions
12
Jupiter and Saturn

• At least 90-95 of the mass of Jupiter and Saturn
  was accreted as gas from the Solar Nebula.
• This form of accretion is expected to lead to
  spin axes oriented nearly perpendicular to
  orbits.
• Indeed, Jupiter's tilt is 3o.
• but Saturn's tilt is 26.7o.
• Why is this? Are our ideas about gas accretion
  wrong, or did something happen to Saturn?

13
Saturn Relevant Periods
Precession Period 1.83106 yr . g18 Secular
Period 1.87106 yr .
Coincidence?
Or perhaps Saturn is trapped in a Spin-Orbit
Resonance!

Neptune's Orbit contains 104 times more angular
momentum than Saturn's Spin.
14
In the Early Solar System
Saturn's Precession Period Increased with Time
- Kelvin-Helmholtz Contraction of Saturn -
Depletion of Circumplanetary Satellite Disk The
g18 Secular Period Increased with Time
-Thinning of the Kuiper Belt -Outward Migration
of Neptune

15
Numerical Simulations
Secular Planetary Theory of Bretagnon - 4 giant
planets - 1000's of planetary frequencies -
We use the 10 strongest secular terms (Von
Woerkom theory) Planetary Spin-Axis Evolution
from Ward -Second order in planetary
e,i Simple Models for Changes to Precession Rates

16
Single Resonant Kick
Integration Time on all plots is 4.5109 years.
Obliquity reaches 13o.
Resonant Kick
We impose this model (Slow Contraction of
Saturn)
Kick occurs when period ratio is 1.0.
17
Single Resonant Kick
Final half billion years of evolution in red.
Polar Plot of the Resonant Angle.
Resonant kick.
Current Position of Saturn's Pole.
18
Simple Trapping into Resonance
Obliquity reaches 27o.
Slow Depletion of the Kuiper Belt 5108 yrs.
Trapping occurs when period ratio is 1.0.
19
Simple Trapping into Resonance
Polar Plot of the Resonant Angle.
Final libration is too Small!
Current Position of Saturn's Pole.
20
Kick Trapping Slow Timescales
Obliquity reaches 27o.
KB Dissipates 5108 yrs.
Saturn Contracts 1.5108 yrs.
Trapping occurs when period ratio is 1.0.
21
Kick Trapping Slow Timescales
Final libration 60o. Period 2108 yrs.
Polar Plot of the Resonant Angle.
Current Position of Saturn's Pole.
22
Kick Trapping Fast Timescales
Obliquity reaches 27o.
KB Dissipates 2108 yrs.
Saturn Contracts 5107 yrs.
Trapping occurs when period ratio is 1.0.
23
Kick Trapping Fast Timescales
Final libration 80o.
Polar Plot of the Resonant Angle.
Current Position of Saturn's Pole.
24
Kick Trapping Fastest Timescales
Obliquity reaches 27o.
KB Dissipates 1108 yrs.
Saturn Contracts 2.5107 yrs.
Trapping occurs when period ratio is 1.0.
25
Kick Trapping Fastest Timescales
Final libration 40o.
Polar Plot of the Resonant Angle.
Current Position of Saturn's Pole.
26
Models for Saturn's Obliquity
1. Giant Collision. Requires a Uranus-mass
object (-) 2. Entire Solar System tilted in
2Myr (Tremaine). 3. Secular Spin-Orbit
Resonance w/ Neptune. Consistant w/ nearby
resonance () Consistant w/ current pole
position ()
27
The Origin of Planetary Obliquities
Spin and Precession Saturn Jupiter Uranus and
Neptune Conclusions
28
Jupiter

• The question is not why is Jupiter's tilt so
  small, but rather why is it so big! The angular
  momentum in the gas entirely overwhelms the
  angular momentum of the core.
• Although Jupiter is tilted by only 3.1o, a tilt
  of significantly less than a degree is expected.

29
Solar System Periods

• in millions of years

• eccentricity inclination
• Jupiter 0.304 0
• Saturn 0.046 0.049
• Uranus 0.419 0.433
• Neptune 1.90 1.87
• Pluto 3.7 3.7
• Additional weaker terms with periods ranging from
  0.01 - 10 Myrs.

• rs. 0

30
Jupiter

• Uranus frequency is nearby ...
• Resonant kick from Uranus did not occur
  -Jupiter's obliquity would have risen well above
  10o.
• However, the resonant angle is currently only
  8o!! Coincidence? Or is Jupiter in the Uranus
  resonance? If it is, then important implications
  for the interior structure of Jupiter.

31
Models for Jupiter's Obliquity
1. Asymmetries in the Solar Nebula. Can be
addressed by Hydrocodes? (?) 2. Entire Solar
System tilted in 2Myr (Tremaine). 3.
Secular Spin-Orbit Resonance w/ Uranus.
Consistant w/ nearby resonance (?)
Consistant w/ current pole position ()
32
The Origin of Planetary Obliquities
Spin and Precession Saturn Jupiter Uranus and
Neptune Conclusions
33
Uranus and Neptune

• Uranus and Neptune are twin planets, but Neptune
  tilt 29.6o, Uranus tilt 97.6o....Very Different!
  Evidence for giant collision?
• Only 20 of the mass of Uranus and Neptune was
  accreted as gas from the Solar Nebula. The other
  80 is from an icy core with unknown spin axis
  orientation.
• But the gas brings in most of the Angular
  Momentum. Prograde spins expected.

34
Uranus and Neptune

• Uranus and Neptune have 16-17 hour days while
  Jupiter and Saturn have 10 hour days.
• It is reasonably unlikely that a giant collision
  will drastically change the spin axis
  orientation, but not dramatically change the spin
  rate. Evidence against a giant collision for
  Uranus?
• By contrast, a secular spin-orbit resonance
  affects the obliquity, but does not affect the
  spin rate.

35
Spin-Orbit Resonance for Uranus?

• The end state for a spin-orbit resonance is 90o
  obliquity. Could Uranus have been tipped by such
  a resonance?
• Possibly, but resonances are weak. And they must
  act gradually since Uranus has such a slow
  precession period.

36
Spin-Orbit Resonance for Neptune?

• Neptune's precession period is too slow to
  resonate with planetary frequencies today.
• But the precession frequency was much faster
  during the tidal evolution of Triton immediately
  following its capture.

37
Precession History of Neptune
Neptune Polar Precession
Obliquity Kicks
Capture Possible
Triton Orbital Precession
Triton's Evolution
38
Models for Uranian and Neptunians Obliquities
1. Giant Impacts. Can the spin periods be
maintained? 2. Entire Solar System tilted in
2Myr Doesn't explain Uranus/Neptune
differences (-). 3. Secular Spin-Orbit
Resonances Uranus End state of resonant
trapping? Neptune Driven by evolution of
Triton?
39
Results of this Study
1. New Understanding of the Origin of Saturn's
Tilt. 2. Natural Explanation for the Close
Similarity of Saturn's Precession and the
g18 Periods. 3. Vindicates the idea that Gas
Accretion Produces Spin Axes Nearly
Perpendicular to Orbits. 4. New Constraints on
the Timescales of Early Solar System
Processes Affecting Saturn and Neptune. 5. New
Constrains Implied by Jupiter's Obliquity.