gabriel tobie , daniel mège, antoine mocquet, christophe sotin
DESCRIPTION
Tidal interactions in the Pluto-Charon system: Origin, evolution, and consequences. Gabriel Tobie , Daniel Mège, Antoine Mocquet, Christophe Sotin. Pluton-Charon : Or bital configuration. One of the rare double system showing a dual synchronous configuration: - PowerPoint PPT PresentationTRANSCRIPT
Gabriel Tobie, Daniel Mège, Antoine Mocquet, Christophe Sotin
Tidal interactions in the Pluto-Charon Tidal interactions in the Pluto-Charon system:system:
Origin, evolution, and consequencesOrigin, evolution, and consequences
Pluton-Charon : Orbital configuration
One of the rare double system showing a dual synchronous configuration:the stable end-product of tidal evolution
Rotation/revolution period: ~ 6.39 days
Radius: Pluton > 1150 - 1200 km ; Charon > 590 – 620 kmDensity: > 1800 – 2100 kg.m-3; > 1600 –1800 kg.m-3
Semi-major axis: 19 405 km; eccentricity: 0.000 (7)
Mass ratio: MC/MP= 10-15 % (as a comparison: Moon/Earth= ~ 1%)
Angular momentum: LPC = 0.33 - 0.46 x (GMPC3RPC)1/2
Angular momentum of the equivalent sphere
containing the whole system
close to the critical angular momentum for rotational stability of a
single object containing the whole mass
Origin of the system ? Evolutionary path toward dual syncrhonization ?
Pluton-Charon : formation models
Giant impact origin: the most plausible scenario (Canup, 2005)
Two end-member models (depending on the initial interior state and collision angle)
Planet-disk formation + re-acrretion in orbit Formation of an intact Charon
Re-accreted Charon > nearly circular orbitIntact Charon > very eccentric orbit3.7 < a < 21 RP; 2.5 < periapse < 5 RP
0.1 < e < 0.8
Pluto-Charon : Subsequent evolution
PPP C CC
Present-day orbital configuration
(circular, dual synchronous)
Possible post-impact orbital configuration
Time requiredfor
orbit circularization
and expansion ?
C
Principle of tidal interaction
P
agDPC
Charon
Pluto
ao: orbital centrifugal acceleration ag: gravitational acceleration exerted by the compagnon body am : tidal acceleration resulting from |ag-ao|
ao
am
+ +
Tidal force on Pluto ~ Mc/MP(RP/DPC)3
Tidal force on Charon ~ MP/MC(RC/DPC)3
Principle of tidal interaction
P
agDPC
Charon
Pluto
as: Spin centrifugal accelerationao: orbital centrifugal acceleration ag: gravitational acceleration exerted by the compagnon body am : tidal acceleration resulting from |ag-ao|
ao
am
+ +
Tidal force on Pluto ~ Mc/MP(RP/DPC)3
Tidal force on Charon ~ MP/MC(RC/DPC)3
as
Principle of tidal interaction
P
agDPC
Charon
Pluto
as: Spin centrifugal accelerationao: orbital centrifugal acceleration ag: gravitational acceleration exerted by the compagnon body am : tidal acceleration resulting from |ag-ao|
ao
am
+ +
Tidal force on Pluto ~ Mc/MP(RP/DPC)3
Tidal force on Charon ~ MP/MC(RC/DPC)3
as
am and as non constant over the surface > Mass redistribution and surface distortion
Flattening and elongation in the Pluto-Charon direction.
Tidal interaction in the present-day system
PPP C
C
Constant distortion
No modulation of the body shape and of their alignment
no exchange of angular momentum and of energy
stable (and boring) configuration
Radio tracking determination of the principal component of the gravitational potential : GM, C20, C22
+ body shape
Key informations on the
differentiation state of the
interior
Past orbital evolution driven by tidal interactions
PC
Pluto had a higher spin rate, and Charon’s orbit was probably eccentric
• Pluto’s spin wp > Charon’s orbital angular velocity wCo
• Charon’s spin-orbit resonance + eccentricity : wCo varies along the orbit, while wC
s not.
• Non-perfect response of the body to tidal forcing (internal friction) > phase lag
• Maximal effect at pericenter: torque due to tidal bulge on fastly rotating Pluto accerelerates Charon, while torque due to delayed tidal bulge on Charon deccelerates it.
Very sensitive to the interior response to tidal forcing (amplitude and phase lag)
Orbital evolution: governing equations
+ angular momentum conservation
Kaula’s formula (1964)
No more valid when the system is close to dual synchronous state
Charon’s semi-major axis and eccentricity
increase due to friction within Pluto
Charon’s semi-major axis and eccentricity
decrease due to friction within Charon
Internal structure
Poissoneequation
EEquations of motion
flattening
elongation
Stresses
Displacement
Potentiel de marée
Radial Distribution of internal friction
Glace I
Silicate
Océan
Fer
Tidal potential
Integration of Hm -> k2/Q
Strain
Computation of tidal deformation and friction
Initial conditions: Interior and orbit
Possible internal structure for Pluton and Charon Radial distribution:sensitivity to deformation
Pluto: 0.02 0.005 0.2
Charon: 0.005 0.0015 0.04
Love number (k2)
Moment of inertia factor (C)
Pluto: 0.4 0.325 0.33
Intact Charon > very eccentric
orbit:
3.7 < a < 21 RP; 2.5 < pericenter < 5 RP
0.1 < e < 0.8Global dissipation function Q: 10-1000
Preliminary tests
Homogeneous interior
Differentiated interior
Differentiated + ocean
aPC=5RP, e=0.1, Q=200
Toward a coupled interior-orbit evolution model
Atmosphère de vapeur: H2O, NH3, N2, CH4, CO2
Grasset & Pargamin, Planet. Space Sci. (2005)
Tobie, Choblet & Sotin, JGR (2003)
Heat transfer: Numerical modelling
Phase diagram: HP-LT experiment
Tidal dissipation and orbital evolution
The example of Titan
Tobie et al. Icarus (2005)
Orbit circularization
Silicate core evolution
Tobie, Mocquet & Sotin, Icarus (2005)
eT=3%
A typical simulation
Rapid despinning and orbit growth: tectonic stresses
Change in flattening for Pluto and in tidal bulge for Charon+ global extension/contractiondue to melting and refreezing
Relaxation with depth
Longitude and latitude dependence
Collins and Pappalardo (2000)
Stress accumulation in the upper crust depends on the rate of change in spin and semi-major axis
Equator > thrust faults Mid-latitudes > strike-slip faults
Pole > normal faults
CONCLUSIONS
The Pluto-Charon system rapidly converges toward a dual synchronous
state (< 100 Myr), relative to the age of the solar system.
The time required to reach a stable configuration is mainly controlled by the
interior state (differentation, thermal structure, liquid layer etc.)
Tidal friction contributes to the thermal budget only during a few millions after
impact.
Ancient tectonic features observed on the surface could be used to recontruct
the early evolution of the system.
To be continued ...