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Gabriel Tobie , Daniel Mège, Antoine Mocquet, Christophe Sotin

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:

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Gabriel Tobie , Daniel Mège, Antoine Mocquet, Christophe Sotin

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  1. Tidal interactions in the Pluto-Charon system:Origin, evolution, and consequences Gabriel Tobie, Daniel Mège, Antoine Mocquet, Christophe Sotin

  2. 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 km Density: > 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 ?

  3. 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 Intact Charon > very eccentric orbit 3.7 < a < 21 RP; 2.5 < periapse < 5 RP 0.1 < e < 0.8 Re-accreted Charon > nearly circular orbit

  4. Pluto-Charon : Subsequent evolution Present-day orbital configuration (circular, dual synchronous) Time required for orbit circularization and expansion ? PP P C C C C Possible post-impact orbital configuration

  5. Principle of tidal interaction ao: orbital centrifugal acceleration ag: gravitational acceleration exerted by the compagnon body am : tidal acceleration resulting from |ag-ao| am F + + ao ag DPC P Charon Tidal force on Pluto ~ Mc/MP(RP/DPC)3 Tidal force on Charon ~ MP/MC(RC/DPC)3 Pluto

  6. Principle of tidal interaction as: Spin centrifugal acceleration ao: orbital centrifugal acceleration ag: gravitational acceleration exerted by the compagnon body am : tidal acceleration resulting from |ag-ao| as am F + + ao ag DPC P Charon Tidal force on Pluto ~ Mc/MP(RP/DPC)3 Tidal force on Charon ~ MP/MC(RC/DPC)3 Pluto

  7. Principle of tidal interaction as: Spin centrifugal acceleration ao: orbital centrifugal acceleration ag: gravitational acceleration exerted by the compagnon body am : tidal acceleration resulting from |ag-ao| as am F + + ao ag DPC P Charon Tidal force on Pluto ~ Mc/MP(RP/DPC)3 Tidal force on Charon ~ MP/MC(RC/DPC)3 Pluto am and as non constant over the surface > Mass redistribution and surface distortion Flattening and elongation in the Pluto-Charon direction.

  8. Tidal interaction in the present-day system • No modulation of the body shape and of their alignment • no exchange of angular momentum and of energy • stable (and boring) configuration Constant distortion P C PP C 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

  9. Past orbital evolution driven by tidal interactions Pluto had a higher spin rate, and Charon’s orbit was probably eccentric P C • Pluto’s spin wp > Charon’s orbital angular velocity wCo • Charon’s spin-orbit resonance + eccentricity : wCo varies along the orbit, while wCs 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)

  10. Orbital evolution: governing equations Kaula’s formula (1964) 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 No more valid when the system is close to dual synchronous state + angular momentum conservation

  11. Computation of tidal deformation and friction Internal structure Radial Distribution of internal friction Glace I Poisson equation Equations of motion Displacement Océan Stresses Strain Silicate Fer Tidal potential Potentiel de marée flattening elongation Integration of Hm -> k2/Q

  12. Initial conditions: Interior and orbit Radial distribution: sensitivity to deformation Possible internal structure for Pluton and Charon Love number (k2) Pluto: 0.02 0.005 0.2 Charon: 0.005 0.0015 0.04 Intact Charon > very eccentric orbit: 3.7 < a < 21 RP; 2.5 < pericenter < 5 RP 0.1 < e < 0.8 Moment of inertia factor (C) Pluto: 0.4 0.325 0.33 Global dissipation function Q: 10-1000

  13. Preliminary tests aPC=5RP, e=0.1, Q=200 Homogeneous interior Differentiated interior Differentiated + ocean

  14. Toward a coupled interior-orbit evolution model Heat transfer: Numerical modelling Tidal dissipation and orbital evolution Atmosphère de vapeur: H2O, NH3, N2, CH4, CO2 The example of Titan Tobie, Mocquet & Sotin, Icarus (2005) eT=3% Tobie, Choblet & Sotin, JGR (2003) Phase diagram: HP-LT experiment Orbit circularization Silicate core evolution Tobie et al. Icarus (2005) Grasset & Pargamin, Planet. Space Sci. (2005)

  15. A typical simulation

  16. Rapid despinning and orbit growth: tectonic stresses Change in flattening for Pluto and in tidal bulge for Charon + global extension/contraction due to melting and refreezing Collins and Pappalardo (2000) Relaxation with depth Longitude and latitude dependence Equator > thrust faults Mid-latitudes > strike-slip faults Pole > normal faults Stress accumulation in the upper crust depends on the rate of change in spin and semi-major axis

  17. 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 ...

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