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Tidal Interactions in the Pluto-Charon System: Origin, Evolution, and Consequences

This article explores the origin and evolution of the Pluto-Charon system, including the impact scenario and subsequent orbital configuration. It delves into the principles of tidal interactions, their effects on the bodies' shape and alignment, and the governing equations for orbital evolution. The article also discusses the internal structure of Pluto and Charon and their sensitivity to tidal deformation.

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Tidal Interactions in the Pluto-Charon System: Origin, Evolution, and Consequences

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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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