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 ...