What is Q?

- tidal dissipation parameter
- 104 - 105 for Jupiter
- 102 for Europa's core
- 25 for Earth's Moon

Europa

- 100 km thick H2O layer overlying silicate core
- proportion of liquid to solid in H2O layer unknown
- Ross & Schubert calculate the tidal response of a three layer model of Europa; ice, water, silicate
- decoupled core is affected by load of lithosphere, decreasing tidal deformation by 14%
- amplitude of tidal distortion < than previously assumed
- if lithosphere is > 30 km, will have subsolidus convection and resulting freezing of liquid layer- results depend on Q
- for Qc = 100, need Ql <25 for internal ocean
- for Qc = Ql = 25, need Q<30 for internal ocean
- an insulating layer would reduce lithospheric temperature gradient, increasing probability of liquid layer (relaxation of topography suggests elevated surface temperatures)
- difficult to find sufficient heat sources without suggesting changes in orbits

- Helfenstein & Parmentier measured intersecting lineaments
- fractures could be formed by tidal despinning or tidal distortion
- fracture pattern indicates principal axis of deformation radial to Jupiter, can't be due to tidal despinning alone at present axis of rotation, is consistent with tidal distortion
- despinning would occur shortly after formation of satellite, while tidal distortion would begin at start of the Io, Europa, Ganymede resonance (as early as 500 m.y. ago)
- for Qc = 100, need Ql <25 for internal ocean

Ganymede

- Malhotra modeled the formation of the current Io, Europa, Ganymede resonance, considering interaction of all three
- orbital evolution of satellites determined by Q of Jupiter
- begin with non-resonant orbits and evolve through several temporary, lower order Laplace-like resonances, to get to the final Laplace resonance (what we see today)
- Laplace resonance:
p = w1/w2 = 1 where w is the angle frequency of the satellite and w= -0.7395o/day wL=w1-w2 - for lower order Laplace-like resonances p=3/4, 2/3, 1/2
- fig 2 and 3 show results of two typical runs, showing 3 stages of evolution; far from resonance, Laplace-like resonance (p=3/4, 1/2 respectively), Laplace resonance
- p=1/2 is interesting because it gives Ganymede a strong eccentricity
(e3 bump) before the Laplace resonance

- Implications for Ganymede
- primordial heat was sufficient to melt water and allow differentiation to occur
- heating due to e3 bump could be comparable to primordial radiogenic heating - could trigger runaway melt
- timing of the e3 bump is ~103 QJ years ago, or ~500 m.y.
- problems include:
- poor constraint on initial w values
- poor knowledge of Q of satellites
- numerical simulations use tidal evolution rate 2-3 orders of magnitude higher than actual rate
- eccentricities of Europa and Ganymede may have been excited more recently than establishment of Laplace resonance