Melting of Io by Tidal Dissipation
S.J. Peale, P. Cassen, R.T. Reynolds.
Science, 1979, vol. 203, p.892 - 894.
"These calculations suggest that Io might currently be the most intensely
heated terrestrial-type body in the solar system"
- Io is in synchronous rotation
- Forced eccentricity from resonance with Ganymede and Europa is much
larger than Io's free value; this plus large tides from Jupiter lead to
vast amount of tidal dissipation. Periodic component of tide = 100m.
- The centre of an homogenous Io would be heated 10x more than the
lunar interior plus would be enhanced by radioactive decay; hence likely
that the interior of Io is melted.
- Heating rate from tidal dissipation in a planet with a solid mantle
and liquid core can be much greater than that in a homogeneous body.
- Increase in total dissipation with increasing core radius; can lead
to runaway melting. Material melts near liquid core so mantle gets
thinner; thinner shell deforms more so heating rate increases runaway
- Because of Io's size, heat is probably transported from Io's
interior by solid-state convection. As core radius increases, tidal
dissipation becomes increasingly greater than the amount of energy which
can be removed by solid-state convection. Therefore, once melting has
occurred at centre, solid-state convection cannot prevent melting from
spreading rapidly through the rest of the satellite - how would volcanism
evolve under this situation?
- Runaway melting results in planet with large molten core and solid
outer shell. Thickness of shell is limited by conduction of heat to
surface, or onset of nonelastic behaviour. For conduction-limited runaway
heating model, lithosphere is only 18 km.
- Conclude: cosmic elemental abundance ratios, Io's density and high
internal temperatures imply a molten iron core with a radius of ~ one third
of Io's radius. Io may have a magnetic field.
Tidally Forced Viscous Heating in a Partially Molten Io
M. N. Ross & G. Schubert
Icarus, 1985, 64, p. 391 - 400
- Io's interior must be partially molten. Flexure of a solid elastic
body requires greater energy than flexure of an equivalent body with a
hollow/fluid-filled interior. Tidal dissipation in a solid Io could not
account for even 10% of the observed energy flux. Degree of partial melt
and its distribution are uncertain. Partially molten decoupled layer could
be entire interior or thin asthenosphere.
- Tidal distortion symmetric around Io-Jupiter line and varies as
variation of Io-Jupiter distance due to Io's orbital eccentricity.
Partially molten asthenosphere model:
- Three-layer model; contribution of core distortion to overall
dissipation assumed negligible and ignored here.
- Fluid motion in asthenosphere driven by periodic tidal distortion
of the outer shell. Fluid circulation velocity increases with decreasing
asthenosphere thickness increase in viscous heating.
- For hot-spot energy flux to be generated in Io's outer shell, Q =
25. Much evidence to suggest Q is greater than this. Authors choose Q =
100 and lithospheric thickness of 90 km. For this value, the ratio of
viscous to elastic heating is 3, so fluid flow in asthenosphere generates
more heat than the flexing of the outer shell.
- Difficult to determine viscosity; assume basaltic composition for
asthenosphere. Rheology of magma depends mainly on volume fraction of
crystals suspended in melt.
- Almost all viscously generated heat flows into zone between 25o and
80o from sub and anti-Jove poles. However, this is not observed on Io;
neither is distribution expected from elastic shell pattern. Surface
distribution of magma "may be due to idiosyncrasies of magma transport",
i.e. heat generated globally and channeled to certain locations. Discuss!
Partially molten interior model
- Entire planet to lithospheric shell partially molten.
- Is this plausible? Possible that interior may cool and freeze out
refractory solid core. Also, magma is buoyant - would it migrate away from
centre leaving a solid interior?
- For a lithosphere thickness of 95 km, interior heat generation is
75% of total observed heat flux (as with previous model). To account for
this, a magma with a crystal fraction of 60% is necessary.
- Conclude: for both models, required viscous dissipation is
associated with silicate magma rather than solid with a few percent partial
melt. Temperature variations in magma with depth may lead to isoviscous
molten layer. Convecting magma should remain well mixed. Hotspots imply
that magmas carry most dissipative heating.