ESS 298: OUTER SOLAR
SYSTEM
Francis Nimmo
Io against Jupiter,
Hubble image,
July 1997
Last Week
• Solar system characteristics and formation –
Hill sphere, “snow line”, timescales
• Kepler’s laws and Newtonian orbits
• Tides
– Synchronous rotation
– Dissipation / heating
– Circularization and outwards migration
Galilean Satellites
• This week
– Preliminaries, common themes
– Io
– Callisto
• Next week
– Ganymede
– Europa
Io
Europa
Ganymede
Callisto
Why are they important?
•
•
•
•
•
Life (!?) – or sub-surface oceans, at any rate
Relatively large (~2000 km), geologically active
Very complicated orbital relationships
Some processes look familiar e.g. plate tectonics (?)
Future exploration target (maybe)
• Why “Galilean”? He discovered them (telescope,
1610)
• Subsequent exploration – Voyagers & Pioneers
(1970’s), Galileo (ended 2003), JIMO??
Voyagers 1 and 2
• A brilliantly successful series
of fly-bys spanning more than
a decade
• Close-up views of all four
giant planets and their moons
• Both are still operating, and
collecting data on
solar/galactic particles and
magnetic fields
Voyagers 1 and 2 are currently at 90 and
75 AU, and receding at 3.5 and 3.1 AU/yr;
Pioneers 10 and 11 at 87 and 67 AU and
receding at 2.6 and 2.5 AU/yr
The Death Star
(Mimas)
Galileo
• More modern (launched 1989) but the
high-gain antenna failed (!) leaving it
crippled
• Venus-Earth-Earth gravity assist
• En route, it observed the SL9 comet
impact into Jupiter
• Arrived at Jupiter in 1995 and
deployed probe into Jupiter’s
atmosphere
• Very complex series of fly-bys of all
major Galilean satellites
• Deliberately crashed into Jupiter Sept
2003 (why?)
• Main source of results
antenna
Where are they?
Distance (Rj)
5
10
15
20
25
30
a
P
e
(106 km) (days)
ms
Rs
(1020 kg) (km)
r
Io
422
1.769
.041
893
1821
3.53
Europa
671
3.552
.010
480
1565
2.99
Ganymede 1070
7.154
.0015
1482
2634
1.94
1883
16.69
.007
1076
2403
1.85
Callisto
(Mg m-3)
Laplace Resonance (1)
• Periods of Io:Europa:Ganymede are in ratio 1:2:4
• This means that successive conjunctions occur at the same point
on the orbit
• So the eccentricities get pumped up to much higher values than if
the satellites were not in a resonance
G
J
I
E
One of the conjunctions
occurring due to the Laplace
resonance. Note that there is
never a triple conjunction.
• High eccentricities mean higher dissipation in the satellites and
a tendency for the orbits to contract (see earlier)
• This tendency is counteracted by dissipation in Jupiter, which
tends to cause the orbits to expand (like the Moon)
• The system is currently (roughly) in equilibrium
Compositions/Formation
• Surface compositions – mainly water ice (except for
Io), plus “contaminants” (spectroscopy)
• Io’s surface is silicates + sulphur
• Interiors – discussed in detail later, but roughly equal
mix of water ice, silicates and iron (how do we know?)
• How did they form?
–
–
–
–
Presumably accreted while Jupiter was forming
Lateral temperature gradient in nebula
May have been earlier satellites that didn’t survive (why?)
Energy of accretion ~0.6 Gms/Rs per unit mass ~2 MJ/kg –
this is enough to heat ice through ~1000 K. Why might this
present a problem?
– Satellites subsequently evolved to their present-day positions
Composition (cont’d)
Earth-based reflectance spectra, from Johnson,
in New Solar System
• Callisto has lower
reflectivity and
shallower absorption
bands, indicating a
higher non-ice
component
• Ganymede and Callisto
show slight differences
between leading and
trailing hemispheres
(why?)
• Non-ice materials are
probably hydrated
minerals (clays)
Differentiation
• Potential energy of a homogeneous satellite is reduced
if the densest components sink to the centre –
differentiation is energetically favoured
• Differentiation is opposed by rigidity of body, so
differentiation is favoured at higher temperatures
• As differentiation proceeds, energy is released, driving
further differentiation – potential runaway
• Heat released may generate thermal expansion and
form a source of stress
• Sinking materials may undergo phase changes leading
to volume changes and either expansion or contraction
• Not all Galilean satellites appear to have differentiated
Ice phase diagram
Ice I
Water
Ice V
• The key point is that because of the densities involved, we
would expect to find liquid water around the ice I – ice V
interface (~200 km depth). Why is this important?
Internal Structures (1)
• Because the satellites are rotating, they are flattened (oblate)
• This means that they do not act as a point mass; the perturbations
to the gravity field can be identified by tracking spacecraft on a
close approach
• Potential V at a distance r for axisymmetric body is given by
2
4


GM 
R
R
V 
1  J 2   P2 ( )  J 4   P4 ( )  

r 
r
r

• So the coefficients J2, J4 etc. can be determined from spacecraft
observations (higher order terms require closer approaches – why?)
• We can relate J2,J4 . . . to the internal structure of the satellite
Internal Structures (2)
• Mean density and J2 are especially useful
• It turns out that we can rewrite J2 in terms
of the differences in moments of inertia of
the planet (look at the diagram ):
CA
J2 
MR 2
C
R
A
• What we would really like is C/MR2 (why?)
• If we can observe the precession of the planet, that gives us (CA)/C and thus C given J2 (where can we do this?)
• Otherwise, we can assume that the planet has no strength
(hydrostatic) and use theory to infer C from J2 (is this OK?)
• In practice, flybys of the Galilean satellites were usually
equatorial (why?), so we determine the equivalent equatorial term
to J2 which is called C22 – the analysis is similar
Internal Structures (3)
• How do we know?
– Mean density
– Moment of inertia, derived from
J2=(C-A)/MR2 and hydrostatic
assumption (is this likely?)
– Other observations (magnetometer)
– Expectations of likely components
(silicates, ices, iron)
Fe core
Fe-FeS core
• Tradeoffs – we only have two
observations (J2 and r) and have
more than two unknowns. MeansContours of Europa ice shell thickness
giving correct mean density for
the results are non-unique
indicated core radius and rock density.
Bold line is MoI constraint. From
Anderson et al., Science, 1998
Magnetometer (1)
•Jupiter’s magnetic pole is
offset from its rotation pole
•So as Jupiter rotates (10
hour period), satellites
experience a time-varying
magnetic field
•A time varying magnetic field induces
eddy currents in a conductor
•These currents generate a secondary
(induced) magnetic field
•The amplitude of the secondary magnetic
field tells us about the conductor, in
particular its conductivity and thickness
Khurana et al. 2002
Magnetometer (2)
• Strong induced signatures have been detected at
Europa, Ganymede and Callisto, indicating a layer of
high conductivity
• A relatively near-surface ocean at least a few km
thick satisfies these observations
• The direction of the induced signal depends on the
orbital geometry; but permanent (static) signals have
also been detected at Ganymede and (possibly) Io
• These static fields are presumably generated by
convection within an iron core, just like the Earth
• We can combine the magnetometer constraints with
the geodetic constraints to infer internal structures . . .
Io – liquid iron core (dynamo), silicate mantle
(partially molten?). No volatiles – why not?
Ganymede – liquid iron core (dynamo), silicate
mantle and ~800 km thick ice shell containing an
ocean (presumably at the I-III/V boundary)
Europa – core and mantle similar to Ganymede, but
ice shell much thinner (~100-200 km) and mostly
liquid (magnetic induction signature)
Callisto – has not differentiated completely (?). An
ice layer ~300km thick, containing an ocean and
overlying a mixture of rock-ice. NB the hydrostatic
assumption is particularly dodgy here – why?
Ice Rheology (1)
• Under applied stress, ice will deform:
brittle
elastic
ductile
depth
– At low stresses and strains, elastically
(recoverable)
– At low temperature and/or high strain
rate, brittle
– At high temperature and/or low strain
rate, ductile
stress
• A good measure of its tendency to deform in a ductile
fashion is the homologous temperature (Th=T/Tmelt) (in K)
– Rock at Earth surface Th~0.2
– Ice at Galilean satellite surface Th~0.4
– Ice in Antarctica/Mars Th~0.8
• So ice at the surface of the Galilean satellites behaves
more like rock than ice on Earth
Ice Rheology (2)
• Ductile deformation is important because it controls convection,
topographic relaxation and tidal dissipation (see later)
• But ice deformation is complicated and involves multiple
mechanisms (see Goldsby and Kohlstedt JGR 2001)
• Each mechanism obeys the same equation:
n  p  Q / RT

  A g s e
Here  is strain rate, A is a constant,  is stress, gs is grain size, T is temperature, Q
is activation energy, R is the gas constant and n and p are constants. A Newtonian
rheology has n=1 and a grain-size independent rheology has p=0.
Increasing stress / strain rate
Diffusion creep
(n=1, grain-size dependent)
Grain-boundary sliding
(n>1, grain-size dependent)
Actually two mechanisms,
slower one dominates
Dislocation creep
(n>1,p=0)
Orbital Evolution
• Recall dissipation in primary drives satellite outwards
• Dissipation in satellite drives satellite inwards and
circularizes orbit
• Possible scenario:
– Io causes dissipation in Jupiter, moves outwards until . . .
– It encounters the 2:1 resonance with Europa; the two bodies
then move outwards in step until . . .
– They encounter the 2:1 resonance with Ganymede
• There are alternative scenarios
• The present-day configuration involves a balance
between dissipation in primary (outwards) and
dissipation in satellites (inwards)
Hypothetical orbital history
time
Io
Europa
Ganymede
2:1 Europa:Ganymede
2:1 Io:Europa
from Peale, Celest. Mech.
Dyn. Ast. 2003
distance (schematic)
Note that we don’t actually know whether the orbits are
currently expanding or contracting
Also note that during capture into resonance, eccentricities
are transiently excited to high values – so what?
Estimating Q
• Recall that the rate of outwards motion of a satellite
depends on planetary dissipation Qp (see Week 1).
• If we assume that Io formed 4.5 Gyr B.P., and has
been moving outwards ever since, we get a lower
bound on Jupiter’s Q of ~105 (why a lower bound?)
• This value is typical of gas giants, but is much higher
than for silicate bodies (~102)
• The Earth’s Q is anomalously high (~12) because the
current continental configuration means oceanic tides
are close to resonance – lots of dissipation
• We’ll calculate the rate of dissipation in a second
Tidal Deformation – Recap.
• Satellite in synchronous rotation – period of rotation
equals orbital period
• Eccentric orbit (due to Laplace resonance) – amplitude
and direction of tidal bulge changes, so surface
experiences changing stresses and strains
• These diurnal tidal strains lead to friction and thus tidal
dissipation (heating)
Diurnal tides can be
large e.g. 30m on
Europa
Jupiter
Satellite
Eccentric orbit
Tidal Heating (1)
• Recall diurnal tidal amplitude goes as eH / m~ in the
limit when rigidity dominates ( m~  1 )
• So strain goes as eH / m~Rs
• Energy stored per unit volume = stress x strain
• In an elastic body, stress  strain x m (rigidity)
• So total rate of work goes as me2H2Rs/ m~ 2
• For tide raised on satellite H=Rs(mp/ms)(Rs/a)3
• From the above, we expect the energy stored E to go as
5
2
Gm
e  Rs 
p
E~ ~  
ms  a  a
2
4
m
R
19
m
38

~
s

Note that here we have used m 
2
2 rgRs
3 ms G
Tidal heating (2)
dE nE

• From the definition of Q, we have
dt Qs
• We’ve just calculated the energy stored E, so given Qs
and n we can thus calculate the heating rate dE/dt
• The actual answer (for uniform bodies) is
5
2
Gm
dE
63 e n  Rs 
p
 ~
 
dt
4m s Qs  a  a
2
• But the main point is that you should now understand
where this equation comes from
• Example: Io m~s  40, Qs  100, e  0.0041
• We get 80 mW/m2, about the same as for Earth (!)
• This is actually an underestimate – why?
How do we calculate Q?
• We can get estimates/bounds on Q by considering orbital
evolution of some satellites (see Week 1)
• For solid bodies, we assume a viscoelastic rheology
• Such a body has a rigidity m, a viscosity h and a
characteristic relaxation (Maxwell) timescale tm=h/m
• The body behaves elastically at timescales <<tm and in a
viscous fashion at timescales >> tm
• Dissipation is maximized
when timescale ~ tm:
t mn
Q
2
1  (t m n)
Tobie et al. JGR 2003
Calculating Q (cont’d)
• Ice has rigidity ~109 Pa and viscosity ~1014 Pa s, so the
Maxwell time is ~105s which is comparable to the
orbital period, so we expect dissipation in the ice shells
• Silicates m~1011 Pa, h~1021 Pa s, so less dissipation
• But silicate viscosity decreases significantly if melting
occurs, which will lead to an increase in dissipation, and
thus a feedback effect
• This runaway situation was first identified by Peale et al.
(1979), who predicted massive volcanism on Io two
weeks before it was observed for the first time
• A similar feedback effect may also occur in ice (see
previous diagram)
Tidal Energy and Stress
• Tidal stresses and heating decrease markedly with distance
• Radiogenic heating is dominant in Callisto and Ganymede
(now), secondary in Europa, and insignificant for Io
C/msRs2 3Gms/5R
(MJ kg1)
Body
H
(m)
3eH dW/dt
dWR/dt
EeH/Rs
(m) (1012 W) (1012 W) (MPa)
Io
7802
312
8900
0.31
0.57
0.3679(4)
1.96
Europa
1966
60
8.1
0.13
0.13
0.346(5)
1.23
Ganymede
1258
5.7
0.074
0.29
0.007
0.311(3)
2.25
Callisto
220
4.6
0.015
0.31
0.006
0.355(4)
1.79
H is static tidal bulge for a fluid body, 3eH gives peak-to-peak diurnal tidal amplitude, dW/dt is tidal
dissipation rate for a uniform body with Jupiter’s mass=1.899x10 27 kg, k=3/2 and Q=100, dWR/dt is
radiogenic heat production within silicate portion of body assuming a heating rate of 3.5x10 -12 W/kg,
EeH/Rs gives the approximate stresses due to diurnal tides with E=10 GPa, C/msRs2 gives the normalized
moment of inertia (Anderson et al. 1996,1998b,2001a,b) and 3Gms/5Rs gives the energy delived during
homogeneous accretion. A uniform body has a normalized MoI of 0.4.
Non-synchronous rotation (1)
• From the satellite’s point of view, the planet travels in the
opposite direction round the sky to the satellite itself
• The tidal bulge always lags the planet’s motion
• In an eccentric orbit the amplitude of the tidal bulge varies and is
largest at the periapse
• The result of the varying bulge is a varying torque, which turns
out to be positive i.e. it should increase the satellite’s rotation
rate slightly above synchronous
Eccentric orbit
satellite
Periapse
Torque increases spin
Larger
planet
Apoapse
Torque opposes spin
Smaller
Non-synchronous rotation (2)
• For an eccentric satellite, the net tidal torque should
lead to non-synchronous rotation
• But the torque may be balanced by a frozen-in mass
asymmetry, leading to synchronous rotation
• A frozen-in mass asymmetry requires a relatively
rigid body (See Greenberg and Weidenschilling, Icarus 1984)
Tidal torque:
e
T 
Q
Mass torque:
T  B  A
• Both the rigidity of the satellite and Q depend on its
internal structure, so there are potential feedbacks
between orbital evolution and rotation state
Internal structure
Orbital behaviour
Impact Cratering
• Main source of impact craters in outer solar system is
comets
• Synchronously rotating satellite will be preferentially
cratered on its leading hemisphere (think raindrops)
• So distribution of impact craters on surface can be used
to test whether NSR has occurred
• Density of impact craters can be used to infer surface age
• Obtaining absolute surface ages requires the impact rate
to be derived, from a combination of current and
historical astronomical observations, and models.
Uncertainties are currently large.
• Note that the impact rate will increase for satellites
closer to the primary (effect of gravitational focusing)
Cratering Statistics
Zahnle et al.
Icarus 1997
Furrowed terrain
Grooved terrain
Expected curves
if NSR is not
occurring
Absolute ages have been revised upwards since (Zahnle et al. Icarus
2003)
Cratering Statistics - Results
• Io – no impact craters observed (!) so surface is very
young (< 1 Myr)
• Europa – few impact craters, surface age ~50 Myr.
Not enough craters to detect if NSR is happening
• Ganymede – bimodal surface, ages ~2 Gyr and ~4
Gyr (uncertainties large). Spatial distribution flatter
than expected, suggests NSR has occurred.
• Callisto – very ancient surface, ~4.5 Gyr. Spatial
distribution very flat, but may be because crater
population is saturated everywhere (i.e. one crater is
destroyed for every new one produced)
Thermal & Orbital Evolution
• We would like to be able to answer the question: how
have the satellites’ orbits and interiors evolved over
solar system history?
• This is difficult because
– Observations are severely limited (e.g. cratering evidence is
not much use on Io or Europa)
– Important parameters (such as Q) are uncertain
– The theoretical problem is difficult. Why?
1) Feedbacks. Orbital evolution, NSR and tidal dissipation all
depend on Q, but Q is dependent on the internal structure of the
satellite, which depends on tidal dissipation . . .
2) Coupling. The satellites can’t be treated as isolated objects,
because of the Laplace resonance. So you have to model their
evolution simultaneously . . .
Thermal & Orbital Evolution (cont’d)
• Nonetheless, progress is being made, both on the
observational and the theoretical front. We’ll discuss
examples of both later in the course.
This is an example of Europa’s shell thickness evolution with time, from Hussmann and
Spohn, Europa’s Ice Shell Meeting, LPI, 2004. The periodicity arises because Io and
Europa’s eccentricities change over time, which changes the dissipation in Europa’s ice
shell and thus the shell thickness. In this model the shell is convecting.
Summary
• Tides are important in determining spin state, orbital
evolution and heating of satellite
• Ice rheology is complicated:
– Near-surface, it will behave like rock on Earth
– At depth, it will flow at a geologically rapid rate
• Cratering observations can provide us with relative
surface ages, but absolute ages are subject to large
uncertainties
• Satellite internal structures are constrained by a
mixture of observations (C/MR2, mean density,
magnetometer) and reasonable expectations
Io
Basic Parameters
Io
a (Rp)
5.9
Period (days)
1.77
Eccentricity
0.004
Radius (km)
1821
Mean density (g/cc) 3.53
g (m s-2)
1.80
C/MR2
0.378
Heat flow (mWm-2) ~2500
Moon
60.3
27.3
0.055
1737
3.34
1.62
0.394
~25
• Note the likely structural similarities with the Moon
What’s it like?
• Volcanically very active (see later)
• Cold – surface temperature about 130K, but variable
(due to volcanism)
• Very tenuous atmosphere (volcanic)
• Sulphur-rich surface – deduced from ground-based
spectroscopic observations (different colours are
different sulphur allotropes)
• Very hostile environment (for people or spacecraft) –
charged particles accelerated by Jupiter’s large
magnetic field
• Not clear whether Io has an internal magnetic field
(Kivelson et al. JGR 2001) – interactions with Jupiter’s
field make identification difficult
Landforms
• Three main types: Volcanoes, Mountains and Paterae
(irregular depressions, similar to calderas)
200km
350km
flow
patera
volcano
Low-sun angle; shadow measurements give
mountain elevations of up to 4km. Lobate flows
are large landslides. Mountains show no signs of
volcanic activity and appear to be fault-bounded.
Amirani lava flow, Io
Lava flows
500km
• Dark flows are the most recent
(still too hot for sulphur to
condense on them)
• Flows appear relatively thin,
suggesting low viscosity
500km
Comparably-sized lava flow on Venus
(Magellan radar image)
Time-Variability
• Changes detected
from Voyager to
Galileo missions
and within
Galileo mission
April 1997
Lava flow
erupted at
Prometheus
between
Voyager and
Galileo missions
(Davies JGR
2003)
July 1999
Sept 1997
Pillan
Pele
400km
Galileo images of
overlapping
deposits at Pillan
and Pele
Volcanic activity (1)
Voyager image of eruption
plume, approximately 300
km high
Fire fountain(?)
• Galileo image of Tvashtar, apparently in the process of erupting
• The CCD was overloaded by the eruption, but it has been
interpreted as a fire-fountain 1.5 km high
Volcanic activity (2)
Galieo nightside image of Pele,
SSI clear filter. Radebaugh et al. 2004
Erta Ale lava lake, Ethiopia. Lake
is 100m across.
• Images suggest molten magma immediately beneath
the surface (at least in some places)
• Volcanic activity erupts about 1 tonne / second sulphur
into the “atmosphere”, some of which may end up on
Europa (contaminants have been detected there)
Ground-based observations
• Have the advantage of longer observation periods and
better spectral resolution than spacecraft
• Spatial resolution is also getting much better thanks to
adaptive optics and Hubble
• The sequence below shows a hot spot which flares up
to equal the brightness of Loki (spot 2) over a few days
1 arcsecond
July 12 1998
From Macintosh et al., Icarus 2003
July 28 1998
Aug 4 1998
Keck interferometer
Energetics (1)
• We can measure the power output of Io by looking at
its infra-red spectrum
• Heat flux is appx. 2.5 W m-2 .This is 30 times the
Earth’s global heat flux.
5
dE
63 e n  Rs  Gm
 ~
 
dt
4m s Qs  a  a
2
2
p
• Assume low rigidity ( m~s  1 ) – why?. To balance the
heat being produced requires Qs=90. Is this reasonable?
What does it imply about viscosity?
• Where does the power ultimately come from?
• A heat loss of 2.5 Wm-2 over 4.5 Gyr is equivalent to
0.03% of Jupiter’s rotational energy
Energetics (2)
• How do we get 2.5 Wm-2 out of the ground?
• A conductive layer (or convective stagnant lid) would
need to be ~1 km thick. Reasonable?
• What about magma transport (advection)?
• Silicate magma generates ~5 GJ/m3 on cooling 1000K
and solidifying
• A resurfacing rate of ~1 cm/yr can account for the
observed surface heat flux
• This resurfacing rate is also consistent with estimates
based on impact craters and IR cooling models
• So Io is unique among the solar system in that its heat
flux is dominated by advection
Interior Structure
After Anderson et al.,
JGR 2001
• Lacks outer ice layer (in
Silicates
contrast to other Galilean
1821 km
-3
3500 kg m
satellites). Why?
• Even though sulphur is
700 km
Fe-FeS
5150 kg m-3
abundant at the surface, the
bulk of the interior must be
silicates/iron from simple Remember these structures are non-unique: the
ones shown assume plausible but not necessarily
cosmochemistry
correct densities.
• Io likely has a crust, but we can’t detect it with current data
• We can’t tell (directly) whether the core or the mantle are
partially or completely liquid.
• Io’s k2=1.29. What is this telling us? (rigidity or mass concn.)
~500km
• Rigid lid is required by high
mountains and is a result of
rapid burial of cooled surface
material
• Bulk of dissipation occurs in
partially molten mantle
• Magma percolates through
mantle and ascends through
cold lid in discrete fractures
i.e. dikes
• Erupted material cools by
radiation and is re-buried
~50km
Interior Structure(?)
Solid lid
Partiallymolten mantle
Solid
mantle
After Moore, Icarus, 2001
Consequences of resurfacing
• Burial leads to large compressive stresses
due to change in radius
• Stress ~ E DR/R ~100 MPa for 2 km burial
• Easily large enough to initiate faulting
• Additional compressive stresses may arise
from reheating the base of the crust
stereo
550 km
10km
Schenk and Bulmer, Science 1998
DR
After McKinnon et al.,
Geology 2001
Low-angle (why?) thrust
faulting is probably
responsible for many of the
mountain ranges seen on Io
Eruption Spectra
• Recall Wien’s law – lmax a 1/T
• So infra-red spectra give temperature information
Davies, JGR 2003
• Single temperature curve
provides poor fit
• Two-temperature curve
provides much better fit
• Short-wavelength “hump”
requires temperatures
>1400K
• So silicate volcanism must
be involved
• Voyager could not resolve
this issue
• Time-evolution gives
cooling history
Plumes
• What’s the exit velocity?
• How do speeds like this get generated?
• Most likely explanation is sulphur
geysers: decompression of sulphur
leads to phase change and volatile
release, driving flow
500 K
250km
Loki
Pele
Constant entropy (adiabatic)
Liq.
Vap.
L+V
Pressure
decreases
200 K
S+V
0K
After Smith et al., Nature 1979
Entropy (J kg-1 K-1)
Energy available per unit
mass is given by change
in enthalpy (internal
energy + PV term).
Typical enthalpy changes
~100 kJ/kg, which results
in velocities of ~400 m/s
Callisto
Basic Parameters
Io
a (Rp)
5.9
Period (days)
1.77
Eccentricity
0.004
Radius (km)
1821
Mean density (g/cc) 3.53
g (m s-2)
1.80
C/MR2
0.378*
* Anderson et al. JGR 2001
+ Anderson
Callisto
26.3
16.7
0.007
2400
1.85
1.24
0.355+
et al. Icarus 2001
• Note the lower density and the fact that Callisto is more
centrally concentrated than Io (see later)
Geological Observations
•
•
•
•
Very heavily cratered – probably saturated
No obvious non-crater landforms – tectonically dead
Some impact basins very large e.g. Valhalla
Also several crater chains (catenae). How did they
form? Why are they useful?
1500km
600km
Mass Wasting
• Lobate features associated with steep crater walls
• Triggered by impacts or devolatilization?
• Plot in similar parameter space to terrestrial landslides,
despite different materials and gravity – why?
From Moore et al. Icarus 1999
Degradation / Sublimation
Moore et al. Icarus 1999
• Callisto systematically lacks small
(<1km) craters relative to
Ganymede
• Craters show significant
degradation on Callisto
• This may be due to the presence
of a highly volatile ice (e.g. CO2)
which is subliming over time
• Evidence for (thin) atmospheric
CO2 supports this hypothesis
Internal Structure
• Two interesting inferences:
– It has an ocean
– It is only partly differentiated
• Where do these inferences come from?
Probable ocean
location
Anderson et al. Icarus 2001. Two layer
model of Callisto showing inner and outer
shell densities which match observations
• Ocean detected with
magnetometer data
• Partial differentiation is the
only way to fit the MoI and
density data (see
)
An Ocean?
• We can (potentially) detect such an ocean because it
allows the shell to flex more than it would do if it were
overlying a solid interior
• Thermal evolution of an ocean will be controlled by
balance between heat added (from below) and heat
transported to the surface
• Present-day chondritic heat flux ~ 5 mW/m2
• Heat flux = k DT/z
(k~3 W/mK, DT~100 K)
• So equilibrium conductive shell thickness ~ 60 km
• This seems reasonable – but what happens if the ice
shell starts to convect?
An Aside on Convection (1)
• Convective vigour (and whether it occurs) is governed by
the Rayleigh number:
r is density, a thermal
Where does
this come from?
•
•
•
•
rgaDTd
Ra 
h
3
expansivity, DT temperature drop
across the layer,  thermal
diffusivity, h viscosity, d layer
thickness
Convection initiates for Ra >~ 1000
3
Is Callisto convecting? Ra  109  d   h 
14
200
km
10
Pas 



So the answer is probably yes
This creates a problem: Convective heat transport is
much more efficient than conduction, and so we would
expect any ocean to have frozen long ago
• How much heat is transported by convection?
An Aside on Convection (2)
• For a temperature-dependent viscosity
material, a stagnant lid develops on top of a
roughly isothermal, convecting interior
• The viscosity is given by hoexp(-[T-To]) z
where ho is the reference viscosity at To and
 is a constant (K-1) set by the rheology
• The stagnant lid thickness  is given by
  dRa
1/ 3
(DT )
T
Stagnant lid
Convection
4/3
• And so the heat flux across the stagnant lid is
1/ 3
 rga 
4 / 3
 
F  k 
 h 
Note that this heat flux
is independent of shell
thickness and DT
Convecting ice shells (cont’d)
• For likely parameters, we get a convective heat flux of
~70 (1014 Pa s /h)1/3 mWm-2
• This value is independent of shell thickness and exceeds
the radiogenic contribution if h < 3x1017 Pa s (which
would result in the ocean freezing)
• Tidal contribution to heating is negligible
• Most likely way of maintaining an ocean is by increasing
the viscosity. Possibilities:
– Antifreeze e.g. NH3 lowers temperature of ocean (and
convecting ice) (see Spohn and Schubert Icarus 2003)
– Silicate particles in ice increase its viscosity
– Very large ice grains (?)
– Non-Newtonian convection less efficient (?)(Ruiz, Nature 2001)
Partially differentiated?
• Partial differentiation implies that the interior of
Callisto never got above 270K (why?)
• 1) How do we stop melting during accretion?
– Accretion energy = 0.6 GM2/R ~ 1.7 MJ/kg
– This would give rise to ~850 K temperature increase
– The nebular temperatures might also cause melting
• 2) How do we stop melting thereafter?
– Chondritic heating ~3.5pW/kg now, x3 over 4.5 Gyr
– Total 1.5 MJ/kg ~750 K temperature increase
• Possible answers (or maybe it is differentiated?):
– 1) Accrete Callisto slowly (so that the energy can radiate)
– 2) Get rid of the heat rapidly enough to avoid deep melting
(but slowly enough so that the shallow ocean survives)
Slow Accretion (?)
• If we assume that satellites accrete from small bodies, the
temperature rise of the satellite is determined by the
accretion rate (slower rate = colder temperature)
• Canup and Ward (A.J. 2002) postulate an accretion disk
round Jupiter which is supplied at a low rate, resulting in
a low density, low disk temperatures and slow formation
timescale (>105 yrs) of the satellites
• These characteristics would all help to generate a partially
undifferentiated Callisto
• The low disk density also means that the satellites can
survive disk torques which move them towards Jupiter
• Is it reasonable to assume that accretion involved only
small objects, and not large collisions?
Removing heat
– 1) the pressure-dependence of ice melting temperature
– 2) accretion leads to radially increasing temperatures
Rock fraction
Rock fraction
temperature
temperature
• A rock-silicate mixture will tend
to separate over time as the rock
heats the surrounding ice
ocean
• Areas with a higher rock fraction
will have a higher viscosity and
thus a lower heat flux
• Near-surface cold ice will retain
its rock and act as an insulator for
Nagel et al. Icarus 2004
any underlying ocean
• A shallow ocean but absence of deep melting is probably
a consequence of:
Orbital evolution
• Recall dissipation in satellite leads to circularization
• Assume no torque from primary, so momentum conserved

E
• In this case, it can be shown that e  
Why?
2eE
• We have previously calculated E (see Io), and so we can
obtain e and circularization timescale te= -e/ e directly:
5
4 ms  a  m~s Qs
 
te 
63 m p  Rs  n
~ Q ) Myr. For a solid rockAt the present day, this gives us (8 m
s s
~
ice mixture, m s ~ 15 and Qs ~ 100 so te~12 Gyr.
But, if there really is an ocean present, then dissipation will be
amplified, Qs reduced and te reduced, leading to potential
problems . . .
Summary
• Io’s silicate volcanic activity is driven by tidal heating
of a partially molten mantle – feedback between
temperature, viscosity and heating
• Callisto, by contrast, has experienced no significant
tidal heating over its history
• Nonetheless, Callisto has an ocean, probably as a result
of incorporating antifreeze e.g. NH3
• How did it develop an ocean and yet (apparently) retain
an undifferentiated interior ?!
• Next time – Europa and Ganymede