What’s going on at Enceladus?
Francis Nimmo (U. C. Santa Cruz)
With help from: James Roberts (APL), Chris Zhang (UCSC), Craig O’Neill
(Macquarie), Bob Pappalardo (JPL), Isamu Matsuyama (Berkeley), John
Spencer (SWRI)
Talk Outline
• Planetary physics
• Why should anyone care
about icy moons?
• Case study: Enceladus
– Why is it active?
– Does it have an ocean?
– How has the ocean evolved?
• Conclusions and the Future
Planetary Physics
How did planetary bodies evolve to their current state?
• Observational science
– Can’t easily run experiments
– Can make predictions
• Data-starved
– Small N cf. astronomers
• Complex problems
– Planets are more complicated than stars
• A young field
– 21st century technology . . . 19th century physics
Icy Moons
3600 km
Why do we care about icy moons?
• Many of them! (large N is good)
• They record a lot of history, and
exhibit a surprising diversity
• They have complex behaviour
(e.g. thermal-orbital coupling)
• They are astrobiologically
important (many have oceans
beneath the ice)
• Lessons elsewhere – Kuiper Belt
Objects, “super Ganymedes” etc.
How did planetary bodies evolve to their current state?
Cassini in the Saturn system
• “Last of the Cadillacs”,
launched 1997
• Highly capable, nuclear
powered
• No scan platform
• In Saturn orbit since 2004
• 8 Enceladus flybys to date,
some as close as 25 km
• Extended extended mission
approved (likely to ~2017?)
Enceladus
M E T D R. T H I P
•
•
•
•
•
Semi-major axis 3.94 Rs
Period 1.37 days
e=0.0045
R=252 km
2:1 eccentricity resonance with Dione
What is it like?
• R=252 km
• r=1610 kg m-3
• Time-varying
tidal bulge ~60m
if fluid
• Mixture of
ancient, heavily
cratered and
young, heavily
tectonized terrain
• Geologically
active! (geysers)
Porco et al., Science 2006
South Pole
“Tiger Stripe” Region
• No impact craters (young)
• Correlate with plume location
• Centred at South Pole
30 km
South Pole
Porco et al. Science
2006
Heat flow and temperature
Spencer et al. Science 2006
Regional heat flow
3.9 – 7.7 GW
(~100 mWm-2)
Plume Fluxes
Tian et al. Icarus 2007
Porco et al. Science 2006
• Mass flux 120-180 kg s-1
• Exit velocity 300-500 ms-1 (vesc~235 ms-1)
Summary of Observations
•
•
•
•
•
[Tiger stripes located at South Pole (Nimmo et al. 2006) ]
S polar heat flow 3.9-7.7 GW (Spencer et al. 2006)
Plume vapour flux 120-180 kg s-1 (Tian et al., Waite et al.)
Vapour velocity 300-500 ms-1 (Tian et al.)
Tiger stripes are hotter than surroundings (Spencer et al.)
August 2008 flyby
Brightness temperatures
Outstanding Questions
How did planetary bodies evolve to their current state?
1.Why is it active? (almost unique)
2.Is there an ocean? (astrobiology)
3.How old is the ocean? (history)
How to explain the activity?
• Tides plus eccentric orbit
Small bulge
Planet
Tidal bulge
• Satellite semi-major axis
Large bulge decreases
• Eccentricity damping
balanced by resonance
with Dione
• Hot tiger stripes?
Tidally-driven shear heating
• Stresses due to tides are time-varying
• Varying stresses can lead to strike-slip motion
• Strike-slip motion leads to shear heating (e.g. San
Andreas fault, Earth)
Nimmo and Gaidos JGR 2002
Europa strike-slip faults
Application to Enceladus
30 km
South Pole
• Assume tiger stripes have cyclical
tidally-driven strike-slip motion
• Motion leads to shear heating:
– Frictional (near-surface)
– Viscous (deeper)
• Sliding velocity u depends on
interior structure (Love number h2)
•
•
•
•
Tiger stripes are hotter than surroundings (as observed)
Heating leads to vapour production (sublimation)
Bulk of vapour recondenses in near-surface
Heat flow and plume flux explained by a single mechanism
Model Details
• Heat diffusion
T
H
2
  T  
t
rC p
Shear heating
Partition parameter
• Vapour diffusion r v
H
2
 D r v  (1   )
(very simplified
t
L
model)
• Vapour production and thermal structure both affected
by partition parameter 
• Both equations solved to steady-state
• Brittle layer thickness solved self-consistently
Temperature Structure
recondensation
vapour
(ice sublimation)
Nimmo et al.,
Nature 2007
=0.1
href=1013 Pa s
• 24 km thick shell, u=8x10-6 ms-1, 500km length
• 1 GW of heat conducted; 6 GW by vapour transport.
Results
Observed S polar heat flow
Plume
Mass
Flux
• Heat transported by conduction & advection (vapour)
• Recondensing ~90% vapour in near-surface gives observed
heat flow; remaining vapour escapes to form plume
• Velocity > 10-6 ms-1 (~10 cm/cycle, h2 > ~ 0.01)
Summary
• S polar heat flow 3.9-7.7 GW
– Tidally-driven shear heating is energy source
– Sliding velocity u>10-6 ms-1 (~10 cm/cycle, h2>0.01)
– Bulk of heat transported by vapour (~2000 kg s-1)
• Plume vapour flux 120-180 kg s-1
– ~10% vapour not recondensing
• Vapour velocity 300-500 ms-1
– Thermal velocity of vapour escaping into shear zone
• Tiger stripes are hotter than surroundings
– Natural consequence of shear-heating model
Love number h2>0.01?
Silicates 100 GPa, 1021 Pa s
• If h2>0.01, an ocean appears to be required (unless ice
shell viscosities are improbably small)
• What about some predictions?
March 2008 Tiger Stripe Map
• 9 - 16 µm brightness
• Resolution 4.1 - 9.6 km
Brightness temperature, K
Model predictions
u  d
d
u
A
B
D
Model 1
Model 3
C
Example results
51% misfit reduction
Conclusions
• Energy source for heat flow and vapour flux is
tidally-driven shear heating
• Large velocities (~10-6 ms-1,~10 cm/cycle) are
required, implying h2>0.01
• A subsurface ocean is implied by h2>0.01
• Vapour flux is due to sublimation of ice, does
not directly sample ocean
• Predicted variations in tiger-stripe heat fluxes
provide reasonable match to observations
So what?
• Different from normal picture of tidal heating
• Likely important in formation of geological
features (here and elsewhere e.g. Europa, Triton)
• Seems to require an ocean
• Possible mechanism for transfer of material from
interior to exterior (astrobiology)
• But the plume doesn’t necessarily sample the
ocean directly
An ocean?
• An ocean would be
important because
– It makes the ice shell more
dissipative
– It provides a potentially
habitable environment
– It provides clues to the
history of Enceladus
• The shear heating model suggests an ocean is
present
• Is an ocean a long-lived feature? (or are we viewing
Enceladus at a special time??)
Ocean lifetime
Roberts and Nimmo 2008
N
• Heat in vs. heat out
• Is the ice shell a good insulator?
Ice shell
Ocean
Silicates
heat production
• Viscoelastic Maxwellian body
• 4 orders of magnitude LESS
heating in silicates
mice = 4 GPa msil = 70 GPa
hice = 3×1013 Pa s hsil = 1017 Pa s
dice = 70 km
Ice: 10-7 W m-3
Core: 10-11 W m-3
Model
N
10-9 Wm-3
• CitcomS
• 2D (axisymmetric) or 3D
• Temperature-dependent
viscosity
• Variable surface temperature
• Tidally-heated
How to maintain an ocean?
convective
radiogenic
Conductive
ice shell
Radiogenic heat flow
Roberts and Nimmo 2008
• Very hard to maintain an ocean!
• Ocean lifetimes few tens of Myr
Results
• Negligible tidal heating in core
• Convection is very efficient at removing heat
across the ice shell (and so is conduction)
• Ocean survives only a few tens of Myr!
• How to get a long-lived ocean?:
–
–
–
–
Antifreeze (e.g. NH3)?
Heat-source in ocean (Tyler Nature 2008)?
Higher eccentricity (more heating in shell)?
Others??
Summary
• Why is Enceladus active?
– Tidal heating, possibly due to shear at tiger stripes
• Does it have an ocean?
– Almost certainly; required for shear heating to work
– But not all of the plume material has to come directly
from the ocean
• How has the ocean evolved?
– Ocean only survives for tens of Myr under presentday circumstances. Is it recent?
– Could have been maintained if eccentricity were
higher in the past – link to orbital evolution
So what?
• Present-day activity and subsurface ocean
imply habitability
• Present-day characteristics provide boundary
conditions for understanding how Enceladus
has evolved
• Are we viewing Enceladus (and other places in
the Saturn system) at a special time?
Closing thought: a special time?
• Enceladus is putting out more heat than it can
generate in equilibrium (Meyer & Wisdom 2008)
• The timescale for 40Ar exhaustion is ~10 Myr
• The ocean will re-freeze within ~10 Myr
• Surface geology indicates several separate episodes
of deformation
Is Enceladus only episodically active?
Are we seeing it at an unusual time?
Episodic behaviour?
• Tidal-thermal feedbacks can lead to episodic
behaviour (Ojakangas and Stevenson 1986)
• Some kinds of convection are episodic:
O’Neill &
Nimmo, 2010
Caveat / Future Work
• Lateral heterogeneity?
• Incorporate recent observations into models
• How to maintain a long-lived ocean?
• Can you re-melt an ocean once frozen?
• Thermal-orbital evolution of system (what
about Dione, Tethys, Mimas?)
• Techniques developed here are useful
elsewhere . . .
Prospects elsewhere?
Europa
70 km
Enceladus
• Shear heating on Europa could also
produce vapour plumes
• Plumes would be harder to see
• Difficult to distinguish from sputtered species
• Future mission approved – Jupiter Europa Orbiter
Summary
• Why is it active? Tidally-driven shear heating
• Does it have an ocean? Almost certainly
• How has the ocean evolved? Unclear; likely
short-lived; perhaps maintained by higher e in
past, or an indication of episodic behaviour?
Update: Ammonia and Salt
Waite et al. Nature 2009
• 0.8% NH3 – presumably
from ocean
• 40Ar exhaustion timescale
~10 Myr (cf. ocean
lifetime)
• “. . . Data require both
liquid water and solid ice”
• No sodium observed in plume vapour (Schneider et
al. Nature 2009) – possibly below detection limits?
• Some grains in the E ring contain a few percent Na
salts (Postberg et al. Nature 2009)
• Suggests presence of a salty ocean
Time-dependent behaviour?
• Enceladus is losing heat at least 3 times faster than the
steady-state tidal heating value (Meyer & Wisdom 2007)
• Previous, higher-eccentricity state (thermal-orbital
feedbacks)?
• Occasional periods of high heat-loss?
O’Neill &
Nimmo, submitted
Model 3
Alex.
Cairo
Baghdad
Damascus
TOTAL
-36%
+57%
-25%
-51%
-18%
Eccentricity evolution
Internal
structure
k2
Q
Tidal heating
k2
( Q , e)
k2/Q is a measure of
how much dissipation
occurs in a body
Orbital
evolution (e)
• This coupling only occurs when tidal dissipation is the
main source of energy
• The feedback makes for complicated thermal-orbital
histories – especially when resonances are involved
Example evolution
Present-day
eccentricity
Zhang and Nimmo,
submitted
Time, Myr
• Complicated behaviour (even for constant k2/Q)
• Problem: equilibrium heat production (Meyer & Wisdom)
• What happens when thermal feedbacks are turned on? –
we’re working on it!
Putting it all together
Shear heating and
vapour production
Subsurface
mass anomaly?
Reorientation
Deep ocean
(freezing out?)
Cold core
Ancient tiger
stripes?
Thick ice shell
N
Thermal-orbital evolution
Start from a near-circular Enceladus with a thick ice shell
and in 2:1 resonance with Dione
Shear heatingQmodel
model
Presentday e
Present-day
heat flow
Equilibrium heat flow too low (Meyer & Wisdom 2007)
Transient heat flow also too low
Orbital evolution in resonance
• Yoder & Peale 1981, Greenberg 1982, Ojakangas &
Stevenson 1989, Meyer & Wisdom in prep.
n11 defines proximity to exact commensurability
For 2:1 resonance we have:
e1
e1 
n11
M 2 C1 n1
M Sn 11

M S c1 2
e1 
e1 1  d1e12
M 2 C1

Effect of near-surface heating
Roberts and Nimmo 2008b
Model relative temperatures
Vapour Production and Transport
SHEAR ZONE
• In steady-state, vapour flux controlled by  and H
recondensation
• Redeposition of vapour in near0.7
surface gives out latent heat (ad hoc!)
0.8
• For =0.1, 6 GW recondensation
0.9
-1
(90% of vapour) and 220 kg s plume
flux, 1 GW conduction.
• Vertical vapour velocity (thermal)
Steady-state
~500 ms-1
vapour density
• Timing of vapour escape not
considered
0
12
6
18
Distance, km
• Vapour production gives colder subsurface and deeper brittle zone
• Complications – porosity feedback, near-surface temperatures etc.
Shell thickness
• Thinner shell gives higher velocity, but less
volume to heat - tradeoff
• Shell thickness > 5 km
=0.1
Predictions
Heating rate
(and thus
temperature)
scales with
mean stress
• Also look for strike-slip offsets
Model Assumptions
• Local heat production depends on timeaveraged shear velocity
• Shear velocity depends on:
– time-averaged tidal shear strain rate
– distance to neighbouring fault
(as strain is distributed between faults)
• We should also take into account the
wavelength range of the data:
• We are ignoring the details of
heat transport here!
d
u
u  d
Two Models
• All models produce the same total power over all
wavelengths
• Model 1 – Original (Nimmo et al. 2007)
– No distance correction, no temperature correction
• Model 2
– Distance and temperature
corrections (hot parts
look hotter, cool parts
look cooler)
9 - 16 µm Power Profiles
Changes?
Reorientation elsewhere?
• Impact basins can cause reorientation (Melosh 1975)
D
2j
Potential anomaly
G20=pGRDr cosj sin2j
Reorientation d depends on latitude
and longitude of load
Slow rotators favour reorientation
R(km)
P(days)
Basin
D (km)
j
d
Mimas
196
0.942
Herschel
135
19.7
2.4
Tethys
530
1.888
Odysseus
450
24.3
9.9
Dione
560
2.737
Aeneas
175
9.0
2.6
Rhea
764
4.518
Tirawa
350
13.1
17.0
Titania
790
8.706
Gertrude
400
14.5
(17.5)
Rate of reorientation
• Heuristic argument (Tsai & Stevenson)
• Reorientation favoured if rotational energy is reduced
• Energy released is dissipated by viscous deformation
which accompanies reorientation
• Reorientation timescale controlled by size of load dC
and viscous relaxation timescale trel
t TPW
fC
~ t rel
dC
f is flattening, C is moment of inertia, trel~1000 yrs for Earth
Effect of tides
c
a
b
• Triaxial ellipsoid (not
oblate spheroid)
• Reorientation around
tidal (a) axis is easy
• Reorientation around b
axis is hard
(tidal axis)
q fL
• Matsuyama and Nimmo (in prep)
• 2 equations, 2 unknowns (d,):
Load
Init. rotn. axis

Q sin( 2q ) cos(   )  sin( 2d )(1  3 cos  )
f
L
f
L
Q sin( 2q ) sin(    )  3 sin d sin( 2 )
f
L
f
L
d
2
a
 fL
Summary
• Shear heating can generate sufficient heat
• Bulk of heat (~7 GW) is transported by vapour
produced at depth and recondensing (~2000
kg/s) in the near-surface
• Temperatures are highest at the tiger stripes
• Remainder of vapour (~200 kg/s) escapes to
form observed plumes
• Shear velocities required imply h2>~0.01
• Shell thickness > 5 km
Reorientation
Nimmo & Pappalardo 2006
• Thick ice shell required
to develop large enough
mass anomaly
Reorientation (1)
• Rotational stability
Rotational
bulge
Mass excess -> equator
Mass deficit -> pole
• Load promotes reorientation (rotation energy is
minimized by placing positive load at equator)
• “Fossil” rotational bulge opposes reorientation
• Both the size of the load and the size of the “fossil”
part of the bulge depend on the rigidity structure
Update - topography
Thomas et al., submitted
• South polar
topographic low
(~0.5km)
• Natural consequence of geysers (~50 Myr)
• Insufficient to cause reorientation on its own (Q~0.2)
• Aided by diapir at depth?
Shear heating and double ridges
Nimmo and Gaidos JGR 2002, Prockter et al. GRL 2005, Han and Showman LPSC 2007
Diurnal tidal stresses
165 W, 70 S,
h2=0.2
Diurnal tidal stresses
Shear velocity scaling
 1 e1 h21 M 1 m2  R1 
 

 2 e2 h22 M 2 m1  R2 
• Shear velocity
3
 a2

 a1



3
u  d
 d 
• Scaling from Europa u  4 x10 
h2 ms-1
 30km 
5
Internal structure
161 km
100 GPa
1021 Pa s
3500 kg m-3
3 GPa
1013 Pa s (nominal)
950 kg m-3
91 km
Strike-slip faults & tidal walking
• How do they form? A consequence of the way tidal
stresses rotate over one diurnal cycle (Tufts et al. 1999).
Vertical (map) view
Tidal
stresses
Friction prevents
block motion
• This ratcheting effect can lead to large net displacements
• Strike-slip motion will lead to shear heating if
sufficiently rapid (Gaidos and Nimmo 2000)
Excess temperature
Tidal Heating at Base of Ice Shell
10-7 W m-3
Convective Regime
Predicted Surface Heat Flux
Observed HF in South Polar region
[Spencer et al., 2006]
Core Heat Flux
Tidal heating
Radiogenic heating
Temperature at 50 km depth
Spectrum of Temperature Structures
Similarities to Silicate Bodies
• Interior structures are similar (except
for thick surface layer of ice)
• Ice in thick shells can undergo phase
changes due to high pressure
• Ice may also convect in thick shells
670 km
• Near-surface ice is cold and rigid and
will deform in a brittle fashion
scarp
Close-up of Miranda rift, showing
large fault scarp (~5km high)
Differences to silicate bodies
• Ice is less dense than water – subsurface oceans, melt
is hard to erupt
• Ice is weaker (less rigid) than rock and near melting
has a viscosity ~106 times lower
• Major source of energy and deformation is tides, not
radioactive decay or accretion
• Interior structure places constraints on mode of
formation (caveat emptor)
• Tidal dissipation means that orbital evolution and
thermal evolution are inextricably linked
• Thermal evolution can be non-monotonic
Common Processes
• Large N means allows identification of
universally important processes – predictions
• Provide constraints on interiors and evolution of
icy bodies
• Processes to examine:
–
–
–
–
Tidal heat production
Shell thickening
Reorientation
Shear heating
• Combination of modelling and observations
Reorientation?
• Density consistent with ice
shell & silicate mantle
• IR data and plume could
indicate subsurface warm,
low density region (diapir)
• Region of low density can
cause satellite to reorient
so that the region ends up
at the nearest pole (see
next slide)
Reorientation - Theory
• Planets have equatorial bulge due
to rotation
• Long-term rotational stability and
energy minimization if rotation
axis = axis of maximum inertia
• Adding a load perturbs the
moments of inertia and leads to
reorientation
• Positive loads move towards equator, -ve towards pole
• The (“fossil”) part of the bulge which does not relax
opposes any reorientation
Reorientation Examples
Pappalardo et al. 1997
Mars – Tharsis Bulge
(roughly equatorial)
Miranda – coronae
Also Earth!
Reorientation Theory
• Matsuyama et al. (2006)
1
Q sin 2q L 
1 

d  tan 
2
 n  Q cos 2q L 
d
qL
Initial load colatitude Size of load compared to fossil bulge
Orientation of load relative to tidal axis (n=1 to n=4)
• The effective load Q
3 5G20
Q 2 2 f
R  (k 2  k 2 )
Degree-2 potential anomaly
Rotation rate
Change in Love number (size
of fossil bulge)
• Both G20 and (k2f-k2) depend on rigidity!
Application to Enceladus
• S pole of Enceladus has high heat fluxes and deformation
• Could a subsurface diapir have caused reorientation?
Equator
Pole
Rigid lid
Low density
diapir
Mass deficit
Equator
Mass excess
Pole
Weak lid
Low density
diapir
Mass deficit
To get polewards motion, a relatively rigid lid is needed
Enceladus Details . . .
• Diapir within silicates or ice shell
• Load depends on density contrast
• Lateral extent fixed by
observations
Nimmo et al., Nature, 2006
3 5G20
Q*  2 2 f
R  (k 2  k 2 )
Matsuyama et al., JGR, 2006
Enceladus Results
 Q sin 2q L 
1

d  tan 1 
2
 n  Q cos 2q L 
Initial load latitude 45o
• Lithospheric thickness > ~1 km (for ice) (consistent
with estimates of Te based on topography)
• Reorientation can be large if density contrast is large
Results
• Low-density blob in silicate core or ice mantle
could explain south polar location of hotspot
• Density contrasts required are large and
suggest compositional, not thermal, origin
• Reorientation requires relatively rigid nearsurface lithosphere (Te > 1 km)
• If diapir is in the ice, a thick ice mantle is
required
• If diapir is in the silicates, a global ocean can’t
exist (because it would decouple the ice shell
from the silicates)
•
•
•
•
Tests
Gravity (~ few mGal at s/c altitude)
Craters (leading/trailing asymmetry)
Tectonics
Fossil terrains?
Fossil terrains?
Sarandib Planitia
Helfenstein et al., Icarus, submitted
How to generate a diapir?
• Thermal convection?
– How does tidal heating influence
convection?
– How to create long-wavelength
structure?
– Time-dependence?
• Compositional convection?
– Partial melting of salty ice can
create buoyant region
• Ongoing work . . .
Figure courtesy
James Roberts
Conclusions
• Subsurface mass anomaly can account for
polar location of tiger stripes
• Anomaly probably compositional (+ thermal?)
in origin
• Observations should be able to test whether or
not reorientation has happened
• Multiple reorientation episodes?