Transcript Powerpoint slides

ESS 298: OUTER SOLAR
SYSTEM
Francis Nimmo
Io against Jupiter,
Hubble image,
July 1997
F. Nimmo ESS298 Fall 2004
Giant Planets
• Interiors
–
–
–
–
–
Composition and phase diagrams
Gravimetry / interior structure
Heating and energy budget
Magnetic fields
Formation
• Rings
• Atmospheres
– Structure
– Dynamics
• Extra-solar planets will be discussed in Week 10
F. Nimmo ESS298 Fall 2004
Giant Planets
Image not
to scale!
F. Nimmo ESS298 Fall 2004
Basic Parameters
a
(AU)
Porb
(yrs)
Prot
(hrs)
R
(km)
M
(1026 kg)
Obliquity
Mag.
Ts
moment K
Jupiter
5.2
11.8
9.9
71492
19.0
3.1o
4.3
165
Saturn
9.6
29.4
10.6
60268
5.7
26.7o
0.21
134
Uranus
19.2
84.1
17.2R
24973
0.86
97.9o
0.23
76
Neptune 30.1
165
16.1
24764
1.02
29.6o
0.13
72
Data from Lodders and Fegley 1998. Surface temperature Ts and radius R are measured
at 1 bar level. Magnetic moment is given in 10-4 Tesla x R3.
F. Nimmo ESS298 Fall 2004
Compositions (1)
• We’ll discuss in more detail later, but briefly:
– (Surface) compositions based mainly on spectroscopy
– Interior composition relies on a combination of models and
inferences of density structure from observations
– We expect the basic starting materials to be similar to the
composition of the original solar nebula
• Surface atmospheres dominated by H2 or He:
Solar
Jupiter Saturn Uranus
H2
83.3% 86.2% 96.3% 82.5%
He
16.7% 13.6% 3.3%
F. Nimmo ESS298 Fall 2004
Neptune
80%
15.2%
19%
(2.3% CH4) (1% CH4)
(Lodders and Fegley 1998)
Interior Structures again
• Same approach as for Galilean satellites
• 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
• We can relate J2,J4 . . . to the internal structure of the planet
F. Nimmo ESS298 Fall 2004
Interior Structure (cont’d)
• Recall how J2 is defined:
CA
J2 
MR 2
C
R
• What we would really like is C/MR2
• If we assume that the planet has no
strength (hydrostatic), we can use theory
to infer C from J2 directly
• For some of the Galilean satellites (which
ones?) the hydrostatic assumption may not
be OK
• Is the hydrostatic assumption likely to be OK for the giant
planets?
• J4,J6 . . . give us additional information about the distribution
of mass within the interior
F. Nimmo ESS298 Fall 2004
A
Results
• Densities are low enough that bulk of planets must be ices or
compressed gases, not silicates or iron (see later slide)
• Values of C/MR2 are significantly smaller than values for a
uniform sphere (0.4) and the terrestrial planets
• So the giant planets must have most of their mass concentrated
towards their centres (is this reasonable?)
Jupiter Saturn Uranus Neptune Earth
105 J2
1470
1633
352
354
108
106 J4
-584
-919
-32
-38
-.02
C/MR2
0.254
0.210
0.225
0.240
0.331
0.69
1.32
1.64
5.52
.155
.027
.026
.003
r (g/cc) 1.33
w2R3/GM .089
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Pressure
• Hydrostatic approximation dP
dr   r (r ) g (r )
• Mass-density relation dMdr( r )  4r(r )r 2
• These two can be combined (how?) to get the
pressure at the centre of a uniform body Pc:
2
GM
Pc 
4R 4
• Jupiter Pc=7 Mbar, Saturn Pc=1.3 Mbar, U/N Pc=0.9 Mbar
• This expression is only approximate (why?) (estimated
true central pressures are 70 Mbar, 42 Mbar, 7 Mbar)
• But it gives us a good idea of the orders of magnitude
involved
F. Nimmo ESS298 Fall 2004
Temperature (1)
• If parcel of gas moves up/down fast enough that it doesn’t
exchange energy with surroundings, it is adiabatic
• In this case, the energy required to cause expansion comes from
cooling (and possible release of latent heat); and vice versa
• For an ideal, adiabatic gas we have two key relationships:
Always true
rRT
P

P  cr 
Adiabatic only
Here P is pressure, r is density, R is gas constant (8.3 J mol-1 K-1), T is temperature,  is
the mass of one mole of the gas,  is a constant (ratio of specific heats, ~ 3/2)
• We can also define the specific heat capacity of the gas at constant
pressure Cp:
rC p dT  dP
• Combining this equation with the hydrostatic assumption, we get:
dT
dz
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
g
Cp
Temperature (2)
• At 1 bar level on Jupiter, T=165 K, g=23 ms-2, Cp~3R,
=0.002kg (H2), so dT/dz = 1.4 K/km (adiabatic)
• We can use the expressions on the previous page to derive how
e.g. the adiabatic temperature varies with pressure

c1/  
1 1
1 1
T  T0 
P  P0
1
(1   )C p

(Here T0,P0 are
reference temp. and
pressure, and c is
constant defined on
previous slide)
This is an example of adiabatic temperature
and density profiles for the upper portion of
Jupiter, using the same values as above,
keeping g constant and assuming =1.5
Note that density increases more rapidly
than temperature – why?
Slope determined by 
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Hydrogen phase diagram
Hydrogen undergoes a
phase change at ~100
GPa to metallic
hydrogen (conductive)
It is also theorized that
He may be insoluble in
metallic H. This has
implications for Saturn.
Interior temperatures
are adiabats
• Jupiter – interior mostly metallic hydrogen
• Saturn – some metallic hydrogen
• Uranus/Neptune – molecular hydrogen only
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Compressibility & Density
radius
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mass
• As mass increases, radius
also increases
• But beyond a certain mass,
radius decreases as mass
increases.
• This is because the
increasing pressure
compresses the deeper
material enough that the
overall density increases
faster than the mass
• The observed masses and
radii are consistent with a
mixture of mainly H+He
(J,S) or H/He+ice (U,N)
Summary
• Jupiter - mainly metallic hydrogen. Low C/MR2 due
to self-compression. Rock-ice core ~10 ME.
• Saturn - mix of metallic and molecular hydrogen;
helium may have migrated to centre due to
insolubility. Mean density lower than Jupiter because
of smaller self-compression effect.
• Uranus/Neptune – pressures too low to generate
metallic hydrogen. Densities and C/MR2 require large
rock-ice cores in the interior.
F. Nimmo ESS298 Fall 2004
From Guillot,
2004
F. Nimmo ESS298 Fall 2004
Magnetic Fields
• Jupiter’s originally detected by radio emissions (electrons being
accelerated in strong magnetic field – bad for spacecraft!)
• Jupiter’s field is ~10o off the rotation axis (useful for detecting
subsurface oceans)
• Saturn’s field is along the rotation axis
• Jupiter’s and Saturn’s fields are mainly dipolar
• Uranus and Neptune both have complicated fields which are not
really dipolar; the dipolar component is a long way off-axis
Earth
Jupiter
Saturn
Uranus Neptune
Spin period, hrs
24
9.9
10.7
17.2
16
Mean eq. field, Gauss
0.31
4.28
0.22
0.23
0.14
Dipole tilt
+11.3o
-9.6o
~0o
-59o
-47o
Distance to upstream
magnetosphere “nose”, Rp
11
50-100
16-22
18
23-26
F. Nimmo ESS298 Fall 2004
Magnetic fields
F. Nimmo ESS298 Fall 2004
How are they generated?
•
•
•
•
Dynamos require convection in a conductive medium
Jupiter/Saturn – metallic hydrogen (deep)
Uranus/Neptune - near-surface convecting ices (?)
The near-surface convection explains why higher-order terms
are more obvious – how? (see Stanley and Bloxham, Nature 2004)
F. Nimmo ESS298 Fall 2004
Energy budget observations
• Incident solar radiation much less than that at Earth
• So surface temperatures are lower
• We can compare the amount of solar energy absorbed
with that emitted. It turns out that there is usually an
excess. Why?
All units in
After Hubbard,
in New Solar System (1999)
1.4
W/m2
reflected
48
3.5
14
incident
8.1
5.4
Jupiter
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0.6
0.6
4.6
13.5
2.6
0.6
0.3
2.0
Saturn
0.3
Uranus
Neptune
Sources of Energy
• One major one is contraction – gravitational energy
converts to thermal energy. Helium sinking is another.
• Gravitational energy of a uniform sphere is
Eg  0.6GM 2 / R
Where does this come from?
• So the rate of energy release during contraction is
dE g
2
GM dR
 0.6 2
dt
R dt
e.g.Jupiter is radiating 3.5x1017 W in excess of incident solar radiation.
This implies it is contracting at a rate of 0.4 km / million years
• Another possibility is tidal dissipation in the interior.
This turns out to be small.
• Radioactive decay is a minor contributor.
F. Nimmo ESS298 Fall 2004
Puzzles
• Why is Uranus’ heat budget so different?
– Perhaps due to compositional density differences inhibiting
convection at levels deeper than ~0.6Rp (see Lissauer and
DePater). May explain different abundances in HCN,CO
between Uranus and Neptune atmospheres.
– This story is also consistent with generation of magnetic
fields in the near-surface region (see earlier slide)
• Why is Uranus tilted on its side?
– Nobody really knows, but a possible explanation is an
oblique impact with a large planetesimal (c.f. Earth-Moon)
– This impact might even help to explain the compositional
gradients which (possibly) explain Uranus’ heat budget
F. Nimmo ESS298 Fall 2004
Rings
• Composed of small (m-m) particles
• Generally found inwards of large satellites. Why?
– Synchronous point (what happens to satellites inward of here?)
– Roche limit (see below)
– Gravitational focusing of impactors results in more impacts
closer to the planet
• Why do we care?
– Good examples of orbital dynamics
– Origin and evolution linked to satellites
– Not volumetrically significant (Saturn’s rings collected together
would make a satellite ~100 km in radius)
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Roche Limit
• The satellite experiences a mean
gravitational acceleration of GMp/a2
• But the point closest to the planet
experiences a bigger acceleration, because
it’s closer by a distance Rs (i.e. tides)
Ms rs
a
Rs
GM p 
1  2GM p Rs
• The net acceleration of this point is 2 1 

Rs 2 
a  (1  a ) 
a3
Mp rp
Rp
• If the (fluid) satellite is not to
break apart, this acceleration has to
GM s 2GM p Rs
M s 2 Rs3
be balanced by the gravitational


 3
2
3
a
Mp
a
Rs
attraction of the satellite itself:
• This expression is usually rewritten in terms of the densities of the
two bodies, and has a numerical constant in it first determined by
1/ 3
Roche:
r 
a
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p

 2.456
Rp
 rs 
Ring locations (1)
Jupiter
Saturn
Roche
limits
Roche
limits
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Ring locations (2)
Uranus
Roche
limits
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Neptune
Roche
limits
Things to notice
• Roche limit really does seem a good marker for ring edges
• Why are some satellites found inwards of the Roche limit
and the synchronous point?
• All the rings have complex structures (gaps)
• Ring behaviour at least partly controlled by satellites:
Galileo image of Jupiter’s rings
F. Nimmo ESS298 Fall 2004
Ring Particle Size
• The rings are made of particles (Maxwell). How do
Starlight being occulted by rings;
we estimate their size?
– Eclipse cooling rate
– Radar reflectivity
– Forward vs. backscattered light
• The number density of the
particles may be estimated by
occultation data (see
)
• Ring thickness sometimes
controlled by satellites (see
previous slide). Typically ~ 0.1
km
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drop in intensity gives information
on particle number density
Ring Composition
• Vis/UV spectra indicate rings are predominantly
water ice (could be other ices e.g. methane, but not
yet detected)
• Some rings show reddening, due to contamination
(e.g. dust) or radiation effects
Cassini colourcoded UV
image; blue
indicates more
water ice
present. Note
the sharp
compositional
variations
F. Nimmo ESS298 Fall 2004
Ring Lifetimes
• Small grains (micron-size)
have lifetimes of ~1 Myr
due to drag from plasma
and radiated energy
• So something must be
continuously re-supplying
ring material:
– Impacts (on satellites) and
mutual collisions may
generate some
– Volcanic activity may also
contribute (Io, Enceladus?)
F. Nimmo ESS298 Fall 2004
Enceladus
Main rings
Hubble image of Saturn’s E-ring. Ring
is densest and thinnest at Enceladus, and
becomes more diffuse further away. This is
circumstantial evidence for Enceladus being
the source of the ring material. It is also
evidence for Enceladus being active.
Why the sharp edges?
• Keplerian shear blurs the rings
– Particles closer in are going faster
– Collisions will tend to smear particles out
with time – this will destroy sharp edges
and compositional distinctions
Ring particle
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faster
slower
• Shepherding satellites
Keplerian shear
Satellite
collision
– Outer satellite is going slower than
particles
– Gravitational attraction subtracts
energy from particles, so they move
inwards; reverse true for inner sat.
– So rings keep sharp edges
– And gaps are cleared around satellites
Ring/Satellite Interactions
Pan opening the Encke division in Saturn’s
rings
F. Nimmo ESS298 Fall 2004
Pandora and Prometheus shepherding
Saturn’s F ring
Sharp edges (cont’d)
• Positions withing the rings which are in resonance with
moons tend to show gaps – why?
• E.g. the Cassini division (outer edge of Saturn’s B ring) is at
a 2:1 resonance with Mimas
• Edge of A ring is at a 7:6 resonance with Janus/Epimetheus
• Resonances can also lead to waves
Waves arising from 5:3 resonance with
Mimas. The light and dark patterns are
due to vertical oscillations in ring height
(right-hand structure) and variations in
particle density (left-hand structure)
F. Nimmo ESS298 Fall 2004
End of Lecture
Thursday’s lecture will be given by Ashwin
Vasavada (JPL)
Next week will be the start of the computer
project
F. Nimmo ESS298 Fall 2004
Atmospheric Composition
• Escape velocity ve= (2 g r)1/2 (where’s this from?)
• Mean molecular velocity vm= (2kT/m)1/2
• Boltzmann distribution – negligible numbers of atoms
with velocities > 3 x vm
• Molecular hydrogen, 900 K, 3 x vm= 11.8 km/s
• Jupiter ve=60 km/s, Earth ve=11 km/s
• H has not escaped due to escape velocity (Jeans
escape)
F. Nimmo ESS298 Fall 2004
Atmospheric Structure (1)
• Atmosphere is hydrostatic: dP
dz   r ( z ) g ( z )
• Assume ideal gas, no exchange of heat with the outside
(adiabatic) – work done during expansion as pressure
decreases is provided by cooling. Latent heat?
• Specific heat capacity at constant pressure Cp:
rC p dT  dP Why?
• We can combine these two equations to get:
gmm
dT
g or equivalently dP
 P

dz
Cp
dz
RT
Here R is the gas constant, mm is the mass of one mole, and
RT/gmm is the scale height of the atmosphere (~10 km)
which tells you how rapidly pressure increases with depth
F. Nimmo ESS298 Fall 2004
Atmospheric Structure (2)
• Lower atmosphere (opaque) is dominantly heated from below
and will be conductive or convective (adiabatic)
• Upper atmosphere intercepts solar radiation and re-radiates it
• There will be a temperature minimum where radiative cooling is
most efficient; in giant planets, it occurs at ~0.1 bar
• Condensation of species will occur mainly in lower atmosphere
mesosphere
radiation
Temperature
(schematic)
Theoretical cloud distribution
CH4 (U,N only)
stratosphere
tropopause
140 K
~0.1 bar
NH3
clouds
troposphere
F. Nimmo ESS298 Fall 2004
80 K
adiabat
NH3+H2S
H2O
230 K
270 K
F. Nimmo ESS298 Fall 2004
Observations
•
•
•
•
•
Surface temperatures
Occultation
IR spectra & doppler effects
Galileo probe and SL9
Clouds and helium a problem
F. Nimmo ESS298 Fall 2004
Atmospheric dynamics
• Coriolis effect – objects moving on a
rotating planet get deflected (e.g. cyclones)
• Why? Angular momentum – as an object
moves further away from the pole, r
increases, so to conserve angular
momentum w decreases (it moves
backwards relative to the rotation rate)
 is latitude
• Coriolis acceleration = 2 w sin()
• How important is the Coriolis effect?
2 Lw sin 
v
is a measure of its importance
e.g. Jupiter v~100 m/s, L~10,000km we get ~35 so important
F. Nimmo ESS298 Fall 2004
Atmospheric dynamics (2)
• Coriolis effect is important because the giant planets
rotate so fast
• It is this effect which organizes the winds into zones
• Diagram of wind bands and velocities
F. Nimmo ESS298 Fall 2004
F. Nimmo ESS298 Fall 2004