Transcript Document 7488077

EART160 Planetary Sciences
Francis Nimmo
Last Week
• Elliptical orbits (Kepler’s laws) are explained by
Newton’s inverse square law for gravity
• In the absence of external torques, orbital angular
momentum is conserved (e.g. Earth-Moon system)
• Orbital energy depends on distance from primary
• Tides arise because gravitational attraction varies
from one side of a body to the other
• Tides can rip a body apart if it gets too close to the
primary (Roche limit)
• Tidal torques result in synchronous satellite orbits
• Diurnal tides (for eccentric orbit) can lead to heating
and volcanism (Io, Enceladus)
Giant Planets
•
•
•
•
•
What determines their internal structure?
How did they form and evolve?
What controls their atmospheric dynamics? (Week 5)
What about extra-solar planets?
Rings not discussed
Giant Planets
Image not
to scale!
Basic Parameters
a
(AU)
Porb
(yrs)
Prot
(hrs)
R
(km)
M
(1026 kg)
Obliquity
Density
g/cc
Ts
K
Jupiter
5.2
11.8
9.9
71492
19.0
3.1o
1.33
165
Saturn
9.6
29.4
10.6
60268
5.7
26.7o
0.69
134
Uranus
19.2
84.1
17.2R
24973
0.86
97.9o
1.32
76
Neptune 30.1
165
16.1
24764
1.02
29.6o
1.64
72
Data from Lodders and Fegley 1998. Surface temperature Ts and radius R are measured
at 1 bar level.
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%
Neptune
80%
15.2%
19%
(2.3% CH4) (1% CH4)
(Lodders and Fegley 1998)
Pressure
• Hydrostatic approximation dP
dr    (r ) g (r )
• Mass-density relation dMdr( r )  4(r )r 2
• These two can be combined (how?) to get the
pressure at the centre of a uniform body Pc:
2
3GM
Pc 
8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
Temperature
• 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
RT
P

P  c 
Adiabatic only
Here P is pressure,  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:
C p dT  dP
• Combining this equation with the hydrostatic assumption, we get:
dT
dz

g
a
Cp
•At 1 bar level on Jupiter, T=165 K, g=23 ms-2, Cp~3R, m=0.002kg (H2), so
dT/dz = 1.4 K/km (adiabatic)
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
Compressibility & Density
radius
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)
From Guillot,
2004
Magnetic fields
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)
Summary
• Jupiter - mainly metallic hydrogen. Rock-ice core
~10 ME.
• Saturn - mix of metallic and molecular hydrogen;
helium may have migrated to centre due to
insolubility. Similar rock-ice core to Jupiter. Mean
density lower than Jupiter because of smaller selfcompression effect (pressures lower).
• Uranus/Neptune – thin envelope of hydrogen gas.
Pressures too low to generate metallic hydrogen.
Densities (and moment of inertia data) require large
rock-ice cores in the interior.
• All four planets have large magnetic fields,
presumably generated by convection in either
metallic hydrogen (J,S) or conductive ices (U,N)
Giant Planet Formation (see Week 1)
• Initially solid bodies (rock + ice; beyond snow line)
• When solid mass exceeded ~10 Me, gravitational
acceleration sufficient to trap an envelope of H and He
• Process accelerated until nebular gas was lost
• So initial accretion was rapid (few Myr)
• Uranus and Neptune didn’t acquire so much gas
because they were further out and accreted more slowly
• Planets will have initially been hot (gravitational
energy) and subsequently cooled and contracted
• We can investigate how rapidly they are cooling at the
present day . . .
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
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.
Puzzles
• Why is Uranus’ heat budget so different?
– Perhaps due to compositional density differences inhibiting
convection at levels deeper than ~0.6Rp .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
Atmospheric Structure (1)
• Atmosphere is hydrostatic:
RT
• Gas law gives us:
P
dP
dz
  ( z) g ( z)

• Combining these two (and neglecting latent heat):
dP
g
 P
dz
RT
Here R is the gas constant,  is the mass of one mole, and
RT/g is the scale height of the (isothermal) atmosphere (~10
km) which tells you how rapidly pressure increases with depth
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
80 K
adiabat
NH3+H2S
H2O
230 K
270 K
Giant planet atmospheric structure
• Note position and order of cloud decks
Extra-Solar Planets
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•
•
•
A very fast-moving topic
How do we detect them?
What are they like?
Are they what we would have expected? (No!)
How do we detect them?
• The key to most methods is that the star will move
(around the system’s centre of mass) in a detectable
fashion if the planet is big and close enough
• 1) Pulsar Timing
A pulsar is a very accurate clock; but there will
be a variable time-delay introduced by the
motion of the pulsar, which will be detected as
a variation in the pulse rate at Earth
pulsar
planet
Earth
• 2) Radial Velocity
Spectral lines in star will be Doppler-shifted by
component of velocity of star which is in
Earth’s line-of-sight. This is easily the most
common way of detecting ESP’s.
Earth
star
planet
How do we detect them? (2)
• 2) Radial Velocity (cont’d)
The radial velocity amplitude is given by
Kepler’s laws and is
1/ 3
 2G 

v  
 Porb 
Earth
i
Does this make sense?
M p sin i
Ms
1
(M s  M p )2 / 3 1  e2
Mp
Note that the planet’s mass is
uncertain by a factor of sin i. The
Ms+Mp term arises because the star
is orbiting the centre of mass of the
system. Present-day instrumental
sensitivity is about 3 m/s; Jupiter’s
effect on the Sun is to perturb it by
about 12 m/s.
From Lissauer and Depater, Planetary Sciences, 2001
How do we detect them? (3)
• 3) Occultation
Planet passes directly in front of star.
Very rare, but very useful
because we can:
1) Obtain M (not M sin i)
2) Obtain the planetary radius
3) Obtain the planet’s spectrum (!)
Only one example known to date.
Light curve during occultation of HD209458.
From Lissauer and Depater, Planetary Sciences, 2001
• 4) Astrometry Not yet demonstrated.
• 5) Microlensing Ditto.
• 6) Direct Imaging Brown dwarfs detected.
What are they like?
• Big, close, and often highly eccentric – “hot Jupiters”
• What are the observational biases?
Note the absence of high
eccentricities at close
distances – what is causing
this effect?
HD209458b is at
0.045 AU from its
star and seems to
have a radius which
is too large for its
mass (0.7 Mj). Why?
Jupiter Saturn
From Guillot, Physics Today, 2004
What are they like (2)?
• Several pairs of planets have been observed, often in
2:1 resonances
• (Detectable) planets seem to be more common in
stars which have higher proportions of “metals” (i.e.
everything except H and He)
There are also claims that
HD179949 has a planet with
a magnetic field which is
dragging a sunspot around
the surface of the star . . .
From Lissauer and Depater,
Planetary Sciences, 2001
Sun
Mean local value of
metallicity
Puzzles
• 1) Why so close?
– Most likely explanation seems to be inwards migration due
to presence of nebular gas disk (which then dissipated)
– The reason they didn’t just fall into the star is because the
disk is absent very close in, probably because it gets
cleared away by the star’s magnetic field. An alternative is
that tidal torques from the star (just like the Earth-Moon
system) counteract the inwards motion
• 2) Why the high eccentricities?
– No-one seems to know. Maybe a consequence of scattering
off other planets during inwards migration?
• 3) How typical is our own solar system?
– Not very, on current evidence
Consequences
• What are the consequences of a Jupiter-size planet
migrating inwards? (c.f. Triton)
• Systems with hot Jupiters are likely to be lacking any
other large bodies
• So the timing of gas dissipation is crucial to the
eventual appearance of the planetary system (and the
possibility of habitable planets . . .)
• What controls the timing?
• Gas dissipation is caused when the star enters the
energetic T-Tauri phase – not well understood (?)
• So the evolution (and habitability) of planetary
systems is controlled by stellar evolution timescales –
hooray for astrobiology!
Summary
• Giant planets primarily composed of H,He with a ~10
Me rock-ice core which accreted first
• They radiate more energy than they receive due to
gravitational contraction (except Uranus!)
• Clouds occur in the troposphere and are layered
according to condensation temperature
• Many (~200) extra-solar giant planets known
• Many are close to the star or have high eccentricities
– very unlike our own solar system
• Nebular gas probably produced inwards migration
Key concepts
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•
•
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•
•
Adiabat, lapse rate, scale height
Hydrogen phase diagram
Hydrostatic assumption
Compressibility, mass-radius relationship
Gravitational contraction
Radial velocity
Inwards migration
Orbital circularization
End of lecture
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 also use the expressions on the previous page to derive
how the adiabatic temperature varies with pressure
a

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 