Transcript Powerpoint slides - Earth & Planetary Sciences

EART162: PLANETARY
INTERIORS
• Francis Nimmo
F.Nimmo EART162 Spring 10
Course Overview
• How do we know about the interiors of (silicate)
planetary bodies? Their structure, composition and
evolution.
• Techniques to answer these questions
–
–
–
–
Cosmochemistry
Orbits and Gravity
Geophysical modelling
Seismology
• Case studies – examples from this Solar System
F.Nimmo EART162 Spring 10
Course Outline
• Week 1 – Introduction, solar system formation,
cosmochemistry, gravity
• Week 2 – Gravity (cont’d), moments of inertia
• Week 3 – Material properties, equations of state
• Week 4 – Isostasy and flexure
• Week 5 – Heat generation and transfer
• Week 6 – Midterm; Seismology
• Week 7 – Fluid dynamics and convection
• Week 8 – Magnetism and planetary thermal evolution
• Week 9 – Case studies
• Week 10 – Recap. and putting it all together; Final
F.Nimmo EART162 Spring 10
Logistics
• Website:
http://www.es.ucsc.edu/~fnimmo/eart162_10
• Set text – Turcotte and Schubert, Geodynamics (2002)
• Prerequisites – some knowledge of calculus expected
• Grading – based on weekly homeworks (40%),
midterm (20%), final (40%).
• Homeworks due by 5pm on Monday (10% penalty per
day)
• Location/Timing – Tu/Th 2:00-3:45 in E&MS D236
• Office hours –Tu/Th 1:00-2:00 (A219 E&MS) or by
appointment (email: [email protected])
• Questions? - Yes please!
F.Nimmo EART162 Spring 10
Expectations
• Homework typically consists of 3 questions
• If it’s taking you more than 1 hour per question on
average, you’ve got a problem – come and see me
• Midterm/finals consist of short (compulsory) and long
(pick from a list) questions
• Results from last two years (on board)
• Showing up and asking questions are usually routes to
a good grade
• Plagiarism – see website for policy.
F.Nimmo EART162 Spring 10
This Week
•
•
•
•
Introductory stuff
How do solar systems form?
What are they made of, and how do we know?
What constraints do we have on the bulk and surface
compositions of planets?
• What processes have affected planets during
formation?
F.Nimmo EART162 Spring 10
Solar System Formation - Overview
• Some event (e.g. supernova) triggers gravitational
collapse of a cloud (nebula) of dust and gas
• As the nebula collapses, it forms a spinning disk (due to
conservation of angular momentum)
• The collapse releases gravitational energy, which heats
the centre
• The central hot portion forms a star
• The outer, cooler particles suffer repeated collisions,
building planet-sized bodies from dust grains (accretion)
• Young stellar activity blows off any remaining gas and
leaves an embryonic solar system
• These argument suggest that the planets and the Sun
should all have (more or less) the same composition
F.Nimmo EART162 Spring 10
Sequence of events
• 1. Nebular disk
formation
• 2. Initial coagulation
(~10km, ~105 yrs)
• 3. Orderly growth (to
Moon size, ~106 yrs)
• 4. Runaway growth
(to Mars size, ~107
yrs), gas loss (?)
• 5. Late-stage
collisions (~107-8 yrs)
F.Nimmo EART162 Spring 10
An Artist’s Impression
The young Sun
gas/dust
nebula
solid planetesimals
F.Nimmo EART162 Spring 10
Observations (1)
• Early stages of solar system formation can be imaged directly – dust
disks have large surface area, radiate effectively in the infra-red
• Unfortunately, once planets form, the IR signal disappears, so until
very recently we couldn’t detect planets (now we know of ~400)
• Timescale of clearing of nebula (~1-10 Myr) is known because young
stellar ages are easy to determine from mass/luminosity relationship.
Thick disk
This is a Hubble image of a young solar
system. You can see the vertical green
plasma jet which is guided by the star’s
magnetic field. The white zones are gas
and dust, being illuminated from inside by
the young star. The dark central zone is
where the dust is so optically thick that the
light is not being transmitted.
F.Nimmo EART162 Spring 10
Observations (2)
• We can use the presentday observed planetary
masses and
compositions to
reconstruct how much
mass was there initially
– the minimum mass
solar nebula
• This gives us a constraint on the initial nebula conditions e.g.
how rapidly did its density fall off with distance?
• The picture gets more complicated if the planets have moved . . .
• The observed change in planetary compositions with distance
gives us another clue – silicates and iron close to the Sun,
volatile elements more common further out
F.Nimmo EART162 Spring 10
Cartoon of Nebular Processes
Disk cools by radiation
Polar jets
Hot,
high r
Dust grains
Infalling
material
Nebula disk
(dust/gas)
Cold,
low r
Stellar magnetic field
(sweeps innermost disk clear,
reduces stellar spin rate)
• Scale height increases radially (why?)
• Temperatures decrease radially – consequence of lower
irradiation, and lower surface density and optical depth
leading to more efficient cooling
F.Nimmo EART162 Spring 10
What is the nebular composition?
• Why do we care? It will control what the planets are
made of!
• How do we know?
– Composition of the Sun (photosphere)
– Primitive meteorites (see below)
– (Remote sensing of other solar systems - not yet very
useful)
• An important result is that the solar photosphere
and the primitive meteorites give very similar
answers: this gives us confidence that our
estimates of nebular composition are correct
F.Nimmo EART162 Spring 10
1.4 million km
Solar photosphere
Note sunspots
(roughly Earth-size)
• Visible surface of the Sun
• Assumed to represent the
bulk solar composition (is
this a good assumption?)
• Compositions are obtained
by spectroscopy
• Only source of information
on the most volatile
elements (which are
depleted in meteorites):
H,C,N,O
F.Nimmo EART162 Spring 10
Primitive Meteorites
• Meteorites fall to Earth and can be analyzed
• Radiometric dating techniques suggest that they formed
during solar system formation (4.55 Gyr B.P.)
• Carbonaceous (CI) chondrites contain chondrules and
do not appear to have been significantly altered
• They are also rich in volatile
elements
• Compositions are very
similar to Comet Halley,
also assumed to be ancient,
unaltered and volatile-rich
1cm
chondrules
F.Nimmo EART162 Spring 10
Meteorites vs. Photosphere
• This plot shows the
striking similarity between
meteoritic and
photospheric compositions
• Note that volatiles (N,C,O)
are enriched in
photosphere relative to
meteorites
• We can use this
information to obtain a
best-guess nebular
composition
Basaltic Volcanism Terrestrial Planets, 1981
F.Nimmo EART162 Spring 10
Nebular Composition
• Based on solar photosphere and chondrite compositions,
we can come up with a best-guess at the nebular
composition (here relative to 106 Si atoms):
Element
H
He C
N
O
Ne
Mg Si
Log10 (No. 10.44 9.44 7.00
Atoms)
6.42 7.32 6.52 6.0
Condens.
Temp (K)
120
180
--
78
--
--
6.0
S
Ar
5.65
5.05 5.95
1340 1529 674
40
Fe
1337
• Blue are volatile, red are refractory
• Most important refractory elements are Mg, Si, Fe, S
Data from Lodders and Fegley, Planetary Scientist’s Companion, CUP, 1998
This is for all elements with relative abundances > 105 atoms.
F.Nimmo EART162 Spring 10
Planetary Compositions
• Which elements actually condense will depend on the
local nebular conditions (temperature)
• E.g. volatile species will only be stable beyond a “snow
line”. This is why the inner planets are rock-rich and the
outer planets gas- and ice-rich
• The compounds formed from the elements will be
determined by temperature (see next slide)
• The rates at which reactions occur are also governed by
temperature. In the outer solar system, reaction rates
may be so slow that the equilibrium condensation
compounds are not produced
F.Nimmo EART162 Spring 10
Temperature and Condensation
Nebular conditions can be used to predict what components of
the solar nebula will be present as gases or solids:
Mid-plane
Photosphere
Earth Saturn
Temperature profiles in a young (T
Tauri) stellar nebula, D’Alessio et al.,
A.J. 1998
Condensation behaviour of most abundant elements
of solar nebula e.g. C is stable as CO above 1000K,
CH4 above 60K, and then condenses to CH4.6H2O.
From Lissauer and DePater, Planetary Sciences
F.Nimmo EART162 Spring 10
Other constraints?
• Diagrams of the kind shown on the previous page allow
us to theoretically predict the bulk composition of a
planet as a function of its position in the nebula
• Fortunately, in some cases we also have remote sensing
or sample information about planetary compositions
– Samples – Earth, Moon, Mars, Vesta (?)
– Remote Sensing – Earth, Moon, Mars, Venus, Eros, Mercury
(sort of), Galilean satellites etc.
• We also know other properties of these bodies, such as
bulk density or mass distribution, which provide further
constraints. These will be discussed in much more detail
in later lectures.
F.Nimmo EART162 Spring 10
Samples
• Very useful, because we can analyze them in the lab
• Generally restricted to near-surface
• For the Earth, we have samples of both crust and
(uniquely) the mantle (peridotite xenoliths)
• We have 382 kg of lunar rocks ($29,000 per pound)
from 6 sites (7 counting 0.13 kg returned by Soviet missions)
• Eucrite meteorites are thought to come from asteroid 4
Vesta (they have similar spectral reflectances)
• The Viking, Pathfinder and Spirit/Opportunity landers
on Mars carried out in situ measurements of rock and
soil compositions
• We also have meteorites which came from Mars – how
do we know this?
F.Nimmo EART162 Spring 10
SNC meteorites
• Shergotty, Nakhla,
Chassigny (plus others)
• What are they?
2.3mm
– Mafic rocks, often cumulates
• How do we know they’re
from Mars?
– Timing – most are 1.3 Gyr
old
– Trapped gases are identical in
composition to atmosphere
measured by Viking. QED.
McSween, Meteoritics, 1994
F.Nimmo EART162 Spring 10
Timing Accretion
• One of the reasons samples are so valuable is that
they allow us to measure how fast planets accrete
• We do this using short-lived radioisotopes e.g. 26Al
(thalf=0.7 Myr), 182Hf (thalf=9 Myr)
• Processes which cause fractionation (e.g. melting,
core formation) can generate isotopic anomalies if
they happen before the isotopes decay
• Some asteroids appear to have accreted and melted
before 26Al decayed (i.e. within ~3 Myr of solar
system formation). How?
• Core formation finished as rapidly as 1 Myr (Vesta)
and as slowly as ~30 Myr (Earth). How do we know?
F.Nimmo EART162 Spring 10
Hf-W system
•
182Hf
decays to 182W, half-life
9 Myrs
• Hf is lithophile, W is
siderophile, so observations
time core formation (related
to accretion process)
Kleine et al. 2002
Late core formation – no excess 182W
Core forms
182Hf
(lithophile)
182W
(siderophile)
Early core formation – excess 182W in mantle
Undiff. planet
Core forms
Differentiated
mantle
F.Nimmo EART162 Spring 10
Remote Sensing
• Again, restricted to surface (mm-mm). Various kinds:
– Spectral (usually infra-red) reflectance/absorption – gives
constraints on likely mineralogies e.g. Mercury, Europa
– Neutron – good for sensing subsurface ice (Mars, Moon)
– Most useful is gammaray – gives elemental
abundances (especially
of naturally radioactive
elements K,U,Th)
– Energies of individual
gamma-rays are
characteristic of
particular elements
F.Nimmo EART162 Spring 10
K/U ratios
• Potassium (K) and uranium (U) behave in a chemically similar
fashion, but have different volatilities: K is volatile, U refractory
• So differences in K/U ratio tend to arise as a function of
temperature, not chemical evolution
K/U
From S.R. Taylor, Solar System Evolution, 1990
• K/U ratios of most
terrestrial planet surfaces
are rather similar (~10,000)
• What does this suggest
about the bulk compositions
of the terrestrial planets?
• K/U ratio is smaller for the
Moon – why?
• K/U ratio larger for the
primitive meteorites – why?
F.Nimmo EART162 Spring 10
Planetary Crusts
• Remote sensing (IR, gamma-ray) allows inference of
surface (crustal) mineralogies & compositions:
–
–
–
–
Earth: basaltic (oceans) / andesitic (continents)
Moon: basaltic (lowlands) / anorthositic (highlands)
Mars: basaltic (plus andesitic?)
Venus: basaltic
• In all cases, these crusts are distinct from likely bulk
mantle compositions – indicative of melting
• The crusts are also very poor in iron relative to bulk
nebular composition – where has all the iron gone?
How can we tell?
F.Nimmo EART162 Spring 10
Gravity
• Governs orbits of planets and spacecraft
• Largely controls accretion, differentiation and
internal structure of planets
• Spacecraft observations allow us to characterize
structure of planets:
– Bulk density (this lecture)
– Moment of inertia (next week)
F.Nimmo EART162 Spring 10
Gravity
• Newton’s inverse square law for gravitation:
r
Gm1m2
F
F
F
2
m2
r
m1
Here F is the force acting in a straight line joining masses m1 and m2
separated by a distance r; G is a constant (6.67x10-11 m3kg-1s-2)
• Hence we can obtain the acceleration g at
R
the surface of a planet:
GM
M
g 2
R
• We can also obtain the gravitational potential
U at the surface (i.e. the work done to get a
unit mass from infinity to that point):
GM
What does the
a
U 
negative sign mean?
R
F.Nimmo EART162 Spring 10
Planetary Mass
• The mass M and density r of a planet are two of its
most fundamental and useful characteristics
• These are easy to obtain if something (a satellite,
artificial or natural) is in orbit round the planet, thanks
to Isaac Newton . . .
3 2
GM  a 
Where’s this from?
a
Here G is the universal gravitational
a
ae
constant (6.67x10-11 in SI units), a is the
semi-major axis (see diagram) and  is the
focus
angular frequency of the orbiting satellite,
e is eccentricity
equal to 2p/period. Note that the mass of the
satellite is not important. Given the mass, the
density can usually be inferred by telescopic Orbits are ellipses, with the planet at
one focus and a semi-major axis a
measurements of the body’s radius R
F.Nimmo EART162 Spring 10
Bulk Densities
• So for bodies with orbiting satellites (Sun, Mars, Earth,
Jupiter etc.) M and r are trivial to obtain
• For bodies without orbiting satellites, things are more
difficult – we must look for subtle perturbations to other
bodies’ orbits (e.g. the effect of a large asteroid on Mars’
orbit, or the effect on a nearby spacecraft’s orbit)
• Bulk densities are an important observational constraint
on the structure of a planet. A selection is given below:
Object
Earth
Mars Moon Mathilde Ida
Callisto Io
Saturn Jupiter
R (km)
6378
3390 1737
27
16
2400
1821
60300 71500
3.93
1.3
2.6
1.85
3.53
0.69
r (g/cc) 5.52
3.34
Data from Lodders and Fegley, 1998
1.33
F.Nimmo EART162 Spring 10
What do the densities tell us?
• Densities tell us about the different proportions of
gas/ice/rock/metal in each planet
• But we have to take into account the fact that most
materials get denser under increasing pressure
• So a big planet with the same bulk composition as a little
planet will have a higher density because of this selfcompression (e.g. Earth vs. Mars)
• In order to take self-compression into account, we need
to know the behaviour of material under pressure i.e. its
equation of state. We’ll deal with this in a later lecture.
• On their own, densities are of limited use. We have to
use the information in conjunction with other data, like
our expectations of bulk composition.
F.Nimmo EART162 Spring 10
Example: Venus
• Bulk density of Venus is 5.24 g/cc
• Surface composition of Venus is basaltic, suggesting
peridotite mantle, with a density ~3 g/cc
• Peridotite mantles have an Mg:Fe ratio of 9:1
• Primitive nebula has an Mg:Fe ratio of 7:3
• What do we conclude?
• Venus has an iron core (explains the high bulk
density and iron depletion in the mantle)
• What other techniques could we use to confirm this
hypothesis?
F.Nimmo EART162 Spring 10
Escape velocity and impact energy
• Now back to gravity . . .
GM
• Gravitational potential U  
r
M
R
r
• How much kinetic energy do we have to add to an
object to move it from the surface of the planet to
infinity?
• The velocity required is the escape velocity:
a
vesc 
2 GM
R
 2 gR
• Equally, an object starting from rest at infinity will
impact the planet at this escape velocity
• Earth vesc=11 km/s. How big an asteroid would
cause an explosion equal to that at Hiroshima?
F.Nimmo EART162 Spring 10
Energy of Accretion
• Let’s assume that a planet is built up like an onion, one
shell at a time. How much energy is involved in putting
the planet together?
early
a
In which situation is
more energy delivered?
later
2
3
GM
Total accretional energy =
5 R
If all this energy goes into heat*, what is the resulting temperature change?
a
3 GM
T 
5 CpR
Earth M=6x1024 kg R=6400km so T=30,000K
Mars M=6x1023 kg R=3400km so T=6,000K
What do we conclude from this exercise?
* Is this a reasonable
assumption?
F.Nimmo EART162 Spring 10
Differentiation
• Which situation has the
lower potential energy?
r1 r2
Equal total
mass
Uniform
density
r1 < r2
• Consider a uniform body with two small lumps of equal
volume V and different radii ra,rb and densities ra,rb
• Which configuration has the lower potential energy?
rb , r b
rb , r a
ra , r a
ra , r b
R
a
PE1=(g0V/R)(rb2ra+ra2rb)
PE2=(g0V/R)(ra2ra+rb2rb)
Surface gravity g0
We can minimize the potential energy by moving the denser
material closer to the centre (try an example!)
Does this make sense?
F.Nimmo EART162 Spring 10
Differentiation (cont’d)
• So a body can lower its potential energy (which gets
released as heat) by collecting the densest components at
the centre – differentiation is energetically favoured
• Does differentiation always happen? This depends on
whether material in the body can flow easily (e.g. solid
vs. liquid)
• So the body temperature is very important
• Differentiation can be self-reinforcing: if it starts, heat is
released, making further differentiation easier, and so on
F.Nimmo EART162 Spring 10
Summary: Building a generic silicate planet
• Planets accrete from the solar nebula, which has a
roughly constant composition (except volatiles)
• The process of accretion leads to conversion of grav.
energy to heat – larger bodies are heated more
• If enough heating happens, the body will differentiate,
leading to a core-mantle structure (and more heating)
• This heat will also tend to melt the mantle, resulting in a
core-mantle-crust structure
• Remote-sensing observations tell us about the
composition of the crust
• Gravitation allows us to deduce the bulk density of the
planet
F.Nimmo EART162 Spring 10
End of Lecture
• Next week – (a lot) more on using gravity to
determine internal structures
• Homework #1 on the web – due next MonF.Nimmo EART162 Spring 10