F.Nimmo EART162 Spring 10 EART162: PLANETARY INTERIORS Francis Nimmo.

F.Nimmo EART162 Spring 10

EART162: PLANETARY INTERIORS

• Francis Nimmo


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


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


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!


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.


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?


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


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)


An Artist’s Impression

The young Sun gas/dustnebula

solid planetesimals


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.

This is a Hubble image of a young solarsystem. You can see the vertical greenplasma jet which is guided by the star’smagnetic field. The white zones are gasand dust, being illuminated from inside bythe young star. The dark central zone is where the dust is so optically thick that the light is not being transmitted.

Thick disk


Observations (2)• We can use the present-

day 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


Cartoon of Nebular Processes

• Scale height increases radially (why?)

• Temperatures decrease radially – consequence of lower irradiation, and

lower surface density and optical depth leading to more efficient cooling

Polar jets

Stellar magnetic field (sweeps innermost disk clear, reduces stellar spin rate)

Disk cools by radiation

Dust grains Infallingmaterial

Nebula disk(dust/gas)

Hot, high

Cold, low


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


Solar photosphere• 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

Note sunspots(roughly Earth-size)

1.4

mil

lion

km


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

1cm chondrules

• They are also rich in volatile elements

• Compositions are very similar to Comet Halley, also assumed to be ancient, unaltered and volatile-rich


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


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):

Data from Lodders and Fegley, Planetary Scientist’s Companion, CUP, 1998This is for all elements with relative abundances > 105 atoms.

Element H He C N O Ne Mg Si S Ar Fe

Log10 (No. Atoms)

10.44 9.44 7.00 6.42 7.32 6.52 6.0 6.0 5.65 5.05 5.95

Condens.

Temp (K)

180 -- 78 120 -- -- 1340 1529 674 40 1337

• Blue are volatile, red are refractory• Most important refractory elements are Mg, Si, Fe, S


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


Temperature and Condensation

Temperature profiles in a young (T Tauri) stellar nebula, D’Alessio et al., A.J. 1998

Nebular conditions can be used to predict what components of the solar nebula will be present as gases or solids:

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

Mid-plane

Photosphere

Earth Saturn


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.


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?


SNC meteorites

• Shergotty, Nakhla, Chassigny (plus others)

• What are they?– 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

2.3mm


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?


Hf-W system

Kleine et al. 2002

• 182Hf decays to 182W, half-life 9 Myrs

• Hf is lithophile, W is siderophile, so observations time core formation (related to accretion process)

182Hf (lithophile)

182W (siderophile)

Late core formation – no excess 182W

Core forms

Undiff. planetDifferentiatedmantle

Early core formation – excess 182W in mantle

Core forms


Remote Sensing• Again, restricted to surface (m-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 gamma-ray – gives elemental abundances (especially of naturally radioactive elements K,U,Th)

– Energies of individual gamma-rays are characteristic of particular elements


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 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?

K/U

From S.R. Taylor, Solar System Evolution, 1990


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?


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)


Gravity

• Hence we can obtain the acceleration g at the surface of a planet:

• Newton’s inverse square law for gravitation:

221

r

mGmF

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)

r

m1

m2

F F

• 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):

MR

2R

GMg

R

GMU What does the

negative sign mean?


Planetary Mass• The mass M and density 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 . . .

23aGM Where’s this from?

Here G is the universal gravitational constant (6.67x10-11 in SI units), a is the semi-major axis (see diagram) and is the angular frequency of the orbiting satellite, equal to 2/period. Note that the mass of the satellite is not important. Given the mass, the density can usually be inferred by telescopic measurements of the body’s radius R

a ae

focus

e is eccentricity

Orbits are ellipses, with the planet at one focus and a semi-major axis a


Bulk Densities• So for bodies with orbiting satellites (Sun, Mars, Earth,

Jupiter etc.) M and 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

(g/cc) 5.52 3.93 3.34 1.3 2.6 1.85 3.53 0.69 1.33

Data from Lodders and Fegley, 1998


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 self-compression (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.


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?


Escape velocity and impact energy• Now back to gravity . . .• Gravitational potential r

M

r

GMU

• 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:

• 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?

R

gRv RGM

esc 22


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 later

In which situation is more energy delivered?

Total accretional energy =

R

GM 2

5

3

If all this energy goes into heat*, what is the resulting temperature change?

RC

GMT

p5

3

Earth M=6x1024 kg R=6400km so T=30,000KMars M=6x1023 kg R=3400km so T=6,000KWhat do we conclude from this exercise?

* Is this a reasonable assumption?


Differentiation• Which situation has the

lower potential energy? 2

Uniformdensity

1

1<2

Equal total mass

• Consider a uniform body with two small lumps of equal volume V and different radii ra,rb and densities a,b

rb,b

• Which configuration has the lower potential energy?

PE1=(g0V/R)(rb2a+ra

2b)

PE2=(g0V/R)(ra2a+rb

2b)

We can minimize the potential energy by moving the denser material closer to the centre (try an example!)

RSurface gravity g0

ra,a

Does this make sense?

rb,a

ra,b


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


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


End of Lecture

• Next week – (a lot) more on using gravity to determine internal structures• Homework #1 on the web – due next Mon

F.Nimmo EART162 Spring 10 EART162: PLANETARY INTERIORS Francis Nimmo.

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