EART162: PLANETARY INTERIORS › ~fnimmo › eart162_10 › Week1.pdfcosmochemistry, gravity •Week...

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!

mailto:[email protected]


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/dust

nebula

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 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.

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 Infalling

material

Nebula disk

(dust/gas)

Hot,

high r

Cold,

low r


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 k

m


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

1cmchondrules

• 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, 1998

This 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. planetDifferentiated

mantle

Early core formation – excess 182W in mantle

Core forms


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 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:

2

21

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 a What does the

negative sign mean?


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 . . .

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 2p/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

a


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

r (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 rM

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

gRvR

GMesc 22 a


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?

a Total accretional energy =

R

GM 2

5

3

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

RC

GMT

p5

3a

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?


Differentiation• Which situation has the

lower potential energy? r2

Uniform

densityr1

r1<r2

Equal total

mass

• Consider a uniform body with two small lumps of equal

volume V and different radii ra,rb and densities ra,rb

rb,rb

• Which configuration has the lower potential energy?

PE1=(g0V/R)(rb2ra+ra

2rb)

PE2=(g0V/R)(ra2ra+rb

2rb)

We can minimize the potential energy by moving the denser

material closer to the centre (try an example!)

R

Surface gravity g0

ra,ra

a

Does this make sense?

rb,ra

ra,rb


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

EART162: PLANETARY INTERIORS › ~fnimmo › eart162_10 › Week1.pdfcosmochemistry, gravity •Week...

Documents

Transcript of EART162: PLANETARY INTERIORS › ~fnimmo › eart162_10 › Week1.pdfcosmochemistry, gravity •Week...