EART 162 PLANETARY INTERIORS Francis Nimmo F Nimmo

EART 162: PLANETARY INTERIORS • Francis Nimmo F. Nimmo EART 162 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 EART 162 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 EART 162 Spring 10

Logistics • Website: http: //www. es. ucsc. edu/~fnimmo/eart 162_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 5 pm on Monday (10% penalty per day) • Location/Timing – Tu/Th 2: 00 -3: 45 in E&MS D 236 • Office hours –Tu/Th 1: 00 -2: 00 (A 219 E&MS) or by appointment (email: fnimmo@es. ucsc. edu) • Questions? - Yes please! F. Nimmo EART 162 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 EART 162 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 EART 162 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 EART 162 Spring 10

Sequence of events • 1. Nebular disk formation • 2. Initial coagulation (~10 km, ~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 EART 162 Spring 10

An Artist’s Impression The young Sun gas/dust nebula solid planetesimals F. Nimmo EART 162 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 EART 162 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 EART 162 Spring 10

Cartoon of Nebular Processes Disk cools by radiation Polar jets Dust grains Infalling material Hot, high r 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 EART 162 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 EART 162 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 EART 162 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 1 cm chondrules F. Nimmo EART 162 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 EART 162 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 Log 10 (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 EART 162 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 EART 162 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 1000 K, CH 4 above 60 K, and then condenses to CH 4. 6 H 2 O. From Lissauer and De. Pater, Planetary Sciences F. Nimmo EART 162 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 EART 162 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 EART 162 Spring 10

SNC meteorites • Shergotty, Nakhla, Chassigny (plus others) • What are they? – Mafic rocks, often cumulates 2. 3 mm • 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. Mc. Sween, Meteoritics, 1994 F. Nimmo EART 162 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. 26 Al (thalf=0. 7 Myr), 182 Hf (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 26 Al 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 EART 162 Spring 10

Hf-W system • 182 Hf decays to 182 W, 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 182 W Core forms 182 Hf (lithophile) 182 W (siderophile) Early core formation – excess 182 W in mantle Undiff. planet Core forms Differentiated mantle F. Nimmo EART 162 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 EART 162 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 EART 162 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 EART 162 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 EART 162 Spring 10

Gravity • Newton’s inverse square law for gravitation: r m 2 F F m 1 Here F is the force acting in a straight line joining masses m 1 and m 2 separated by a distance r; G is a constant (6. 67 x 10 -11 m 3 kg-1 s-2) • Hence we can obtain the acceleration g at the surface of a planet: R M • 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): a What does the negative sign mean? F. Nimmo EART 162 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. . . Where’s this from? a Here G is the universal gravitational constant a ae (6. 67 x 10 -11 in SI units), a is the semi-major axis (see diagram) and w is the angular focus frequency of the orbiting satellite, equal to e is eccentricity 2 p/period. Note that the mass of the satellite is not important. Given the mass, the density Orbits are ellipses, with the planet at can usually be inferred by telescopic one focus and a semi-major axis a measurements of the body’s radius R F. Nimmo EART 162 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 EART 162 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 EART 162 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 EART 162 Spring 10

Escape velocity and impact energy • Now back to gravity. . . • Gravitational potential 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 • 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 EART 162 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 later In which situation is more energy delivered? Total accretional energy = If all this energy goes into heat*, what is the resulting temperature change? a Earth M=6 x 1024 kg R=6400 km so DT=30, 000 K Mars M=6 x 1023 kg R=3400 km so DT=6, 000 K What do we conclude from this exercise? * Is this a reasonable assumption? F. Nimmo EART 162 Spring 10

Differentiation • Which situation has the lower potential energy? r 1 r 2 Equal total mass Uniform density r 1 <r 2 • Consider a uniform body with two small lumps of equal volume DV and different radii ra, rb and densities ra, rb • Which configuration has the lower potential energy? rb, rb rb, ra ra, rb R a PE 1=(g 0 DV/R)(rb 2 ra+ra 2 rb) PE 2=(g 0 DV/R)(ra 2 ra+rb 2 rb) Surface gravity g 0 We can minimize the potential energy by moving the denser material closer to the centre (try an example!) Does this make sense? F. Nimmo EART 162 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 EART 162 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 EART 162 Spring 10

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 EART 162 Spring 10