Planetary interiorsPlanetary interiors

Topics to be coveredTopics to be covered

• Models of interior structure (6 1)Models of interior structure (6.1)• Seismology of Earth’s interior

S i l (6 2 1)– Seismology (6.2.1)– Density profile of the Earth (6.2.2.1)

• Structure of other terrestrial bodies (6.3)• Structure of the giant planets (6.4)g p ( )

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Bulk properties of the planetsBulk properties of the planetsSu

nnc

e fr

om S

ing

dist

anIn

crea

si

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Primary materials Why are planets made of these?B th (Because they (or at least their constituent atoms) are )abundantly produced by stars (see chapter on planet

• The primary building blocks of the planets are metals (ρ ~ 8g/cm3), ili t ( 3 / 3) i ( 1 / 3) d H & H ( l b t

chapter on planet formation)

silicates (ρ ~ 3g/cm3), ices (ρ ~ 1g/cm3) and H & He (ρ low, but varies with pressure)

• Because materials with higher condensation temperatures will be able to condense closer to the Sun when the planets were forming, p gwe can use the bulk densities of the planets to infer that– Mercury, Venus, Earth and Mars (terrestrial planets) are rock/metal– Jupiter and Saturn (gas giants) are primarily H/He (but probably have an

ice/rock core))– Uranus and Neptune (ice giants) contain a lot of ices

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Hydrostatic equilibriumHydrostatic equilibrium• If the material in the interior of the planet is

not moving then there must be zero netnot moving, then there must be zero net force everywhere inside (note: this ignores possible convection inside the planet)

• The weight of material above any point t b b l d b l dmust be balanced by an equal upward

pressure. (Hydrostatic equilibrium)• The weight depends on:

– Density of material abovee s ty o ate a abo e– Composition of material– Temperature (and phase)– Pressure above (relating to density)

• Thus the accurate determination of aThus the accurate determination of a planet’s internal structure, from the outside, can be difficult.

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Melting pointMelting point•The melting point of most materials is also a function of pressure•The increase in melting point with pressure for many (not all) common materials means that a body could yhave an outer liquid layer on top of a hotter solid lower layer.

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Equation of stateEquation of state• To determine the phase of a

particular portion of the planet, we need the phase diagram for theneed the phase diagram for the material at the temperature T and also the pressure P in question

• The information in a phase diagram is equivalent to knowing the equation of state of the material, relating ρ, T and P

• Note that mixtures may beNote that mixtures may be complicated, involving the coexistence of different minerals as liquids and solids together.

• Even pure materials may exist in a• Even pure materials may exist in a variety of solid and liquid states, each with different crystal structures, densities, etc. An example of a phase diagramp p g

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Equation of stateEquation of state• For an ideal gas, it’s simply P = nkT• The equation of states for highly compressed q g y p

gases, liquid and solids may be much more complicated

• For a solid or liquid one usually tries to fit an• For a solid or liquid, one usually tries to fit an empirical relation to whatever laboratory data is at hand. At higher temperatures or pressures, this may involve lasers and/or diamond anvilthis may involve lasers and/or diamond anvil cells (to generate high temperatures and pressures) or studying as best one can the

ff t f h k ( l i ) leffects of shocks (e.g. explosions) on samples.• Some progress can alos be made sometimes

from theoretical quantum mechanicalfrom theoretical quantum mechanical calculations, but the equation of state is often largely unknown for planetary interiors 8/76

Giant planetsGiant planets• Giant planet T

ranges from 50-150 K in t h tatmosphere to

10,000-20,000 K (hotter than surface of the S ) t th iSun) at their centres.

• Pressure ranges up to 20-80 Mbar pat their center

• That their composition is primarily H and Heprimarily H and He can be guessed from their bulk densities (1.33 and 0.69 g/cm3 forand 0.69 g/cm for J &S resp)

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Hydrogen in Jupiter and SaturnHydrogen in Jupiter and Saturn• Below 1 Mbar,

molecular H2 is 2dominant

• Beyond 1 Mbar liquid H2 begins to q 2 gdissociate to atomic H, a process complete at 3 Mbarat ~3 Mbar

• At higher temps, H may become degenerate or adegenerate or a plasma; however, the nature of the transition and itstransition and its location is controversial. Dashed lines = adiabats for the giant planets, the

expected T-P profiles for convective interiors 10/76

JupiterI J it (86 4% h d• In Jupiter, (86.4% hydrogen 12.6% helium by number)the transition from molecular hydrogen to atomic occurs b t 0 95 d 0 8 Rbetween 0.95 and 0.8 RJ

• Owing to the close packing of molecules/atoms at these pressures, their electron p ,orbitals overlap, allowing electrons to “hop” easily from one atom to the next (fluid metallic hydrogen, either y g ,molecular or atomic)

• This highly conductive fluid allows a strong magnetic field to be producedto be produced

• A core of rock/ice, around which the gas originally accumulated through gravity (perhaps 10 30 Earth masses)(perhaps 10-30 Earth masses) remains at the core

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Hydrogen and heliumHydrogen and helium• Helium in the core does

t h t lliMixed

not reach a metallic state at pressures seen in the giant planetsH d H t f ll• He and H are not fully mixed at all points in the giant planetsTheir miscibility (ability• Their miscibility (ability to dissolve each other) varies with temperature and pressureand pressure

• At lower temperatures and pressures, H and He don’t mix as well

Separate

He don t mix as well

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SaturnSaturn• Atmosphere is observed

to contain 96.7% hydrogen and 3 3%

Molecular hydrogen

hydrogen and 3.3% helium by number– Missing helium (compare to

Jupiter)• Because temperature at a

given pressure is lower than Jupiter, immiscibility i f iis more of an issue

• It is thought that droplets of helium condense out of the H/He mixture and rainthe H/He mixture and rain down into the core (releasing grav. potential energy an internal heat Rock/ice coreenergy, an internal heat source) Metallic hydrogen Rock/ice core

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Understanding Jovian planet sizes and densities

Stacking pillows increases the height but eventuallyheight, but eventually compression occurs.

14

IcesW t i j tit t• Water is a major constituent of the planets, particularly the outer planets and their satellites

• Solid water has at least 10 different crystalline forms varying in density from 0.92/cm3 for ordinary ice (ice y (Ih, h=hexagonal, Ic=cubic is lower T form) to 1.66g/cm3

for ice VII• Interiors of the icy satellitesInteriors of the icy satellites

are expected to vary from T=50-100K and P=0 at the surface to several hundred K and a few tens of kbars atand a few tens of kbars at their centers

• Water in the cores of the giant planets is likely supercritical (neither a liquid Phase diagram for watersupercritical (neither a liquid nor a gas)

Phase diagram for water. Dashed lines indicate adiabats for the giant planets 15/76

Uranus and Neptune• Uranus and Neptune are

often called “ice giants” because they are expected to b l l t

H2/He/CH4/NH3 gasslush?

be largely water• Pure water is naturally slightly

ionized into H3O+ and OH- at 1 part in 10 million at room ptemperature; this is enhanced at higher T

• A mix of ice, non-conducting NH3 and isopropanol

rocky core

NH3 and isopropanol (“synthetic Uranus”) also ionizes slightly at high pressure and thus becomes conducting.conducting.

• This conductivity is sufficient to account for the magnetic fields of Uranus and Neptune, as the standard dynamo

Possible structure of Uranus and Neptuneas the standard dynamo effect requires circulating conductive fluids. 16/76

Rocks and metalsRocks and metals• A great variety of g y

minerals can be produced by the handful of rocky/metal yelements that are most common on the terrestrial planetsp

• The particular mineral depends on the temperature pressuretemperature, pressure and relative abundance of the constituents.

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The Earth’s mantle

• Earth’s mantle begins below thebegins below the 5-70 km thick crust

• The next layer, the mantle, is 2900 km thick and comprises 80% of the Earth’s volumeEarth s volume.

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The Earth’s mantleThe Earth s mantle

• ComposedComposed primarily of olivine (=peridotite)( peridotite) (Mg,Fe)2SiO4

olivine is rare in the

Olivine

– olivine is rare in the crust)

• and pyroxene• and pyroxene(Mg,Fe)SiO3

Pyroxene19/76

• From the different speeds ofFrom the different speeds of propagation of seismic waves (later) we know that olivine changes to a (more densely-changes to a (more denselypacked) spinel crystal structure at about 400 km

• This breaks down to periclase• This breaks down to periclase(MgO) and enstatite (MgSiO3) at about 660 kmM SiO i t bl t hi h• MgSiO3 is very stable at high pressures and may be the dominant mineral in the E th’ i t iEarth’s interior

• Note: the book calls MgSiO3 perovskite, but that’s CaTiO3. MgSiO is enstatite but has theMgSiO3 is enstatite but has the same structure as perovskite and geologists often refer to it that way 20/76

EnstatiteEnstatite

Periclase (green) on matrix

PerovskitePerovskite

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The Earth’s coreThe Earth s core• The Earth’s core is likely

primarily iron from its densityLiquid

primarily iron from its density• Iron is well-studied up to 200

kbar but has not especially well-studied at high T and P

• The liquid can be solidified by high P

• It is known to have at least 5 solid phases (allotropes) withsolid phases (allotropes) with different structures and densities.

• One allotrope, α-Fe is “normal” iron β Fe is a nonnormal iron, β-Fe is a non-magnetic allotrope (though the lattice remains unchanged!) that’s stable between about 760 and 900Phase diagram (Fe) between about 760 and 900 C

g ( )

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Iron and sulfur• The Earth’s core has a density 5-10%

lower than pure iron which indicates a mixture with S,O or H ,

• FeO is expected to combine with crustal minerals, but FeS is expected to settle in the core

• FeS shows eutectic behaviour: an alloy of FeS + Fe melts at temperatures below that of either Fe

F Sor FeS– At 1 bar, Fe melts at 1808K, FeS at 1469K

and a 27% S + 73% Fe mixture melts at 1262K

Pyrrhotite (FeS + S alloy)1262K

• At higher pressures, the melting temperature can be depressed by as much as 1000K, allowing the material , gto remain liquid at lower temperature.

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Earth’s core• The Earth’s core is about

7,100 kilometers in diameter, slightly larger than half theslightly larger than half the diameter of Earth and about the size of Mars.

• The outermost 2,250The outermost 2,250 kilometers of the core are liquid. Currents flowing in the core are thought to generate E th' ti fi ldEarth's magnetic field.

• The innermost part of the core, about 2,600 kilometers i di t i d fin diameter, is made of a similar material to the outer core, but it is solid and perhaps even a giant singleperhaps even a giant single crystal of iron.

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Earth’s core temperature• Earth gets hotter toward the center. At the bottom of the continental

crust, the temperature is about 1000 ̊C. The temperature increases about 1 ̊C per kilometer below the crust. Geologists believe the t t f E th' t i b t 3700 t 4300 ̊C Th itemperature of Earth's outer core is about 3700 to 4300 ̊C. The inner core may be as hot as 7000 ̊C -- hotter than the surface of the Sun. But, because it is under great pressure, the center of Earth remains solid.

Depth-temperature profile p p pof the Earth

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Earth’s crystal core• Seismic waves from earthquakes pass

through the earth's core faster when they travel parallel to the Earth's axis th h th t l i th l fthan when they travel in the plane of the equator. The transit time difference is 2-4 seconds.

• Apparently, the Earth's core is not pp yperfectly spherical or its properties are different in different directions.

• The natural vibration or "ringing" frequencies of the Earth are "split," thatfrequencies of the Earth are split, that is, instead of a series of single "tones" we detect a series of closely paired frequencies. This is symptomatic of a core that is anisotropic; that is, its

Iron crystal configurations. Body-centered cubic (bcc), face-centered cubic (fcc) and core that is anisotropic; that is, its

properties are different in different directions.

• These could be explained if the Earth’s inner core is a giant crystal aligned

centered cubic (fcc) and hexagonal close-packed (hcp) .Bcc seems to be ruled out.Tromp, J. (1993) Nature 366, inner core is a giant crystal aligned

with its spin axis. p ( )

678-681 26/76

Gravity fieldGravity fieldGM p

g −=ΦIf a planet were perfectly spherical, it would produce a gravitational field outside rgwould produce a gravitational field outside it equivalent to that of a point source.

In reality planets are not perfectly spherical. The equipotential surface is called q pthe geoid.

A glass of water will have aA glass of water will have a surface parallel to the geoid at any spot; a plumb bob will hang

di l t itperpendicular to it.Earth’s geoid (exaggerated)

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Gravity fieldGravity field• If the planet is axisymmetric, its gravitational potential

can be approximated by a series expansion

⎥⎥⎤

⎢⎢⎡

⎟⎠⎞

⎜⎝⎛−−=Φ ∑

∞

)(cos1),,( nn

ne

g PJRGMr θφθ⎥⎥⎦⎢

⎢⎣ ⎠⎝

∑=2

)()(n

nng rrφ

wherewhere • the angle θ is the colatitude• the angle φ is the longitude

R th l t’ t i l di• Re the planet’s equatorial radius, • Pn(cosθ) are Legendre polynomials • Jn are the gravitational moments of the planet, which are n g pmeasures of their non-sphericity.

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Gravity field and Jn• J1 = 0 by our choice of coordinates (C of M at origin)• For rotating fluid bodies, Jn=0 where n=odd (e.g. giant

)planets)

⎟⎟⎞

⎜⎜⎛

−⎟⎞

⎜⎛−⎟

⎞⎜⎛−−=Φ L)(cos)(cos1

42

θθ PRJPRJGM ee⎟⎟⎠

⎜⎜⎝

−⎟⎠

⎜⎝

−⎟⎠

⎜⎝

−−=Φ L)(cos)(cos1 4422 θθ Pr

JPr

Jr

• The coefficients J2, J4 etc. can be determined from spacecraft 2, 4 pobservations (the deviation of their orbits from that for a spherical planet)

• We can relate J2,J4 . . . to the internal structure of the planet• For the terrestrial planets non-zero odd moments as well as non-For the terrestrial planets, non zero odd moments, as well as non

axisymmetric components of the geoid have been measured.29/76

Gravitational moments of the lplanets

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Isostatic equilibrium• Consider a planet with a solid crust on a

liquid interior layery• Floating objects displace their own weight in

the substance on which they float– A large low-density mass (mountain) in isostatic

equilibrium is compensated by a ʺdeficiencyʺ of mass underneath with total mass of displacedmass underneath, with total mass of displaced matter (liquid) equal to the mass of the mountain

– A small dense mass (ocean crust, impact basin with thin crusts) in isostatic equilibrium has ʺextraʺ mass underneath it, so it sits lower than a low-density masslow density mass

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Low-density wood blocks float high and have deep “roots”, whereas high-density blocks float low and have shallow “roots.”

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33

Isostatic reboundIsostatic rebound• In areas formerly covered by ice sheets

(around the Baltic Sea and Hudson Bay for example) sea cliffs and beachBay, for example), sea cliffs and beach ridges are now found nearly 300 m above sea level! 14C ages on marine shells and driftwood show that these features are postglacial (less thanfeatures are postglacial (less than 14,000 years old). They were formed at sea level and have risen from isostatic rebound.

• Isostatic rebound usually occurs at an exponentially declining rate. The half-recovery time israte. The half recovery time is commonly several thousand years, thus recovery is still continuing around the Baltic Sea and Hudson Bay, albeit much more slowly than it

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Bay, albeit much more slowly than it did immediately following deglaciation.

Earth’s upper layersEarth s upper layers• Crust: ocean crust (as

little as 5km thick) and continental cr st ( p tocontinental crust (up to 70km thick)

• Lithosphere: crust + rigid upper layers of mantle (extends down to about 80 km deep)

• Asthenosphere: liquid, highly viscous layer ofhighly viscous layer of mantle upon which the lithosphere floats.

• The base of the lithosphere is conventionally defined as the 1300 C isotherm since mantle

k b l thi t t ffi i tlrocks below this temperature are sufficiently cool to behave in a rigid manner.

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Thickness of Earth’s crustThickness of Earth s crust

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Geothermal Gradients in the EarthGeothermal Gradients in the Earth

• The geothermal gradient varies widely with geography from 5oC/km to• The geothermal gradient varies widely with geography from 5 C/km to 75oC/km on Earth.

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Heat sourcesHeat sources• If we observe planets and compare their luminosities (emitted heat)

with the amount of sunlight they receive several show signs of anwith the amount of sunlight they receive, several show signs of an excess, pointing to an internal heat source eg. Earth emits 75 erg cm-2 s-1 (0.075 W m-2) or 31 TW total

• Heat sources– Gravitational

• Accretion• Differentiation

– Radioactive decayy– Tidal dissipation

• Heat losses– Conduction

R di ti– Radiation– Convection– Plate tectonics, volcanism

Map of Earth’s heat flow 38/76

Accretional heatingAccretional heating• Planets (or at

l t th i )least their cores) are thought to be accumulations of smaller bodiessmaller bodies (planetesimals) brought together by gravity.by gravity.

• The potential and/or kinetic energy of these gybodies is converted largely into heat upon i timpact.

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Accretional heatingAccretional heating• Assuming the material

i i i ld th GME /&&coming in is very cold, the energy input will be mainly due to the gravitational energy of the infalling

rmGMEin /≈energy of the infalling body

• The protoplanet will radiate energy as a black-

ATEout4σ≈&

radiate energy as a black-body and cool.

• If accretion is slow, heat will be radiated into space faster , pthan it is delivered and the body will not heat up

• If accretion is fast, heat will be “buried” and the temperature of the body will increasetemperature of the body will increase.

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Differentiation• The potential energy of a homogeneous planet is reduced

if the densest components sink to the centre –differentiation is energetically favoureddifferentiation is energetically favoured

• Differentiation is opposed by the rigidity of body, so differentiation is generally favoured at higher temperatures

• Small/cold bodies may not be able to differentiate

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Differentiation• Differentiation releases gravitational

energy, driving further differentiation – positive feedback, potentialpositive feedback, potential runaway

• Heat released may generate thermal expansion and form a source ofexpansion and form a source of stress

• Sinking materials may undergo phase changes leading to volume changes and either expansion or contraction (Mercury)

• Differentiation may be ongoing in the giant planets as denser helium settles to the core (Saturn in

Helium “rain-out” on Saturn(

particular)42/76

Scarps on MercuryScarps on Mercury

• As we saw last week, Mercury is thought to have shrunk by a few km as it cooled, creating scarpsy , g p

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Energy budget of the outer planets• Incident solar radiation much less than that at Earth, so

surface (cloud top) temperatures are lowerf• We can compare the amount of solar energy absorbed

with that emitted. It turns out that there is usually an excess (not for Uranus though). Why? ( g ) y

48 14 3.5 1.4reflected

After Hubbard,in New Solar System (1999)All units in W/m2

8 1

13.5

2 6

4.6

0 6

0.6

0 3

0.6incident

emitted

5.4

8.1

2.0

2.6 0.6

0.3

0.3emitted

Jupiter Saturn Uranus Neptune44/76

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• Gravitational energy of a uniform sphere is

RGMEg 5/3 2=

dRGMdEg23

So the rate of energy release during contraction is

dtRdtg

25−=

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 for the giant planets.g p

• Radioactive decay is also a minor contributor for the outer planets.45/76

Puzzles1. Saturn has an excess heat loss that cannot be explained by

primordial (accretional) heating, ongoing contraction, di ti it tid l h tiradioactivity or tidal heating.

– However, it is consistent with gravitational energy released by differentiation as denser helium comes out of solution with hydrogen and sinks to the planet’s core.

2. Why is Uranus’ heat budget so different (no internal heat source)?source)? – 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.abundances in HCN,CO between Uranus and Neptune atmospheres.

– These compositional differences may have been caused by an impact with a large protoplanetary body at early times, which may have also caused Uranus’s large obliquity (tilt).have also caused Uranus s large obliquity (tilt).

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Differentiation of the EarthDifferentiation of the Earth

• For the accretion time of the Earth (~100For the accretion time of the Earth ( 100 million year time scale), the temperature is not expected to have risen much directlynot expected to have risen much directly from accretional heating (some debate).

• Yet the Earth is differentiated which• Yet the Earth is differentiated, which requires a rather large temperatureWh ld th t h t h• Where could the extra heat have come from?

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Radioactive decayRadioactive decay• Early on, short-lived y

radionuclides (26Al -> 26Mg in particular, 0.74 Myr half-life) would have y )contributed much more than longer-lived radionuclides do now

• About 50% of the Earth’s current excess heat is Current radionuclides of geological interest

thought to be due to radioactivity– 235U, 238U, 232Th, 40K with half-lives of 0.71, 4.5, 13.9

and 1.4 Gyr respectively are now the major y p y jcontributors

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Tidal heatingPP

bR

mM

θplanet

• Tidal potential at P bmGV −= (recall acceleration = - )V∇

aM satellite

Tidal potential at P

• Cosine rule

b2/12

cos21⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛+⎟

⎠⎞

⎜⎝⎛−=

aR

aRab θ

( )V∇

• (R/a)<<1, so expand square root

⎥⎦⎢⎣

( ) ⎥⎤

⎢⎡

+−⎟⎞

⎜⎛+⎟

⎞⎜⎛+−= L1cos31cos1 2

2

θθ RRmGV ( )⎥⎥⎦⎢

⎢⎣

+⎟⎠

⎜⎝

+⎟⎠

⎜⎝

+ 1cos32

cos1 θθaaa

GV

C M it ti l Tide raising part ofConstant=> No acceleration

Mean gravitationalacceleration (Gm/a2)

Tide-raising part ofthe potential

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Tidal bulges• We can rewrite the tide-raising part of the potential as

( ) )(cos1cos312

223 θθ HgPRmG −=−−

• Where P2(cos θ) is a Legendre polynomial, g is the surface gravity of the planet, and H is the equilibrium tide

( ) )(cos1cos32 23 θθ HgPR

aG

g y p q

2RGMg =

3

⎟⎠⎞

⎜⎝⎛=

aR

MmRH

a = semimajor axis ofsatellite orbit

R = planet radius

• For a uniform fluid planet with no elastic strength, the amplitude of the tidal bulge is 5H/2

⎠⎝ aM pm/M = mass ratio

• An ice shell decoupled from the interior by an ocean will have a tidal bulge similar to that of the ocean

• For a rigid body the tide may be reduced due to the• For a rigid body, the tide may be reduced due to the elasticity of the planet

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Rigidity or shear modulus~• We can write a dimensionless number which

tells us how important the rigidity or shear modulus μ is compared with gravity:

μ~

modulus μ is compared with gravity:

gRρμμ

219~ = (g is surface gravity, ρ is density)

• For Earth, μ ~1011 Pa, so ~3 (gravity and rigidity are comparable)

gRρ2μ~

p )• For a small icy satellite, μ ~1010 Pa, so ~ 102 (rigidity

dominates)μ~

• We can describe the response of the tidal bulge and tidal potential of an elastic body by the Love numbers h2 and k2, respectively 2/5 2/3respectively

μ~12/5

2 +=h

μ~12/3

2 +=k

51/76

Tidal dissipation• For a rigid body, the tidal bulge amplitude is given by h2 H

– The quantity k2 is important in determining the tidal torque

Th t f tid l di i ti th t f b i d• The rate of tidal dissipation, the rate of energy being pumped into the satellite being flexed by the larger parental body, like the Earth or Jupiter is (homogeneous moon, synchronous

225

221 GMRkE p⎟⎞

⎜⎛&

rotation)

22

2ne

aaQE p⎟

⎠⎜⎝

=

where n is the mean motion of the satellite, a is the semimajor axis, R is the radius of the satellite or moon, e is the eccentricity of the orbit, Q is the seismic quality factort e ecce t c ty o t e o b t, Q s t e se s c qua ty actoor dissipation factor of the satellite and is (inversely) related to the viscosity. 52/76

Tidal dissipationTidal heating involves both viscoelasticity through Q and as well asTidal heating involves both viscoelasticity through Q and μ as well as orbital mechanics, and is time-dependent. Lower Q and lower μ = greater amount of tidal dissipation. This can also lead to positive feedback from temperature dependence of μ (higher T = lower rigidity) and Q (though intemperature dependence of μ (higher T = lower rigidity) and Q (though in most simple fluids Q increases with T as the liquid becomes less viscous at larger T).Tidal dissipation is responsible for volcanism observed in Io (predictionsTidal dissipation is responsible for volcanism observed in Io (predictions made before the arrival of Pioneer in 1979 by Pat Cassen at NASA Ames) and other icy planets. Tidal heating may also be important In Ganymede and also in Europa (subsurface ocean?).and also in Europa (subsurface ocean?).

Some values of Q•Probably ~2x105 – 5x105 for Jupitery p•~17 - 43 for Io, 200 - 500 for Europa •~100 for terrestrial planets (40-104

for most rocks and metals)

Europa 53/76

Ohmic heatingOhmic heating• If a conducting object moves through

i ti fi ld dda varying magnetic field, eddy currents will be set up inside it which will dissipate heatOh i h ti b i t t f• Ohmic heating may be important for Io, Jupiter’s innermost large moon.

• Ohmic heating has been invoked to melt planetesimals (in the early Sun’smelt planetesimals (in the early Sun s strong magnetic field) and thus to explain some properties of meteorites

• Ohmic heating is being touted by• Ohmic heating is being touted by Agriculture Canada for industrial sausage production(!)

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SeismologySeismology• The study of the mechanical properties of the Earth,

primarily by tracing the passage of elastic waves through it.• These waves may be generated by earthquakes,

volcanoes, meteorite impacts or artificially.

• Two types– Body wavesy

(S & P) through the bulk of the E thEarth

– Slower surface wavestravel in thetravel in the near-surface layers 55/76

Surface wavesSurface waves• Larger amplitude and longer duration that body waves, g p g y

but slower to arrive. They are usually most destructive.• Rayleigh waves move the surface in vertical ellipses, just

like water waves (v~70% of S wave vel)like water waves (v 70% of S wave vel)• Love waves move horizontally, across the direction of

motion (v~90% of S wave vel)

Rayleigh wavesRayleigh waves

Love waves56/76

Body wavesBody waves• Travel through the interior of the Earth• Are reflected/refracted at interfaces in• Are reflected/refracted at interfaces in

density/composition or slowly refracted by gradients in Earth’s internal properties.

• Two types– P (Primary, Push or Pressure) waves

• Longitudinal waves, compression and rarefaction along g , p gdirection of motion

• Similar to sound waves• Can travel through liquid

S (S S S )– S (Secondary, Shake or Shear) waves• Shear waves, oscillations transverse to propagation• Similar to EM waves, or waves in a rope

C t t l th h li id• Cannot travel through liquid

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Body wavesBody waves

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P and S wave propagationIncreasing sound speed with depth means body waves curve typically upwards

PCP waves

•S waves cannot pass through liquid•P waves can travel through liquid but

PKP waves

•This led to the discovery of a liquid layer in the Earth’s core, as there is a S-wave shadow zone opposite seismic sources where no direct s-

are reflected (PCP) and refracted (PKP)•There is also a P-wave shadow zonewhere refraction prevents the arrival seismic sources where no direct s-

waves are receivedwhere refraction prevents the arrival of direct p-waves

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Seismology and the interior of the EarthTh M h M h i i– The Moho or Mohorovicic discontinuity between the crust and mantle

• Varying depth: 5-10 km y g pbelow ocean floor, 35 km below continents, <60 km below mountain ranges

• 200-300 m thick200 300 m thick• P wave velocity increases

– Discontinuities in upper mantle

• Depths below 670 km• Stepwise increasing P and S

wave velocitiesPhase and density changes• Phase and density changes of material, e.g., olivine →spinel → enstatite

60/76

Seismology and the interior of the Earth– The interface between the

solid mantle and liquid outer corecore

• 3000 km depth• P wave velocity

decreases S wavesdecreases, S waves disappear

– The interface between the liquid outer core and the solidliquid outer core and the solid inner core

• 5200 km depthP wave velocity increases• P wave velocity increases

• S waves reappear

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Interior of the Moon

• crust– depth <5 km under p

maria, – up to >100 km

under highlands– on average thicker

on the far side, center-of-mass to center-of-geometry

Back side of Moon

center-of-geometry displacement of 1.7 km towards the Earth in the Earth-Moon direction

– fractured at <25 km depth

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Interior of the Moon• mantle

– upper mantle at depths <500 km, pp polivine

– middle mantle at depths <1000 km, olivine and pyroxene

– lower mantle at depths <1400 km, S wave velocity decreases, partially molten?

• core– P wave velocity increases, solid– radius <220-450 kmradius <220-450 km– iron-rich

• seismically active zones – near surface (meteors)– at depths of 700-1200 km (tidal) 63/76

Mercury• Lithosphere

– depth 200 km– scarps (1-3km high) possibly due to– scarps (1-3km high) , possibly due to

contraction after cooling• Mantle

– depth 600 km– depth 600 km– rocky, silicate material– ”abnormally” thin

• overal Fe content of Mercury is 2x chondriticoveral Fe content of Mercury is 2x chondritic

• Core – size 75% of the planetary radius (high bulk

density)density)– iron, or FeS– outer liquid core, probably convective

(magnetic field)( g )– large core may be primordial, or due to a large

late impact that vaporized much of the mantle 64/76

Venus• Similar interior structure to Earth as• Similar interior structure to Earth, as

suggested from size and mean density• Surface heat flow probably less than on

Earth– interior may be heating up– with radioactive heating most effective in

mantle, the core may be relatively cooler• Lithosphere:osp e e

– high surface temperature suggests it is relatively thin, depth about 20 km

– heat loss less than on Earth: hot-spot and volcanic activity possibly more importantvolcanic activity possibly more important

– absence of planet-wide tectonic plate activity (which is lubricated by H2O on Earth)

– crust may be too buoyant to subduct

Computer generated surface view of Venus’ Eistla Regio (from the crust may be too buoyant to subduct

– may lead to catastrophic crust renewal every few ~108 years

g (northeast).

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VenusM tl• Mantle– Lower-viscosity asthenosphere

may be lacking due to volatile (particularly water) depletion(particularly water) depletion

• Core– probably less FeS than Earth’s

core owing to its formation closercore owing to its formation closer to the Sun (hotter = less volatile sulfur) which implies higher freezing Tg

– Venus has no magnetic field, which implies that there is no conductive core

– possible state: • frozen solid• liquid but without liquid to solid

phase change that drivesphase change that drives convection in Earth’s core

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Mars• Surface and mantle high in

FeO relative to Earth, as well as in volatiles (Na,P,K and ( , ,Rb)

• Lithosphere– Low surface temperature p

suggests relatively thick lithosphere

– elevation difference 5 km between S and N hemispheresbetween S and N hemispheres

– absence of plate tectonics– significant early heat loss from

large shield volcanos (eg. Ol mp s Mons)Olympus Mons)

– topographic features are not fully isostatically compensated, consistent with thick rigid Topographic map of Marsglithosphere Topographic map of Mars

(Mars Global Surveyor)67/76

Mars• Mantle

– silicate compositionprobably be enriched in FeO– probably be enriched in FeO

– volcanic magma sources at a depth of 200 km (based on viscosity)viscosity)

• Core– solid Fe-Ni, or liquid Fe-FeS

with larger radiuswith larger radius– weak magnetic field implies

no liquid layer but models do not reproduce this

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Interior structure of the terrestrial planets

69

Jupiter• Internal structure is

modelled, but constrained by mass, radius, rotation, , ,oblateness, internal heat sources, Jn, etc

• CoreProbably relatively– Probably relatively small, 5-10 Earth masses

– Probably an inner rocky/iron and anrocky/iron and an outer ice-rich component, but could also be homogeneous

– Much mass was present after solid-body accretion, but some may have been added later byadded later by gravitational settling

Adiabatic (fully convective) model 70/76

Jupiter• Core envelope

– High-Z (Z>2) elements constitute 15-30 Earth masses distributed withinmasses distributed within core and its surrounding envelope

– Enriched in high-Z t i l b f t 3 5material by a factor 3-5

compared to chondritic composition

• MantleMantle– Large amount of ices of

H2O, NH3, CH4 and S-bearing materials

M t i t ll• Most internally generated heat is attributed to gravitational contractiongravitational contraction and accretion in the past 71/76

Saturn• Similar interior structure to

Jupiter• Like Jupiter, the total mass p ,

of high-Z elements is about 15-30 Earth masses

• As Saturn is smaller and less massive than Jupiter, the relative abundance of high-Z elements is thereby greater– consistent with

atmospheric C, N, and S hi h h dwhich appears enhanced

by a factor 2-3 relative to Jupiter

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Saturn• Like Jupiter, the magnetic

field is generated in a metallic hydrogen region– The field is weaker than

Jupiter’s due to a metallic envelope of smaller extent

• Internal excess heat is generated about equally by– Gravitational

t ti / ticontraction/accretion– Release of gravitational

energy due to He ”rainout” onto the coreonto the core

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Uranus and Neptune• Neptune is 3% smaller and 15% eptu e s 3% s a e a d 5%

more massive than Uranus• Models much less constrained

than J&S• H and He constitute only a few

Earth masses of material• High-Z element mass is similar toHigh Z element mass is similar to

Jupiter and Saturn– Consistent with atmospheric C

and S abundances enhanced about 50 times relative to Jupiter and Saturn

• Rock core– Possibly about 1 Earth mass, but

may be absent– Possibly differentiated: iron in

lid h k b li idsolid phase, rock may be liquid

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Uranus and Neptune

• Mantle– Constitutes 80% of the mass– Icy composition: hot, dense, y p , ,

ionic oceans of H2O and minor NH3, CH4, N2, H2S

• Atmosphere– Outer 5-15% of the radius– H- and He-rich

• Internal magnetic fields g– indicate electrically

conductive and convective icy interiors (P too low for

t lli H)metallic H)– generated at 0.5-0.8 radii

from the core

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Interior structure of the giant planets

76