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Home , Moment of inertia factor

Interior Structure of Terrestrial Tilman Spohn Überblick Überblick Komplexe Systeme Weltraum

ErosionErosion durchdurch Sonnenwind;Sonnenwind; ImpakteImpakte Biosphäre

Hydrosphäre Atmosphäre

Kruste Biogeochemiche Wechselwirkungen stabilisieren die VulkanismusVulkanismus AusgasenAusgasen Oberflächentemperatur (Kohlenstoff Zyklus) Mantel Weltraum

Magnetosphäre ErosionErosion durchdurch AbschiirmungAbschiirmung Sonnenwind;Sonnenwind; ImpakteImpakte Biosphäre

Hydrosphäre Atmosphäre

Kruste

Subduktion,Subduktion, VolatilrückführungVolatilrückführung undund VulkanismusVulkanismus AusgasenAusgasen verstärkteverstärkte KühlungKühlung

Mantel

KonvektiveKonvektive KühlungKühlung

Kern

DynamoDynamo Die Allianz Interior Structure 7 Tilman Spohn, IfP Münster 0.5 ME 0.8 ME 1 ME 2.5 ME 5 ME Interior Structure

Interior Structure models aim at determining the of major chemical reservoirs the depths to chemical discontinuities and phase transition boundaries the variation with depth of thermodynamic state variables (r, P, T) and transport parameters

Folie 9 > Spohn Of Particular Interest…

Core radius State of the core Inner core radius Heat flow from the core Transport parameters

Folie 10 > Spohn Interior Structure

Constraints Moment of inertia factor field, Topography Rotation parameters Tides Surface rock chemistry/ mineralogy Cosmochemical constraints Laboratory data Magnetism MGS Gravity Field of Mars Future: Seismology! Heat flow

Folie 11 > Spohn Doppler Principle

12 T. Spohn, IfP June 24, 2003 Mars

Jupiter

Ganymede

Chemical Components:

Gas (H, He), (NH3, CH4, H2O), Rock/Iron 13 Page 14 > Objectives and Accomplishments > Prof. Dr.Tilman Spohn

Chemistry

Chondritic ratio Fe/Si = 1.71

Mg2SiO4 (olivine) mantle and Fe core

16 Surface Rock

17 SNC Meteorites Samples from Mars?

„ SNC: Shergotty,Nahkla, Chassigny „ Most of them are young: a few 100 million to 1 billion years „ Basalts

18 Tilman Spohn, IfP Münster e Φ /

r

= g u

2 h

e Φ / i Φ

=

2 k is characterized by is proportional to the imaginary part

HGF Alliance Week, Berlin,14 May 2008 Berlin,14 Week, Alliance HGF st st 1 that depends on internal structure, rheology, and )

2 k Tidal dissipation Tidal deformation ... the potential Love number Dynamic Tidal Response Constraint ... the radial displacement Love number temperature. It is also dependent on orbital parameters. Im(

Laboratory Data Breuer and Spohn, 2003 Breadboard model

Folie 23 > Spohn The HP3 instrument

9 Tractor mole 9 Heaters and temperature sensors on tether 9 Accelerometer and Permittivity Probe in payload compartment 9 Tilt sensors and Tether length sensors Gravity

Gravitational Potential

J2 and Moments of Inertia More Complete Representation

e.g., Spohn et al., 1998 oder auch Spohn in Bergmann Schäfer Radau-Darwin-Relation for Planets in

Rotation parameter m: Graviational acceleration at equator/ Rotation acceleration at equator Planetary Data

Mercury Mars

Radius 0.38 0.95 1.0 0.54 0.27 0.41 0.28 Mass 0.055 0.815 1.0 0.107 0.012 0.018 0.015 [kg/m3] 5430. 5250. 5515. 3940. 3340. 1940. 3554.

3 ρ0 [kg/m ] 5300. 4000. 4100. 3800. 3400. 1800. 3600. MoI 0.34 ? 0.3355 0.3662 0.3905 0.3105 0.378

Rc/Rp 0.76 0.55 0.546 0.51 0.25 0.3 0.5 Dipole Moment 4.9 <0.4 7980. <2.5 <4x10-9 14 ? [1019 A m2]

Folie 28 > Spohn Average moment of inertia

I C 2 2 2 −= J 2 MRP MRP 3 Simple Two-Layer Model RP

ρm

Rc ρc

4 π (( 33 ) +−= RRRM 3ρρ) 3 ccmcP 5 5 I 2 ⎛⎛ ⎛ R ⎞ ⎞⎛ ρ ⎞ ⎛ R ⎞ ⎛ ρ ⎞⎞ ⎜⎜1−= ⎜ c ⎟ ⎟⎜ m ⎟ + ⎜ c ⎟ ⎜ c ⎟⎟ MR2 5 ⎜⎜ ⎜ R ⎟ ⎟⎜ ρ ⎟ ⎜ R ⎟ ⎜ ρ ⎟⎟ P ⎝⎝ ⎝ P ⎠ ⎠⎝ ⎠ ⎝ P ⎠ ⎝ ⎠⎠

Folie 30 > Spohn Two-layered structural models

Non-uniqueness of even simple

interior structure models with ρs = 0 three unknowns: mantle and core density, core radius two constraints: mean density, MoI factor

Reduce ambiguities by MarsMoonMercury cosmochemistry core ranging from pure Fe to eutectic Fe-FeS

31 Moment-of-Inertia factor constraint

• MoI factor constraints • mantle density if similar to bulk density 0.375 and a high-density core 0.350 exists (e.g., Moon). 0.325 0.300 • core density if similar 0.275 to bulk density and 0.250 low-density outer shell exists (e.g., ).

Folie 32 > Spohn Structural Equations

Sohl and Spohn,1997; Valencia et al., 2005. Equation of State

Relates local density ρ (p,T) to ambient pressure p and temperature T. Linear thermal pressure correction (1). Isothermal compression (2).

(2)

(1) αKT =const. „Harmonic solid“

−1 ⎛⎞⎛⎞11∂∂∂ρρ⎛⎞P α KT =×⎜⎟⎜⎟ ==⎜⎟const ⎝⎠⎝⎠ρρ∂∂∂TPTPT⎝⎠V ddlnα lnα =−α K dT T dP dKln dKln TT=−α K dT T dP Mixing

36 Tilman Spohn, IfP Münster Temperature

Temperature requires some additional considerations Heat transfer model Model of interior chemistry Model of initial temperature

37 Tilman Spohn, IfP Münster Stagnant Lid

Convection tolerates an order of magnitude viscosity increase in convecting layer Therefore a stagnant lid forms on top through which the viscosity increases dramatically

38 Tilman Spohn, IfP Münster Thermal Structure

−β Boundary layer thickness δ =−()RRRac α gTRΔ−() R3 Ra = c κν

Adiabat dTα T T |ad ==γ dPρ cP KT

α KT 1 γ = ρρcP 39 Interior Structure: The Data Set

Relevant data with satisfying accuracy are available only for Earth, Moon, and Mars Moon and Mars: Mass, MoI-factor, Samples, Surface Chemistry, Lunar seimology Venus: Small rotation rate precludes a calculation of the MoI- factor from J2 under the assumption of hydrostatic equilibrium Mercury: MoI from Peale‘s experiment

Galilean Satellites: C22 and, in some cases, C20 Others: Density from mass and radius

Folie 40 > Spohn Mars Two-Layer Model

MoI=0.3662

Folie 42 > Spohn Fe Mars 15 weight-% S

FeS

Perovskite

MoI=0.3662 Sohl and Spohn, 1997 Sohl and Spohn, 1997 Mars

Sohl and Spohn, 1997 44 The Crust: MGS

Average thickness ~ 50 km, but ambiguous Crust thickness variations from gravity Minimum underneath hellas Maximum underneath Tharsis Crust production rate peaked in the Noachian and Period ends Gyr b.p. extended into the Hesperian Noachian 3.5 – 3.7 Hesperian 2.9 – 3.2 Amazonian today

45 HGF Alliance Week, Berlin,14 May 2008 Berlin,14 Week, Alliance HGF st st 1 Martian Interior - Summary s Mars‘ core te lli s te te should be a y lli S r te n u a y a c s S r close to le r r n u li e a a c rs a e r G M M lil aeutectic a e G M M

Chudinovskh and Boehler, 2007

47 MERCURY

Folie 48 > Spohn Two-Layer Models

Mercury MarsMoon after Siegfried and Solomon 1974

HGF Alliance Week, Berlin,14 May 2008 Berlin,14 Week, Alliance HGF st st 1 iron core radius 1860 ± 80 km silicate shell 500 to 700 km thick ... moderate depth variation of density and seismic velocities ... lack of pressure-induced phase transitions Volatile-poor, refractory composition assumed Low mantle pressures suggest Interior Structure of Mercury HGF Alliance Week, Berlin,14 May 2008 Berlin,14 Week, Alliance HGF st st 1 under the 2 = 0.295 ± 0.066 2 Interior Structure of Venus - Summary consistent with liquid consistent with liquid state of the core. Small rotation rate does not allow to calculate MoI-factor from J k Interior structure usually scaled to Earth‘s mantle pressure conditions. assumption of hydrostatic equilibrium. • Wieczorek et al., 2006 al., et Wieczorek

HGF Alliance Week, Berlin,14 May 2008 Berlin,14 Week, Alliance HGF st st 1 Lunar Interior - Summary Galilean Satellites Galilean Satellites

HGF Alliance Week, Berlin,14 May 2008 Berlin,14 Week, Alliance HGF st st 1 Satellites: Data

Io Ganymede Moon

Mass (1020 kg) 894. 480. 1482. 1077. 1340. 735. Radius (km) 1816. 1569. 2631. 2400. 2575 1738.. Density (kg m-3) 3570. 2970. 1940. 1860. 1880. 3340. C/MR² 0.378 0.346 0.3105 0.358 ? 0.393

HGF Alliance Week, Berlin,14 May 2008 Berlin,14 Week, Alliance HGF st st 1 Models of Interior Structure Internal Oceans

„ The icy satellites Europa, Ganymede, Callisto, Titan, Triton,... May have internal oceans „ Competition between heat transfer and heating rates „ Melting point gradient Internal Oceans

„ The icy satellites Europa, Ganymede, Callisto, Titan, Triton,... May have internal oceans „ Competition between heat transfer and heating rates „ Melting point gradient

Model

„ Heat Transfer „ Conduction „ Convection with strongly T dependent viscosity (Solomatov, Grasset, Parmentier, Sotin...

„ η = η0 exp(A(Tm/T-1)), 14 A=25, η0 = 10 Pa s „ Viscosity increases through mixed sublayer by 1 O.o.M. l0 „ Nu = a Raβ „ Radiogenic Heating Equilibrium Model Nu = a Ra0.25, k = 3.3 W m-1 K–1, A=24, H=4.5 pW kg–1

Ganymede, Callisto d. Titan Europa

Callisto u. Ammonia (5 wt.%)

Ganymede, Callisto d. Titan Europa

Callisto u. Ocean Thicknesses

NH -H O 3 2 H2O In Lieu of a Summary Slide: Planetary Data

Mercury Venus Earth Mars Moon Ganymede Io

Radius 0.38 0.95 1.0 0.54 0.27 0.41 0.28 Mass 0.055 0.815 1.0 0.107 0.012 0.018 0.015 Density [kg/m3] 5430. 5250. 5515. 3940. 3340. 1940. 3554.

3 ρ0 [kg/m ] 5300. 4000. 4100. 3800. 3400. 1800. 3600. MoI 0.34 ? 0.3355 0.3662 0.3905 0.3105 0.378

Rc/Rp 0.76 0.55 0.546 0.51 0.25 0.3 0.5 Dipole Moment 4.9 <0.4 7980. <2.5 <4x10-9 14 ? [1019 A m2]

Folie 64 > Spohn