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Interior Structure of Terrestrial Planets Tilman Spohn Überblick Überblick Komplexe Systeme Weltraum

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Interior Structure of Terrestrial Planets Tilman Spohn Überblick Überblick Komplexe Systeme Weltraum Interior Structure of Terrestrial Planets 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 Mars the masses 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 Mass Moment of inertia factor Gravity 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), Ice (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 1st HGF Alliance Week, Berlin,14 May 2008 Dynamic Tidal Response Constraint Tidal deformation is characterized by ... the potential Love number k2 = Φi /Φe ... the radial displacement Love number h2 = g ur /Φe Tidal dissipation is proportional to the imaginary part Im(k2 ) that depends on internal structure, rheology, and temperature. It is also dependent on orbital parameters. 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 hydrostatic equilibrium Rotation parameter m: Graviational acceleration at equator/ Rotation acceleration at equator 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 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 MRRR=π (( 3 −ρ 3) +3 ρ) 3 P c m c c 5 5 I 2 ⎛⎛ ⎛ R ⎞ ⎞⎛ ρ ⎞ ⎛ R ⎞ ⎛ ρ ⎞⎞ =⎜⎜1 −⎜ c ⎟ ⎟⎜ m ⎟ + ⎜ c ⎟ ⎜ c ⎟⎟ MR2 5 ⎜⎜ ⎜ R ⎟ ⎟⎜ ρ ⎟ ⎜ R ⎟ ⎜ ρ ⎟⎟ P ⎝⎝ ⎝ P ⎠ ⎠⎝ ⎠ ⎝ P ⎠ ⎝ ⎠⎠ Spohnlie30 >oF 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 densities 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., Mercury). 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 1st HGF Alliance Week, Berlin,14 May 2008 Martian Interior - Summary Galilean Satellites Mercury Mars Chudinovskh and Galilean Satellites Boehler, 2007 Mars‘ Mercury should be close to core Maeutecticrs 47 MERCURY Folie 48 > Spohn Two-Layer Models Mercury MarsMoon 1st HGF Alliance Week, Berlin,14 May 2008 Interior Structure of Mercury Volatile-poor, refractory composition assumed iron core radius 1860 ± 80 km silicate shell 500 to 700 km thick Low mantle pressures suggest ... moderate depth variation of density and seismic velocities ... lack of pressure-induced phase transitions after Siegfried and Solomon 1974 1st HGF Alliance Week, Berlin,14 May 2008 Interior Structure of Venus - Summary • Small rotation rate does not allow to calculate MoI-factor from J2 under the assumption of hydrostatic equilibrium. k2 = 0.295 ± 0.066 consistent with liquid state of the core. Interior structure usually scaled to Earth‘s mantle pressure conditions. 1st HGF Alliance Week, Berlin,14 May 2008 Lunar Interior - Summary Wieczorek et al., 2006 Galilean Satellites 1st HGF Alliance Week, Berlin,14 May 2008 Galilean Satellites Satellites: Data Io Europa Ganymede Callisto Titan 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 1st HGF Alliance Week, Berlin,14 May 2008 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.
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