Terrestrial Exoplanet Radii, Structure and Tectonics. Diana Valencia (OCA), KITP, 31 March 2010

Transcription

1 Terrestrial Exoplanet Radii, Structure and Tectonics Diana Valencia (OCA), KITP, 31 March 2010

2 Earth s Structure Olivine Structure Romanowicz, 2008

3 Earth s Structure Upper mantle (Mg,Fe)2SiO4 α +(Mg,Fe)2Si2O6 410km 660km Lower Mantle (Mg,Fe)SiO3 and (Mg,Fe)O 2890km 5150km Solid Inner Core Fe+Ni Liquid Outer Core Fe+alloy (Si, S, O) Transition Zone (Mg,Fe)2SiO4 β and γ +(Mg,Fe)2Si2O6 PPV+MW

4 Internal Structure Model Planets made of Mg, Si, O, Fe, H 2 O, H/He Input: M, Psurf, Tsurf, guess R, gsurf, dρ dr = ρ(r)g(r) φ(r) dg m(r) = 4πGρ(r) 2G dr r 3 dm dr = 4πr2 ρ(r) dr dp dr = ρ(r)g(r) dt dr = q and k + EOS( ) dt dr = g(r)γ(r) T φ(r) Output: R(M, ); (r), P(r), g(r), m(r), I/MR 2, D,...

5 Earth and rocky super-earths Valencia et. al, 2006

6 Mass-Radius Relationships R/RE=a (M/ME) 0.26 Valencia et. al, 2006 Salpeter & Zapolsky 1967 Stevenson 1982 Exponent robust to EOS, Temperature Structure and CMF

7 Mass-Radius Relationships Seager et al 2007 Fortney et al 2007 H2O MgSiO3 Fe Sotin et al 2007, Grasset et al 2009

8 Generalized M-R relationship Uranus Radius (km) max radius min radius Neptune H2O (Earth-like: Fe/Si) IMF: ice-mass fraction Valencia et al. 2007b Venus 1M Earth 2M 4M Mass 7M 10M 15M R/REarth= ( IMF) (M/MEarth) 0.262( IMF)

9 Super-Earth Composition M=5M 40 Maximum Radius Mantle Fixed Si/Fe ratio Late delivery of H2O Terrestrial Side Minimum Radius Core Radius (km) H2O Valencia et al. 2007b There is degeneracy in composition. Some compositions are improbable.

10 Super-Earth Composition M=5M 40 Maximum Radius Mantle Fixed Si/Fe ratio Late delivery of H2O Terrestrial Side Minimum Radius Core Charbonneau et al, 2009 Radius (km) H2O Valencia et al. 2007b There is degeneracy in composition. Some compositions are improbable.

11 Toblerone Diagram 1M 2.5M 5M 7.5M 10M Valencia et al. 2007b Radius (km) Rogers & Seager, 2010

12 CoRoT-7b: the first transiting super-earth Leger et al, 2009 Queloz et al, 2009 Radius = 1.68 ± 0.09 R E Period = days Age = Gy Mass = 4.8 ± 0.8 M E

13 Can it retain an atmosphere? No, unless it is constantly resupplied Energy limited calculation based on UV flux dm = 3 F EUV dt 4 G K tide = g/s For more details on see Lammer et al 09 within an order of magnitude of the escape rate of HD b Even if it has a silicate atmosphere, it is thick enough for UV absorption

14 Rocky CoRoT-7b Uranus Neptune silicate atmosphere Radius [km] CoRoT-7b Mg-silicate mantle 37%, core 63% Mg-silicate planet Iron planet Earth-like Undifferentiated Earth-like R p =1.68R R cmb =0.86R silicate mantle iron solid core super-moon silicate (little Planet iron) 6000 M=5.6M M=5.3M M=4.0M Mass [M Earth ] Valencia et al, 2010

15 Rocky CoRoT-7b Uranus Neptune silicate atmosphere Radius [km] CoRoT-7b Mg-silicate mantle 37%, core 63% Mg-silicate planet Iron planet Earth-like Undifferentiated Earth-like R p =1.68R R cmb =0.86R silicate mantle iron solid core silicate Planet 6000 M=5.6M M=5.3M Mass [M Earth ] Valencia et al, 2010

16 Rocky CoRoT-7b Uranus Neptune silicate atmosphere Radius [km] CoRoT-7b Mg-silicate mantle 37%, core 63% Mg-silicate planet Iron planet Earth-like Undifferentiated Earth-like R p =1.68R R cmb =0.86R silicate mantle iron solid core silicate Planet 6000 M=5.6M M=5.3M Mass [M Earth ] Valencia et al, 2010

17 H2O Vapor CoRoT-7b % vapor Uranus Neptune T [K] Vapour adiabats Liquid molecular fluid Ice VII plasma superionic Ice X Radius [km] % vapor 20% vapor 10% vapor 3% vapor Earth-like CoRoT-7b 100 1e-6 1e-5 1e-4 Ice I 1e P [GPa] Ice II-VI Evaporation Timescale ~ 1 Gy e3 5e Mass [M Earth ] 20 Valencia et al, 2010

18 H2O Vapor CoRoT-7b % vapor Uranus Neptune T [K] Vapour adiabats Liquid molecular fluid Ice VII plasma superionic Ice X Radius [km] % vapor 20% vapor 10% vapor 3% vapor Earth-like CoRoT-7b 100 1e-6 1e-5 1e-4 Ice I 1e P [GPa] Ice II-VI Evaporation Timescale ~ 1 Gy e3 5e Mass [M Earth ] 20 Valencia et al, 2010

19 Hydrogen or Helium? % H-He Uranus % H-He Neptune Radius [km] % H-He 0.01% H-He Earth-like CoRoT-7b Evaporation Timescale ~ 1 My! Mass [M Earth ] 20 Valencia et al. 2010

20 CoRoT-7b s origin? Valencia et al Volatile Origin 318 a) in situ Rocky Origin Mass [M ] H-He planets vapor planets rocky cores 8 CMF f = b) inward migration Mass (M E ) 6 5 cored planet CMF f =0.33 silicate planet Corot-7b s Mass Mass [M ] H-He planets vapor planets Time (Gyr) rocky cores Age[Ga]

21 CoRoT-7b s origin? Valencia et al Volatile Origin Unconstrained Rocky Origin Mass [M ] H-He planets a) in situ vapor planets rocky cores 8 CMF f = b) inward migration Mass (M E ) 6 5 cored planet CMF f =0.33 silicate planet Corot-7b s Mass Mass [M ] H-He planets vapor planets Time (Gyr) rocky cores Age[Ga]

22 GJ 1214b Radius = ± 0.13 R E Mass = 6.55 ± 0.98 M E Period = 1.58 days Temp = K See also: Rogers & Seager, 2010 Miller-Ricci & Fortney 2010 Charbonneau et al 2009

23 Solid GJ 1214b? Uranus Neptune GJ 1214b Radius [km] CoRoT-7b Ice-planet Mg-silicate planet Earth-like Fe-planet Mass [M Earth ]

24 Teq=500K H/He in GJ 1214b? HAT-P-11b GJ 436b Teq=2000K Uranus 10% H-He GJ 1214b 1% H-He 0.1% H-He Neptune Kepler-4b Earth-like 10% H-He GJ 436b HAT-P-11b CoRoT-7b Uranus Neptune Kepler-4b Teq=500K, Age=5Ga GJ 1214b 1% H-He 0.01% H-He 0.1% H-He CoRoT-7b Earth-like Teq=2000K, Age=5Ga In preparation

25 GJ 1214b: escape rate CoRoT-7b GJ 1214b = 0.34 E Age = 3-10 Gy dm = 3 F EUV dt 4 G K tide Selsis et al, 2007

26 Habitability from a Planetary Perspective: Follow the water... Surface temperature depends on insolation, interior heat flux and atmospheric response atmospheric composition Interior processes: tectonics, volcanism, magnetic field

27 Can a massive rocky planet have plate tectonics? Walker 1981, Kasting 1996 Strong, coherent plate; deformation on boundaries; PT is the surface expression of mantle convection

28 Plate Tectonics and Mantle Convection Navier Stokes equations Classical Boundary layer theory Numerical modeling Laboratory Experiments Bernard Convection Bercovici, et al. 2000

29 Conditions for PT 1. Deformation of the plate 2. Negative buoyancy Valencia et al, 2007, 2009 O Neill & Lenardic 2007 Van Heken & Tackley, 2009 Sotin & Jackson, 2009 Valencia, 2009 Kite et al Energy dissipation at subduction zones is not enough to halt PT Valencia et al, 2009

30 Can terrestrial super-earths have plate tectonics?

31 Can terrestrial super-earths have plate tectonics? under debate

32 Can terrestrial super-earths have plate tectonics? under debate Valencia et al 2007:... as mass increases, the process of subduction, and hence plate tectonics, becomes easier. Therefore, massive super-earths will very likely exhibit plate tectonics O Neill and Lenardic 2007:...these results suggest super-earths may in fact be in an episodic or stagnantlid regime, rather than a mobile lid regime similar to Earth s plate tectonics.

33 Similarities Fixed Tsurf Coulomb failure criterion for plate deformation Stress comes from convection Ra

34 Similarities Fixed Tsurf Coulomb failure criterion for plate deformation Stress comes from convection Ra Differences Valencia et al: Classical Boundary Layer Structure model to scale parameters Dominated by radioactive heating OL 2007 Scaled a numerical model (Moresi and Solomatov, 1998) Constant density scaling Mixed heating

35 Classical Boundary Layer Theory u 0 D Ra Ra v 0 velocity u stress xy plate length L timescale L Turcotte & Schubert, 2002 Internally heated: 4 Ra = ρgαd q/κη(t)k D/2δ ~ Ra 1/4

36 Convective Parameters on super-earths 200 Plate thickness (km) M Mars Venus Earth 1M Mass super-earths 3M 10M towards gaseous planets M Stress (MPa) 1/2 u~κ/d Ra xy ~η(t) u/d Valencia et al., 2007c

37 Convective Parameters on super-earths Plate P-T structure is nearly invariant with mass 200 Plate thickness (km) M Mars Venus Earth 1M Mass super-earths 3M 10M towards gaseous planets M Stress (MPa) 1/2 u~κ/d Ra xy ~η(t) u/d Valencia et al., 2007c

38 Convective Parameters on super-earths Plate P-T structure is nearly invariant with mass 200 Plate thickness (km) M Mars Venus Earth 1M Mass super-earths 3M 10M towards gaseous planets M Stress (MPa) 1/2 u~κ/d Ra xy ~η(t) u/d Valencia et al., 2007c Super-Earth s: thinner plates and larger driving forces

39 Plate deformation: Coulomb Failure Criterion σ zz For deformation: τ yield stress > 1 σ τ PRINCIPAL STRESS - LITHOSTATIC PRESSURE NORMAL HOR. STRESS - PRINCIPAL σ xx = σ zz + σ xx τ xy SHEAR STRESS UNDER PLATE τ= 0.5 Δσxx sin2θ σ= σzz Δσxx (1+cos2θ) yield stress = S0 + μ(σ-λσzz) Water reduces strength

40 Stress vs. Strength on Faults MPa 100 shear stress Dry fault strength Earthquake s stress release values Wet fault strength µ= M 2M 3M 5M 7M 10M 6300 km km Water could matter for Earth but not for super-earths Valencia et al., 2009b

41 PT on super-earths? Scaling Factor = R/R E Numerical Model by: Moresi and Solomatov (1998) Coulomb Failure Criterion Non-newtonian rhelogy (plateness, zones of weakness) O Neill & Lenardic, 2007

42 Plate Tectonics on super-earths 1/2 u~κ/d Ra xy ~η(t) u/d O Neill & Lenardic, 2007

43 Plate Tectonics on super-earths 1/2 u~κ/d Ra xy ~η(t) u/d O Neill & Lenardic, 2007 Small planets are cold and large planets are hot. Convective stress is dominated by internal viscosity, so hotter means lower convective stress. If the yield of the lithosphere is constant, hot planets can not have plate tectonics

44 Other Studies Sotin & Jackson 2009 predict a high stress/strength ratio for internally heated and mixed heated systems Yield stress (MPa) Van Heck & Tackley 2009 show that for planets that are heated internally the stress/strength ratio is constant with mass, and for planets that are heated from below the ratio increases Internally heated cases 2D spherical annulus Mobile lid Rigid lid Planet size / Earth s size Yield stress (MPa) Bottom heated cases 2D spherical annulus Mobile lid Rigid lid 95 * S^3 95 * S^(2/3) Planet size / Earth s size

45 Plate Tectonics on Exo-Earths? R/RE=2 Van Heck & Tackley, 2009

46 Plate Tectonics on Exo-Earths? R/RE=2 Van Heck & Tackley, 2009

47 Additional slides

48 Uncertainties in the Interior Temperature (K) M 1M ppv+mw Valencia et al. 2009a pv+mw rw+wd olivine +pyroxenes Super-Earths mantles are mostly composed of PPV What is PPV s stability region? Are there any other phase transitions? Pressure (Mbar) Virtually incompressible oxide: Gd 3 Ga 5 O 12 (Mashimo et al 06) Dissociation of silicates at high P? MgSiO3 --> MgO + SiO2 (Umemoto et al 06) (Grocholski et al 10 doesn t agree) Murakami et al 2004