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

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

Earth s Structure Olivine Structure Romanowicz, 2008

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

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,...

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

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

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

Generalized M-R relationship 25500 Uranus Radius (km) 19000 14000 10000 8000 max radius min radius Neptune H2O (Earth-like: Fe/Si) IMF: ice-mass fraction 6400 5000 Valencia et al. 2007b Venus 1M Earth 2M 4M Mass 7M 10M 15M R/REarth= (1+0.56 IMF) (M/MEarth) 0.262(1-0.138 IMF)

Super-Earth Composition M=5M 40 Maximum Radius 30 0 10 100 20 90 50 12650 80 60 Mantle 70 70 80 12000 100 90 60 11350 0 50 10 20 40 30 Fixed Si/Fe ratio Late delivery of H2O 10650 Terrestrial Side10000 40 30 50 60 9350 20 70 80 10 4000 6000 8000 10000 12000 14000 16000 Minimum Radius 90 100 0 Core Radius (km) H2O Valencia et al. 2007b There is degeneracy in composition. Some compositions are improbable.

Super-Earth Composition M=5M 40 Maximum Radius 30 0 10 100 20 90 50 12650 80 60 Mantle 70 70 80 12000 100 90 60 11350 0 50 10 20 40 30 Fixed Si/Fe ratio Late delivery of H2O 10650 Terrestrial Side10000 40 30 50 60 9350 20 70 80 10 4000 6000 8000 10000 12000 14000 16000 Minimum Radius 90 100 0 Core Charbonneau et al, 2009 Radius (km) H2O Valencia et al. 2007b There is degeneracy in composition. Some compositions are improbable.

Toblerone Diagram 1M 2.5M 5M 7.5M 10M Valencia et al. 2007b 40 00 60 00 80 0 10 0 00 12 0 00 14 0 00 16 0 00 0 Radius (km) Rogers & Seager, 2010

CoRoT-7b: the first transiting super-earth Leger et al, 2009 Queloz et al, 2009 Radius = 1.68 ± 0.09 R E Period = 0.854 days Age = 1.2-2.3 Gy Mass = 4.8 ± 0.8 M E

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 = 10 11 g/s For more details on see Lammer et al 09 within an order of magnitude of the escape rate of HD 209458b Even if it has a silicate atmosphere, it is thick enough for UV absorption

Rocky CoRoT-7b 30000 Uranus Neptune 20000 silicate atmosphere Radius [km] 12000 10000 8000 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 1 2 3 4 5 6 8 10 15 20 Mass [M Earth ] Valencia et al, 2010

Rocky CoRoT-7b 30000 Uranus Neptune 20000 silicate atmosphere Radius [km] 12000 10000 8000 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 1 2 3 4 5 6 8 10 15 20 Mass [M Earth ] Valencia et al, 2010

Rocky CoRoT-7b 30000 Uranus Neptune 20000 silicate atmosphere Radius [km] 12000 10000 8000 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 1 2 3 4 5 6 8 10 15 20 Mass [M Earth ] Valencia et al, 2010

H2O Vapor CoRoT-7b 30000 20000 100% vapor Uranus Neptune T [K] 16000 13000 10000 8000 6000 4000 3000 2000 1000 600 300 Vapour adiabats Liquid molecular fluid Ice VII plasma superionic Ice X Radius [km] 10000 8000 6000 4000 50% vapor 20% vapor 10% vapor 3% vapor Earth-like CoRoT-7b 100 1e-6 1e-5 1e-4 Ice I 1e-3 0.01 0.1 P [GPa] Ice II-VI Evaporation Timescale ~ 1 Gy 1 10 100 1e3 5e3 3000 1 2 3 4 5 6 8 10 Mass [M Earth ] 20 Valencia et al, 2010

H2O Vapor CoRoT-7b 30000 20000 100% vapor Uranus Neptune T [K] 16000 13000 10000 8000 6000 4000 3000 2000 1000 600 300 Vapour adiabats Liquid molecular fluid Ice VII plasma superionic Ice X Radius [km] 10000 8000 6000 4000 50% vapor 20% vapor 10% vapor 3% vapor Earth-like CoRoT-7b 100 1e-6 1e-5 1e-4 Ice I 1e-3 0.01 0.1 P [GPa] Ice II-VI Evaporation Timescale ~ 1 Gy 1 10 100 1e3 5e3 3000 1 2 3 4 5 6 8 10 Mass [M Earth ] 20 Valencia et al, 2010

Hydrogen or Helium? 30000 10% H-He Uranus 20000 1% H-He Neptune Radius [km] 10000 8000 6000 0.1% H-He 0.01% H-He Earth-like CoRoT-7b Evaporation Timescale ~ 1 My! 4000 3000 1 2 3 4 5 6 8 10 Mass [M Earth ] 20 Valencia et al. 2010

191 159 127 CoRoT-7b s origin? Valencia et al. 2010 Volatile Origin 318 a) in situ Rocky Origin Mass [M ] 100 10 95 191 222 254 286 15.9 14.3 7.9 H-He planets 9.5 12.7 11.1 vapor planets rocky cores 8 CMF f =0.22 1 0.01 0.1 1 10 7 222 254 318 286 b) inward migration Mass (M E ) 6 5 cored planet CMF f =0.33 silicate planet Corot-7b s Mass Mass [M ] 100 10 95 15.9 14.3 7.9 H-He planets 9.5 12.7 11.1 vapor planets 4 0 0.5 1 1.5 2 2.5 3 Time (Gyr) rocky cores 1 0.01 0.1 1 10 Age[Ga]

191 159 127 CoRoT-7b s origin? Valencia et al. 2010 Volatile Origin Unconstrained Rocky Origin Mass [M ] 100 10 95 191 222 254 318 286 15.9 14.3 7.9 H-He planets 9.5 12.7 11.1 a) in situ vapor planets rocky cores 8 CMF f =0.22 1 0.01 0.1 1 10 7 222 254 318 286 b) inward migration Mass (M E ) 6 5 cored planet CMF f =0.33 silicate planet Corot-7b s Mass Mass [M ] 100 10 95 15.9 14.3 7.9 H-He planets 9.5 12.7 11.1 vapor planets 4 0 0.5 1 1.5 2 2.5 3 Time (Gyr) rocky cores 1 0.01 0.1 1 10 Age[Ga]

GJ 1214b Radius = 2.678 ± 0.13 R E Mass = 6.55 ± 0.98 M E Period = 1.58 days Temp = 393-555 K See also: Rogers & Seager, 2010 Miller-Ricci & Fortney 2010 Charbonneau et al 2009

Solid GJ 1214b? 30000 Uranus Neptune 20000 GJ 1214b Radius [km] 16000 12000 10000 CoRoT-7b Ice-planet Mg-silicate planet Earth-like Fe-planet 8000 6000 1 2 3 4 5 6 8 10 15 20 Mass [M Earth ]

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

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

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

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

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

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 2009 3. Energy dissipation at subduction zones is not enough to halt PT Valencia et al, 2009

Can terrestrial super-earths have plate tectonics?

Can terrestrial super-earths have plate tectonics? under debate

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.

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

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

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

Convective Parameters on super-earths 200 Plate thickness (km) 100 50 10 0.1M Mars Venus Earth 1M Mass super-earths 3M 10M towards gaseous planets 200 100 50 10 20M Stress (MPa) 1/2 u~κ/d Ra xy ~η(t) u/d Valencia et al., 2007c

Convective Parameters on super-earths Plate P-T structure is nearly invariant with mass 200 Plate thickness (km) 100 50 10 0.1M Mars Venus Earth 1M Mass super-earths 3M 10M towards gaseous planets 200 100 50 10 20M Stress (MPa) 1/2 u~κ/d Ra xy ~η(t) u/d Valencia et al., 2007c

Convective Parameters on super-earths Plate P-T structure is nearly invariant with mass 200 Plate thickness (km) 100 50 10 0.1M Mars Venus Earth 1M Mass super-earths 3M 10M towards gaseous planets 200 100 50 10 20M 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

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 + 0.5 Δσxx (1+cos2θ) yield stress = S0 + μ(σ-λσzz) Water reduces strength

Stress vs. Strength on Faults MPa 100 shear stress Dry fault strength Earthquake s stress release values Wet fault strength µ=0.2 10 1M 2M 3M 5M 7M 10M 6300 km 11500 km Water could matter for Earth but not for super-earths Valencia et al., 2009b

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

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

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

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 150 125 100 75 50 25 0 Internally heated cases 2D spherical annulus Mobile lid Rigid lid 1 1.2 1.4 1.6 1.8 2 Planet size / Earth s size Yield stress (MPa) 900 800 700 600 500 400 300 200 100 0 Bottom heated cases 2D spherical annulus Mobile lid Rigid lid 95 * S^3 95 * S^(2/3) 1 1.2 1.4 1.6 1.8 2 Planet size / Earth s size

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

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

Additional slides

Uncertainties in the Interior Temperature (K) 5000 4500 4000 3500 3000 2500 2000 1500 1000 10M 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? 500 0 10 1 0.1 Pressure (Mbar) 0.01 0.001 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