1. E. M. Parmentier Department of Geological Sciences Brown University in collaboration with: Linda Elkins-Tanton; Paul Hess; Yan Liang Early planetary differentiation processes with implications for long term evolution (planetary evolution as an “initial value problem”)

2. Outline 1) Planetary accretion and magma oceans (MOs) - Moon is the type example – highly fractionated compositions - For the Earth - how many MOs and how deep? - Shallow vs. basal MO 2) Idealized fractional solidification of a MO - unstable stratification and overturn of solidified mantle - how realistic is fractional solidification idealization? solid state overturn during solidification buoyant liquid-solid segregation 3) Is there a hidden reservoir of heat and incompatible elements? 4) Convective heating and mixing of stably stratified fluid layer and the preservation of a hidden reservoir

3. Composition of the lunar surface - Mare basalt volcanism at ~3.9 Gyr to 2.5 Gyr – long after MO solidification - Basalts generated at >400 km depth – olivine-pyroxene multiple saturation - Mantle source composition residual to anorthositic crust crystallization - Global asymmetry in emplacement of basalts and the PKT

4. Chambers, Icarus, 2001. Chambers, EPSL 2004. Timescales and mixing in terrestrial planetary accretion

5. Tonks and Melosh JGR 1993 Magma ocean formation due to a large impact

6. Tonks and Melosh JGR 1993

7. S. Labrosse, J. W. Hernlund & N. Coltice Nature 450, 866-869, 2007. Basal magma ocean Develops first 100 Myr and persists during the evolution of the Earth Due to heat generated during core formation Suggest that perovskite fractionation explains trace elements in continental crust + MORB mantle

8. Idealizations: convection in liquid maintains adiabatic gradient and homogeneous liquid composition crystal fraction >50% forms a stress- supported network and behaves as a porous solid solid retains its solidus temperature and composition

10. Effect of atmosphere on cooling and solidification of 500 km deep MO non-convecting grey atmosphere following Abe (1979)

11. Time scale for solid state overturn Taking:  = 10 18 Pa-s  = 2 x 10 -4 kg/m 3 /m g = 10 m/sec 2 d = 500 km Gives:  RT ≈ 0.1 Myr

12. The “double diffusion problem” of melt migration in a convecting, compacting, permeable matrix Buoyancy sources matrix density melt distribution

13. Idealizations: convection in liquid maintains adiabatic gradient and homogeneous liquid composition crystal fraction >50% forms a stress- supported network and behaves as a porous solid solid retains its solidus temperature and composition region of compaction and melt-solid segregation Does solidification occur by freezing or squeezing (i.e. compaction)?

14. L = compaction length = (K  solid /  liquid ) 1/2 Buoyant rise of liquid in pore space: Permeability: dependence on  Wark and Watson, 2003 K  b 2  3 b

15. L = compaction length = (K  solid /  liquid ) 1/2 Buoyant rise of liquid in pore space:

16. Boyet and Carlson (2005) Melt-solid fractionation during the first 100 Myr of Earth evolution

17. Hidden reservoir Complement to continental crust and depleted MORB mantle For a chondritic earth – hidden reservoir would contain 20-30% of incompatible trace elements produce about this fraction of global heat flux (U, Th,K) excess 40 Ar (from decay of 40 K over earth evolution) low 142 Nd – requires formation in first ~100 Myr How would it form? Magma ocean is a prime candidate multiple shallow MOs followed by overturn deep, basal MO Could it be preserved? thermal convective mixing

19. Farnetani, GRL, 24, 1583, 1997; Alley and Parmentier, PEPI 108, 15, 1998; Davaille, Nature, 402, 756, 1999; Hunt and Kellogg, JGR 106, 6747, 2001; Gonnermann, et al., GRL, 29, 1399, 2002; Samuel and Farnetani, EPSL 207, 39, 2003.

20. Convective instability in a continuously stratified fluid layer

22. Some numbers:  =.25x10 -6 /m  =10 -5 / o C give R=10 -1 f = 200 mW/m 2 k = 3 W/m- o K Then z*~500 km after 4 Gyr How long could stable stratification be preserved?

23. Planetary evolution is an “initial value problem”: the structure of the Earth today is not independent of how it formed and evolved in its first hundred Myr.

24. horizontally averaged values idealized structure

25. Densities of solids and coexisting liquid Stolper et al. (1981); Walker and Agee (1988)