219 20. Core Formation and Evolution Core Formation (Terrestrial Planets) Core formation is the biggest differentiation event in the life of any terrestrial planet. At least in the cases of Earth and Mars, we know that it is an ancient event from isotope systematics. In large bodies, it is a high energy event because of the large energy released from accretion and the energy released from core formation itself. The process can occur at multiple scales: migration along grain boundaries, migration of iron along cracks, segregation of iron in a magma ocean, and diapir descent in the deep mantle. The above cartoon (from p239, Origin of the Earth and Moon) illustrates the likely range of processes.220 The next cartoon (immediately above) is from the same book, and intended specifically for Earth. As explained below it is only part of the core formation process but it is the one that has received most attention. Here is a sketch of this scenario for a large planet such as Earth: As the planet forms, enormous amounts of energy are released, sufficient to melt outer portions of the planet. The energy available from accretion, expressed as a temperature rise is221 ΔT =GMRCp≈ 40000K.MM⊕⎛ ⎝ ⎜ ⎞ ⎠ ⎟ 2 / 3 (20.1) using terrestrial values for specific heat. Of course, some of this energy may escape as radiation from the planet surface, but extensive melting seems unavoidable because much of the accreting mass arrives in big chunks rather than as a fine “rain” of small particles. Extensive melting and comminution leads to an “emulsion “ of iron and silicates but the iron can then “rain out” to a level where the material is less extensively melted. The presence of such a level is likely because of the steep increase of melting point with depth within the planet. Descent of iron the rest of the way is then by diapiric flow, which is geologically fast (one suspects) because the silicates are soft at this time and the blobs are large. The level at which the blobs form is the depth of last equilibration for the iron, so the core-forming fluid (and the mantle left behind)may carry a memory of this pressure and temperature. There is some evidence to support this picture from a consideration of siderophile elemental abundances in the mantle. (see next figure, also same book, p283). These correspond plausibly with the base of a magma ocean ~500 km deep. The significance of this figure lies in the possible identification of the pressure (27Gpa) and temperature (~2250K) of last equilibration. This picture omits the major part of core formation in which giant impacts deliver large amount of iron at once. These impact simulations (e.g as in the222223 work of Canup, previous page) suggest that the iron core of the projectile is broken up at least to the scale of hundreds of kilometers. It is less obvious whether the iron is broken up all the way to cm scale droplets before reaching the core. In that sense, part of the core formation process may involve core merging (the amalgamation of previously formed cores). Recent data on Hf -W and other isotopic systems suggest a lot of emulsification following a giant impact but the process may nonetheless involve imperfect equilibration, as would happen in core merging. (See Halliday, A.N. Mixing, volatile loss and compositional change during impact-driven accretion of the Earth, Nature 427 (6974): 505-509 FEB 5 2004). In core merging, there are giant impacts in which the impacting bodies at least partially preserve their pre-existing cores. These cores then combine without complete re-equilibration with adjacent mantle. In this scenario the apparent “time” of earth core formation can predate the actual time of Earth formation and the “memory” of the core (in terms of composition) may be that of events that occurred in much smaller bodies than Earth itself. (from Stevenson, Nature, v451, p261(2008) Heating During Core Formation In addition to the heating that arises from accretion, there is a lot of heat released as the core forms. Consider the gravitational energy of a differentiated body relative to that of a undifferentiated body:224 Egrav,undiff= −3GM25REgrav,diff= −Gmdmr( m)0M∫= −3GMo25R{1 − x5+ x3[A2x2+54(1− x2)(A − 2)]}Mo≡43πρoR3 for our “usual” model of core and mantle (core with radius xR and density Aρ0 , mantle with density ρ0.). Typically, the change in gravitational energy is about 0.1 times the total, which is still equivalent to a 4000K or so heating of everything for an Earth mass. The consequence of this together with the accretional heating suggests that the core is likely to form completely molten despite the fact that pressure freezing could in principle occur. Core Convection A terrestrial planetary core, like the mantle, will only convect if it has an unstable density distribution. If there are no compositional gradients, then this means that the mean temperature gradient must reach the adiabat. As we have discussed, the convective state will be close to the adiabat because it has such a low viscosity. Unlike the mantle, this is not an easy constraint to meet because it implies a substantial heat flow by conduction alone. The reason is that the core is a metal and hence a much better thermal conductor than the mantle. For a Gruneisen gamma of about unity, the adiabatic temperature gradient in Earth’s core is about -0.5K/km. If the thermal conductivity is about 3 x 106 cgs, so the conductive heat flow along the adiabat is about Fcond = -k(dT/dr)ad ≈ 15 erg/cm2-sec (20.2) The actual heat flow out of the core, Fcore , might plausibly be given by the time rate of change of the thermal heat content divided by the surface area. This cooling of the core is determined by the overlying mantle (mantle convection).225 Fcore ≈ −[MCpdT/dt]//4πR2 (20.3) where M is the core mass and Cv is the specific heat. For a drop of 100K per billion years, this gives Fcore ≈ 20 erg/cm2.sec, which is uncomfortably close to the conductive heat transport. Irrespective of the uncertain numbers, notice that a core can only convect if it is cooling! The most recent estimates of core conductivity are larger by about a factor of two (see, for example, Pozzo et al,